Evaluation of Active Heat Sinks Design Under Forced Convection—Effect of Geometric and Boundary Parameters

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Article Evaluation of Active Heat Sinks Design under Forced Convection—Effect of Geometric and Boundary Parameters

Eva C. Silva 1,2,* , Álvaro M. Sampaio 1,2,3 and António J. Pontes 1,2

1 IPC—Institute of Polymers and Composites, Department of Polymer Engineering, Campus de Azurém, University of Minho, 4800-058 Guimarães, Portugal; [email protected] (Á.M.S.); [email protected] (A.J.P.) 2 DONE Lab—Advanced Manufacturing of Polymers and Tools, Campus de Azurém, University of Minho, 4800-058 Guimarães, Portugal 3 Lab2PT, School of Architecture, Campus de Azurém, University of Minho, 4800-058 Guimarães, Portugal * Correspondence: [email protected]

Abstract: This study shows the performance of heat sinks (HS) with different designs under forced convection, varying geometric and boundary parameters, via computational fluid dynamics simulations. Initially, a complete and detailed analysis of the thermal performance of various conventional HS designs was taken. Afterwards, HS designs were modified following some additive manufacturing approaches. The HS performance was compared by measuring their temperatures and pressure drop after 15 s. Smaller diameters/thicknesses and larger fins/pins spacing provided better results. For fins HS, the use of radial fins, with an inverted trapezoidal shape and with larger holes was advantageous. Regarding pins HS, the best option contemplated circular pins in combination with frontal holes in their structure. Additionally, lattice HS, only possible to be produced by additive manufacturing, was also studied. Lower temperatures were obtained with a hexagon unit cell. Lastly, Citation: Silva, E.C.; Sampaio, Á.M.; a comparison between the best HS in each category showed a lower thermal resistance for lattice HS. Pontes, A.J. Evaluation of Active Heat Sinks Design under Forced Despite the increase of at least 38% in pressure drop, a consequence of its frontal area, the temperature Convection—Effect of Geometric and was 26% and 56% lower when compared to conventional pins and fins HS, respectively, and 9% and Boundary Parameters. Materials 2021, 28% lower when compared to the best pins and best fins of this study. 14, 2041. https://doi.org/10.3390/ ma14082041 Keywords: heat sink; computational fluid dynamics; simulation; ANSYS Fluent; additive manufacturing; lattice structures; design of experiments Academic Editors: Scott M. Thompson and Ludwig Cardon

Received: 27 February 2021 1. Introduction Accepted: 15 April 2021 All electronic devices dissipate heat during their operation. By providing heat dis- Published: 18 April 2021 sipation, a heat sink prevents overheating and plays an imperative role in temperature regulation. Through extended surfaces, heat sinks increase heat dissipation from a heat Publisher’s Note: MDPI stays neutral source to the surroundings, providing low thermal resistance (Equation (1)) and a low- with regard to jurisdictional claims in published maps and institutional affil- pressure loss path between them [1]. They can be divided into two main categories: active iations. and passive cooling techniques. The use of natural techniques is known as passive thermal management while forced heat dissipation, e.g., by cooling fans, improving heat transfer, is referred to as active thermal management [2–5]. The main advantages of passive cooling techniques are their simplicity and lower cost of operation. However, the associated heat transfer coefficient (h) is low [6]. Forced convection with cooling fans is a process frequently Copyright: © 2021 by the authors. found in a variety of electronic products ranging from personal computers to avionics Licensee MDPI, Basel, Switzerland. control systems [7]. Airflow speed is actively increased, enhancing heat transfer [6]. The This article is an open access article distributed under the terms and most typical material for heat sinks is aluminium, offering a good balance between weight, conditions of the Creative Commons cost, and thermal properties [8–11]. Attribution (CC BY) license (https:// Nowadays, as electronic components continue to dissipate more heat and, with new de- creativecommons.org/licenses/by/ velopments, are getting more compact, their cooling techniques must also be improved [7]. 4.0/). Due to its geometric freedom and the capability to build complex internal structures and

Materials 2021, 14, 2041. https://doi.org/10.3390/ma14082041 https://www.mdpi.com/journal/materials Materials 2021, 14, 2041 2 of 19

with high total area to volume ratio, additive manufacturing can be a useful way to produce heat sinks that match or outperform the thermal performance of traditional aluminium heat sinks [12]. Chinthavali et al. [13] produced the first heat sink for electronic components by additive manufacturing using powder-bed fusion (PBF) equipment. The toughness of the heat sink produced with the additive manufacturing aluminium alloy was similar to the strength of the heat sink produced by conventional methods, but the thermal performance was lower for lower temperatures. Later, Syed-Khaja et al. [14] used PBF to fabricate a heat sink design that showed key enabling advantages such as the reduction in volume, weight, and chip temperatures. To date, several other studies have emerged regarding heat sinks produced by additive manufacturing [5,15–20]. This study aims to evaluate the performance of different heat sinks. In the first stage, the influence of different geometric and boundary parameters on the performance of conventional fins/pins heat sinks will be evaluated. Based on those results, the design of the heat sinks will be changed considering some additive manufacturing approaches and compared with lattice heat sinks, which are complex structures only possible to be produced by additive manufacturing. Finally, the best heat sink design for forced convection environments, among the studied, will be revealed. Heat sinks performance was evaluated considering their thermal resistance (Equation (1)), which is one of the main indicators and should be as low as possible. It is expressed as: ∆T R = (1) Qheat where ∆T is the difference between the minimum temperature of the heat sink and the fluid temperature at the inlet and Qheat is the total heat applied at the base of the heat sink, given by multiplying the heat flux by the base area [21,22]. In this work, both the heat source and air flow inlet velocity are constant parameters and were defined at the base of the heat sink and the beginning of the wind tunnel, respectively. The performance of a heat sink design was evaluated by measuring their temperature after 15 s of applied heat and air flow (directly correlated with the thermal resistance according to Equation (3)). Besides the temperature control, the air pressure drop after 15 s was used as an auxiliary control metric to compare studies where the temperature differential was residual or an anormal air pressure was identified.

1.1. Conventional Heat Sinks Design and Topology Heat sink design is the most important variable for better performance. It minimizes thermal resistance by expanding the surface area available for heat transfer while ensuring that the air flows through the heat sink [3]. Choosing the type of heat sink (pins, fins, or blades) is an ambiguous task. Under forced convection, Wong et al. [23] defended that fins are the best choice (among fins, blades, and circular pins), while Abdelsalam et al. [24] compared in-line blades with fins and concluded that the first was better. In its turn, Jonsson and Moshfegh [25] tested different heat sinks models considering Reynolds numbers in a range between 3350 and 13,400 using ANSYS Fluent software and concluded that it is not favorable to use pin heat sinks at higher Reynolds numbers. When choosing a fin heat sink, it is typical to choose the conventional rectangular fins. Still, other forms of fins have been tested, such as triangular or trapezoidal fins [26,27], with fillets [28] or holes. Jaffal [29] analysed the thermal performance of different fin heat sinks geometries, via experimental and computational studies, at a certain heat flux interval. It was found that the heat transfer coefficient is dependent on heat flux and that the heat sink with perforated blades showed the best thermal performance. Through simulations in ANSYS software, Ibrahim et al. [30] investigated the effect of perforation geometry (circular, rectangular, and triangular) on the heat transfer of perforated fin heat sinks, under different boundary conditions. In all cases, these perforations increased the heat transfer coefficient and decreased heat sink temperature, regardless of perforation geometry. Tijani Materials 2021, 14, 2041 3 of 19

and Jaffri [31] also studied the effect of circular perforations on pins or fins heat sinks under forced convection. Inlet velocity and heat flux were constant and perforated pins or fins had the highest heat transfer coefficients, improving thermal efficiency up to 4% compared to solid pins or fins. When choosing a pin heat sink, several authors agree that square pins are not a good choice [32–34] and that pressure drop is higher when pins arrangement is staggered [25,35– 37]. However, there is no agreement regarding the best pins shape. Under forced convection, either circular [33,38], elliptical [32,39–42], dropform [43,44], and rhombus [45,46] can be advantageous. Gururatana and Li [40] compared elliptic and rectangular staggered pins with the same length-to-thickness ratio but with different hydraulic diameters. As boundary conditions, an inlet velocity of 6 m/s at 27 ◦C rendered a Reynolds number of 1192 (laminar flow). Through ANSYS Fluent simulations, they concluded that elliptic fins produced a higher heat transfer rate when the pressure drop is the same. Moreover, Zhou and Catton [39] investigated the thermal and hydraulic performance of different pin heat sinks with distinct pins shapes including square, circular, elliptic, and dropform. The elliptic pins had the best overall performance, regardless of inlet velocity and the ratio of pin widths to pins spacing. There are still other unusual shapes that can be a good choice [47,48]. Maji et al. [47] investigated the thermal performance of heat sinks with perforated circular pins. Results were taken for Reynolds numbers from 4700 to 44,500 and concluded that, up to a certain perforated area, perforated pins required lower pumping power than solid pins to reach the same thermal performance. Perforated pins were also investigated by other authors that also agree on their advantages [49,50]. The greatest fin or pin spacing is dependent on the air velocity, i.e., as the velocity increases, the fin spacing can decrease [3,51]. However, the dependence of heat transfer with fin or pin spacing is not clear. According to some authors [37,39,44], the heat transfer increases with increasing fin or pin density, i.e., with reduced spacing. Contrarily, according to other authors, greater heat transfer is obtained for the opposite [37,52,53].

1.2. Lattice Heat Sinks As mentioned above, in the field of electronics cooling, where oversized heat sinks are inhibited by volume constraints, the use of additive manufacturing offers the ability to deliver components without the design restrictions of conventional manufacturing methods [48,54]. Lattice structures have showed high potential in increasing forced convection heat transfer. They consist of orderly unit cell arrangements, which can have different configurations such as hexagon, honeycomb, and pyramidal [55]. They have large surface area-to-volume ratios, are light, and promote tortuous fluid paths, promoting fluid mixing. Their advantage over metal foams are constant periodicity and homogeneity allowing optimization of the ligament configuration and diameter, better mechanical properties, and greater ease of production with emerging additive manufacturing technologies [54–56]. The study of the fluid flow through them has become popular in thermal management [55–59]. Although the lattice structure heat sink allows a high surface area to volume ratios, its performance may be limited by the absense of interaction between the cooling air and structure [7]. According to Ho et al. [55], pressure drop and Nusselt number of Rhombi- Octet lattice structures increased with decreasing unit cell size and the highest Nusselt number was obtained with the lattice structure with the smallest ligament width. The same conclusion was obtained by Son et al. [60]. Regarding the best unit cell topology for thermal management, there is no clear conclusion. For example, according to Yan et al. [61], the X-type lattice heat sink provides overall heat removal capacity up to two times higher than tetrahedral or the Kagome lattice heat sink. Its morphology resulted in a large scale spiral main flow that interacts with several secondary flows, causing three times higher pressure drop for a given Reynolds number. Still, superior heat transfer was achieved by the X-type lattice. The same conclusion was not made by Hyun and Torquato [62]. They suggested that Kagome structures have desirable heat-dissipation properties due to the large hexagonal holes through which fluid may flow, Materials 2021, 14, x FOR PEER REVIEW 4 of 19

Materials 2021, 14, 2041 number. Still, superior heat transfer was achieved by the X-type lattice. The same conclu-4 of 19 sion was not made by Hyun and Torquato [62]. They suggested that Kagome structures have desirable heat-dissipation properties due to the large hexagonal holes through which fluid maycompared flow, compared to triangular to triangular and hexagonal and hexagonal cells. More cells. recently, More Dixit recently, et al. Dixit [63] concludedet al. [63] that concludedoctet topologythat octet dissipatestopology dissipates more heat more at the heat lowest at the Reynolds lowest Reynolds numbers numbers while SC-BCC-truss while SC-BCCoutperforms-truss outperforms other architectures other architectures as the ﬂuid as velocitythe fluidincreases. velocity increases.

2. Problem2. Problem Description Description 2.1. CFD Methodology 2.1. CFD Methodology As in other studies involving heat sinks, the main goal is to reach heat sink tem- As in other studies involving heat sinks, the main goal is to reach heat sink tempera- peratures as low as possible, minimizing thermal resistance. The computational domain tures as low as possible, minimizing thermal resistance. The computational domain (Fig- (Figure1 ) includes a heat sink (main dimensions 50 × 50 × 50 mm3) and a wind tun- ure 1) includes a heat sink (main dimensions 50 × 50 × 50 mm3) and a wind tunnel, de- nel, designed so that the total ﬂow converges to the heat sink, avoiding the bypass phe- signed so that the total flow converges to the heat sink, avoiding the bypass phenomenon nomenon [25,55]. It was considered a fan diameter of 80 mm. The dimensions of the [25,55]. It was considered a fan diameter of 80 mm. The dimensions of the domain are a domain are a length of 300 mm and a converging width and height from 80 mm to 52 mm. length of 300 mm and a converging width and height from 80 mm to 52 mm. Heat sink is Heat sink is placed inside the domain, 200 mm away from the inlet and 50 mm from placed inside the domain, 200 mm away from the inlet and 50 mm from the outlet. the outlet.

Pressure sensors outlet Temperature sensor (0, 24.5, 200); (0, 24.5, 250) (0, 24.5, 225) 100 mm 52 mm

Inlet (fan)

y 50 mm z 80 mm 100 mm x

FigureFigure 1. Computational 1. Computational domain. domain.

The geometryThe geometry was meshed was meshed using usingANSYS ANSYS Meshing Meshing by applying by applying body bodysizing sizing operation operation and, depending on the heat sink model under study, were considered tetrahedral or hexa- and, depending on the heat sink model under study, were considered tetrahedral or hex- hedral elements. Element size varied in a range between 0.4 mm and 1.2 mm and the total ahedral elements. Element size varied in a range between 0.4 mm and 1.2 mm and the number of elements was the one whose results converged, with minimal computational total number of elements was the one whose results converged, with minimal computa- effort, i.e., sufficient to ensure mesh independence of the simulated results. tional effort, i.e., sufficient to ensure mesh independence of the simulated results. Mesh geometry (Figure2) was brought into Fluent, where solver settings were defined. Mesh geometry (Figure 2) was brought into Fluent, where solver settings were de- This includes defining material properties, selecting appropriate physical models, prescrib- fined. This includes defining material properties, selecting appropriate physical models, ing operating and boundary conditions, and providing initial values. Table1 includes the Materials 2021, 14, x FOR PEER REVIEWprescrib ing operating and boundary conditions, and providing initial values. Table5 of 119 in- main properties of the materials adopted for each component: aluminium for the heat cludes the main properties of the materials adopted for each component: aluminium for sink and ideal air as the fluid passing through the heat sink. The air flow was assumed the heat sink and ideal air as the fluid passing through the heat sink. The air flow was incompressible with constant properties. assumed incompressible with constant properties.

Table 1. Main properties of the materials considered for each component.

Aluminium Air Property (Heat Sink) (Fluid Domain) Density (kg·m3) 2719 1.225 Specific heat (J·kg−1·°C−1) 871 1006.43 Thermal conductivity (W·m−1·°C−1) 202.4 0.0242 Viscosity (kg·m−1·s −1) - 1.7894 × 10−5

FigureFigure 2. Lattice 2. Lattice heat heat sink sink mesh. mesh.

As initial values, the system was considered at a room temperature of 20 °C. The outlet vent condition was used for the outlet boundary and the wind tunnel wall considered adiabatic. The remaining boundary conditions (heat source temperature and inlet air velocity) were established according to each specific case. During compute solution, the discretised conservation equations (Equations (4)–(6)) are solved iteratively until convergence, i.e., when changes in solution variables from one iteration to the next are negligible (residual response less than 10 × 10−6). As the most widely-used engineering turbulence model for industrial applications, standard Ϗ-Epsilon viscous model (Equations (6) and (7)) was selected. The pressure-velocity coupling was achieved through the SIMPLE scheme [64] and the Least Squares Cell Based gradients were choose as the spatial discretization scheme [65]. Pressure drop across the heat sink and its temperature were reported after 15 s on the respective sensors (Figure 1). The temperature sensor was located where, as general rule, the heat sink temperature was the minimum [66]. Considering a time step size of one second with 10 maximum iterations per time step, the 15 s were found to be a good balance between good results and computational effort (Figure 3) once, in most cases, the temperature reached the steady-state condition.

Figure 3. Temperature contours vs. time for each type of heat sink.

2.2. CFD Governing Equations Computational Fluid Dynamics (CFD) consists of predicting fluid flow, heat, and mass transfer and related phenomena by solving numerically a set of governing mathematical equations. CFD analysis complements testing and experimentation by reducing total effort and cost required for experimentation and data acquisition. There are a number of commercial CFD software packages available for application in thermal design. One of them is ANSYS. Based on the finite volume method, ANSYS solvers discretised the

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Table 1. Main properties of the materials considered for each component.

Aluminium Air Property (Heat Sink) (Fluid Domain) Density (kg·m3) 2719 1.225 Speciﬁc heat (J·kg−1·◦C−1) 871 1006.43 Thermal conductivity (W·m−1·◦C−1) 202.4 0.0242 FigureFigure 2.Viscosity Lattice 2. Lattice heat (kg ·heatm sink−1 ·sinks −mesh.1) mesh. - 1.7894 × 10−5

AsAs Asinitial initial initial values, values, values, the the thesystem system system was was consideredconsider considered at edat a roomaat room a room temperature temperature temperature of 20of ◦ 20C.of The°C.20 °C.The outlet The outletventoutlet vent condition vent condition condition was was used was used for used for the forthe outlet theoutl outlet boundaryet boundary boundary and and the and the wind thewind wind tunnel tunnel tunnel wall wall consideredwall consid- consid- eredadiabatic.ered adiabatic. adiabatic. The The remainingThe remaining remaining boundary boundary boundary conditionsconditions conditions (heat (heat source source source temperature temperature temperature and and and inlet inlet inlet air air air velocity)velocity)velocity) were were were established established established acco according accordingrding to toeach to each each specific speciﬁc specific case. case. case. DuringDuringDuring compute compute compute solution, solution, solution, the the thediscretised discretised discretised co conservationnservation conservation equations equations equations (Equations (Equations (Equations (4)–(6)) (4)–(6)) (4)–(6)) areare aresolved solved solved iteratively iteratively iteratively until until until conv convergence, convergence,ergence, i.e., i.e., i.e., when when when changes changes changes in insolution in solution solution variables variables variables from from from one one one iterationiterationiteration to to theto the thenext next next are are arenegligible negligible negligible (residual (residual (residual response response response less less less than than than 10 10 ×10× 10 10×− 610−).6 −).As6). As Asthe the themost most most widely-usedwidely-usedwidely-used engineering engineering engineering turbulence turbulence turbulence model model model for for for industrial industrial industrial applications, applications, applications, standard standard standard Ϗ Ϗ-Epsilon-Epsi--Epsilon lonviscousviscous viscous model model model (Equations (Equations (Equations (6) (6) (6) and and and (7)) (7)) (7)) was was was selected. selected. selected. The The The pressure-velocity pressure-velocity pressure-velocity coupling coupling coupling was was wasachievedachieved achieved through through through the the theSIMPLE SIMPLE SIMPLEscheme scheme scheme [ 64[64] [64]] and and and the the theLeast Least Least Squares Squares Squares Cell Cell Cell Based Based Basedgradients gradients gradients were were werechoosechoose choose as as the asthe the spatial spatial spatial discretization discretization discretization scheme scheme scheme [ 65[65].]. [65]. PressurePressurePressure drop drop drop across across across the the theheat heat heat sink sink sink and and and its its temperatureits temperature temperature were were were reported reported reported after after after 15 15 s15 on s s on on thethe therespective respective respective sensors sensors sensors (Figure (Figure (Figure 1).1 ).The1). The The temperature temperature temperature sensor sensor sensor was was was located located located where, where, where, as as generalas general general rule,rule,rule, the the theheat heatheat sink sinksink temperature temperature was was was the theminimu the minimu minimumm [66].m [66]. [Considering66]. Considering Considering a time a time a step time step size step size of size one of one of secondonesecond second with with 10 with maximum 10 maximum 10 maximum iterations iterations iterations per per time time per step, timestep, the step, the15 s 15 were the s were 15 found s found were to be foundto abe good a togood bebalance abalance good betweenbalancebetween good between good results results good and resultsand computational computational and computational effort effort (Figure (Figure effort 3) once,(Figure 3) once, in3 most) in once, most cases, in cases, most the the cases,temper- temper- the aturetemperatureature reached reached the reached thesteady-state steady-state the steady-state condition. condition. condition.

FigureFigureFigure 3. Temperature 3. 3.Temperature Temperature contours contours contours vs. vs. timevs. time time for for eachfor each each type type type of ofheat of heat heat sink. sink. sink.

2.2.2.2.2.2. CFD CFD CFD Governing Governing Governing Equations Equations Equations ComputationalComputationalComputational Fluid Fluid Fluid Dynamics Dynamics Dynamics (CFD) (CFD) (CFD) consists consists ofof predicting predictingof predicting fluid fluid fluid flow, flow, heat,flow, heat, andheat, and mass and masstransfermass transfer transfer and and related and related related phenomena phenomena phenomena by solving by bysolving solv numericallying numerically numerically a set a of set a governing setof governingof governing mathematical mathe- mathe- maticalequations.matical equations. equations. CFD CFD analysis CFD analysis analysis complements complements complements testing testing testing and and experimentation and experimentation experimentation by reducingby byreducing reducing total totalefforttotal effort effort and and cost and cost required cost required required for for experimentation forexperimentation experimentation and and dataand data data acquisition. acquisition. acquisition. There There There are are aarea numbernum- a num- berofber of commercial commercial of commercial CFD CFD CFD software software software packagespackages packages available available for forapplication application application in in thermal in thermal thermal design. design. design. One One One of ofthemof them them is is ANSYS.is ANSYS. ANSYS. Based Based Based on on onthe the thefinite finite finite volume volume volume method, method, method, ANSYS ANSYS ANSYS solvers solvers solvers discretised discretised discretised the the the domain into a finite set of control volumes in which general conservation equations for mass (Equation (2)), momentum (Equation (3)) and energy (Equation (4)) are solved [67].

→ ∇· ρ u = 0 (2)

→ → → u ·∇ ρ u = ∇P + ∇· µ∇ u (3) → u ·∇ ρCpT = ∇·(k∇Ti) (4) Materials 2021, 14, x FOR PEER REVIEW 5 of 19

Materials 2021, 14, x FOR PEER REVIEW MaterialsMaterials 2021Materials, 14, 2021x FOR2021, 14 ,PEER ,14 x ,FOR x FORREVIEW PEER PEER REVIEW REVIEW 6 of 19 6 of 19 6 of6 of19 19

domain into a finite set of control volumesdomaindomain in intodomain which a finiteinto intogeneral a set finitea finiteof conservation controlset set of of control volumes control equations volumes volumesin which for in in whichgeneral which general conservationgeneral conservation conservation equations equations equations for for for mass (Equation (2)), momentum (Equationmass (Equation (3))massmass and (Equation (Equation energy (2)), momentum (Equation(2)), (2)), momentum momentum (Equation(4)) are (Equation solved (Equation (3)) and[67]. (3)) energy (3)) and and energy(Equation energy (Equation (Equation (4)) are (4)) solved (4)) are are solved[67]. solved [67]. [67]. Figure 2. Lattice heat sink mesh.Materials 2021, 14, 2041 6 of 19 ∇∙(𝜌𝑢⃗) =0 ∇∙(𝜌𝑢⃗)∇∙=0∇∙(2)(𝜌𝑢 (⃗𝜌𝑢)⃗=0) =0 (2) (2)(2)

(𝑢⃗ ∙∇)(𝜌𝑢⃗) =∇P+∇∙(μ∇𝑢⃗) As initial values, the system was considered at a room temperature of 20 °C. The (𝑢⃗(∙∇𝑢⃗ ∙∇)(𝜌𝑢)(⃗𝜌𝑢)(3)⃗=∇P+∇∙(μ∇𝑢) =∇P+∇∙(μ∇𝑢→ ⃗) ⃗) (3) Note that ρ and µ are the fluid(𝑢⃗ density∙∇)(𝜌𝑢⃗) and=∇P+∇∙(μ∇𝑢 viscosity and⃗) u is the velocity vector. The(3) (3) outlet vent condition was used for the outlet boundary and the wind tunnel wall consid- 𝑢⃗ energy∙∇𝜌𝐶𝑇 equation = ∇ ∙ (𝑘∇𝑇 for solid) regions [68] can be written(4) as: ered adiabatic. The remaining boundary conditions (heat source temperature and inlet air 𝑢⃗ ∙∇𝜌𝐶𝑢⃗∙∇𝜌𝐶𝑢𝑇⃗ ∙∇𝜌𝐶 =𝑇 ∇ ∙𝑇 (𝑘∇𝑇 =) ∇= ∙ ∇(𝑘∇𝑇 ∙ (𝑘∇𝑇) ) (4) (4)(4) velocity) were established accoNoterding that to𝜌 andeach 𝜇 specific are the case. fluid density and viscosity and 𝑢⃗ is the velocity vector.2 The Note thatNoteNote 𝜌 andthat that 𝜇𝜌 are𝜌and and the 𝜇 𝜇are fluid are the thedensit fluid fluidk ysdensit ∇ anddensitT =viscosityy yand0 and viscosity viscosityand 𝑢⃗ andis and the 𝑢⃗ velocity𝑢is⃗ isthe the velocity vector.velocity vector.The (5)vector. The The During compute solution,energy the equation discretised for cosolidnservation regions equations[68]energy can be energy (Equationsequation writtenenergy equation equationas:for (4)–(6)) solid for for regions solid solid regions [68] regions can [68] be[68] canwritten can be be written as: written as: as: are solved iteratively until convergence, i.e., when changes in solutionThese variables equations from one are solved with the presumption that radiation heat transfer 𝑘 ∇ 𝑇=0 (5) −6 𝑘 𝑘∇ ∇𝑇=0𝑇=0 (5)(5) iteration to the next are negligible (residual response less thanis negligible.10 × 10 ). As the most 𝑘∇ 𝑇=0 (5) widely-used engineering turbulenceThese equations model are for solved industrial with applications, the presumptionTheseThe equationsThese standard These thatequations equations are radiation Ϗ -Epsilon -Epsi-solved are are heatsolvedwith viscoussolved transfer the with presumptionwith model the is the negligible. presumption used presumption inthat this radiation studythat that radiation isradiation heat a semi-empirical transfer heat heat transfer is transfer negligible. model is isnegligible. negligible. lon viscous model (Equations (6)The and standard (7)) was Ϗ-Epsilon selected. viscous The pressure-velocitybased modelThe on used modelstandardThe inThe transport this standardcoupling standard Ϗ -Epsilonstudy equations Ϗ is-Epsilon Ϗ a-Epsilonviscous semi-empirical for viscous model viscous the turbulence modelused model in used this kineticused instudy in this energy this isstudy astudy (semi-empirical) is and isa semi-empiricala its semi-empirical dissipation model model model was achieved through the basedSIMPLE on scheme model transport[64] and the equations Least Squaresrate basedfor (theε ), Cellonbased obtainedturbulencebased model Based on on gradientsmodeltransport from modelkinetic the transport transport followingenergyequations equations(Ϗ equations) transport forand the its for turbulencedissipa- for equations: the the turbulence turbulence kinetic kineticenergy kinetic energy( Ϗenergy) and ( Ϗits ()Ϗ and)dissipa- and its its dissipa- dissipa- were choose as the spatial discretizationtion rate (ε), obtained scheme from[65]. the following transport equations: tion ratetion tion(ε), rate obtained rate (ε ),(ε obtained), obtained from the from fromfollowing the "the following following transport! transport transport equations:# equations: equations: Pressure drop across the heat sink and its temperature were reported∂ after 15∂ s on ∂ µt ∂ 𝜕 𝜕 𝜕 𝜇 𝜕Ϗρ + 𝜕 𝜕 ρ u 𝜕=𝜕 µ +𝜕 𝜕 𝜇 𝜇+𝜕ϏG𝜕Ϗ+ G − ρε − Y + S (6) the respective sensors (Figure 1). The temperature(𝜌Ϗ) + (sensor𝜌Ϗ𝑢 ) =was located𝜇 + where, 𝜕 +𝐺 as general+𝐺𝜕 −𝜌𝜀−𝑌i 𝜕+𝑆 𝜇 𝜕Ϗ b M ∂t (𝜌Ϗ) ∂+Ϗx(i𝜌Ϗ(𝜌Ϗ)(𝜌Ϗ𝑢+) + )(=𝜌Ϗ𝑢∂(x𝜌Ϗ𝑢j )𝜇=)Ϗ= +σ𝜇𝜇∂x(6) + j+𝐺 + +𝐺+𝐺+𝐺−𝜌𝜀−𝑌Ϗ +𝐺+𝐺 −𝜌𝜀−𝑌−𝜌𝜀−𝑌+𝑆 +𝑆+𝑆Ϗ (6)(6) 𝜕𝑡 𝜕𝑥 𝜕𝑥 𝜎Ϗ 𝜕𝑥 Ϗ Ϗ Ϗ Ϗ (6) rule, the heat sink temperature was the minimum [66]. Considering a time step𝜕𝑡 size𝜕𝑡 of𝜕𝑡𝜕𝑥 one 𝜕𝑥𝜕𝑥 𝜕𝑥 𝜕𝑥𝜕𝑥𝜎Ϗ 𝜕𝑥𝜎Ϗ𝜎Ϗ𝜕𝑥𝜕𝑥 second with 10 maximum iterations𝜕 per time 𝜕step, the 15 s 𝜕were found𝜇 to𝜕𝜀 be a good𝜀 balance " 𝜀 # 2 ∂ 𝜕 𝜕∂𝜕𝜕 𝜕 𝜕 ∂ 𝜕 𝜕µ𝜇𝜕 𝜕𝜀∂ε 𝜇𝜇 𝜕𝜀𝜕𝜀𝜀ε 𝜀 𝜀 𝜀ε 𝜀 𝜀 (𝜌𝜀) + (𝜌𝜀𝑢 ) = 𝜇 + +𝐶 (𝐺 +𝐶 𝐺 ) −𝐶 t+𝑆 (7) (ρε(𝜌𝜀) +)+ (𝜌𝜀(ρε𝜌𝜀)(𝜌𝜀𝑢+u)i+) =) (=𝜌𝜀𝑢(𝜌𝜀𝑢)𝜇=µ)=+ + 𝜇𝜇 + +𝐶 + + C1ε+𝐶(+𝐶(𝐺Gk+𝐶+ (C𝐺3(𝐺ε𝐺G+𝐶)b)+𝐶−𝐶−𝐺C2𝐺)ερ−𝐶) −𝐶+𝑆+S ε +𝑆(7)+𝑆 (7)(7) between good results and computational𝜕𝑡 effort𝜕𝑥 (Figure 3)𝜕𝑥 once, in 𝜎most 𝜕𝑥 cases, the𝑘 temper- 𝑘 (7) ∂t𝜕𝑡 𝜕𝑡∂𝜕𝑡x𝜕𝑥i 𝜕𝑥𝜕𝑥 ∂ x𝜕𝑥j 𝜕𝑥𝜕𝑥σ𝜎ε 𝜕𝑥∂xj𝜎𝜎𝜕𝑥𝜕𝑥 𝑘k 𝑘 𝑘 𝑘k 𝑘 𝑘 ature reached the steady-state condition. In these equations, GϏ represents the generation of turbulence kinetic energy due to InIn thesetheseIn equations,equations,In these these equations, equations, GϏ representsrepresents G ϏG representsϏ represents the the generation generation the the generation generation of of turbulence turbulence of of turbulence turbulence kinetic kinetic kineticenergy kinetic energy energydue energy due to due due to to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoy- thethe mean mean velocity velocity gradients, gradients,b G bG isb isthe the generation generation of of turbulen turbulencece kinetic kinetic energy energy due due to to buoy- buoy- tothe the mean mean velocity velocity gradients, gradients, G isG btheis generation the generation of turbulen of turbulencece kinetic kinetic energy energy due to due buoy- to M ancy, Y represents the contribution of the ancy,flucM tuating YM Mrepresents dilatation the in contribution compressible of turbu- the fluctuating dilatation in compressible turbu- buoyancy,ancy, Y ancy,representsYM representsY represents the contribution the the contribution contribution of the of fluc theoftuating the fluctuating fluc dilatationtuating dilatation dilatation in compressible in compressiblein compressible turbu- turbu- 1 2 3 lence to the overall dissipation rate, C ε, C ε and C ε are constants, σϏ and σε are the1 ,turbu-1 2 2 3 3 σ σ turbulencelence tolence thelence to overall to the to the the overall overall dissipation overall dissipation dissipation dissipation rate, C rate, 1rate,ε, rate,C2ε C Cand1 Cεε,CCε ,C 2Cε3ε εand εandare and Cconstants,C Cε3 εareε areare constants, constants,constants, σϏ and σϏε σ andareϏ andand the ε σσ areturbu-εε areare the the turbu- turbu- lent Prandtl numbers for Ϗ and ε, respectively. SϏ and Sε are user-defined source terms. thelent turbulent Prandtllentlent Prandtl numbers PrandtlPrandtl numbers numbersnumbers for Ϗ and for forfor εϏ, Ϗandrespectively.and and εε, , εrespectively. respectively., respectively. SϏ and SSϏ ε S andareϏ and user-definedSSε Sareε are user-defineduser-defined user-defined source source sourceterms. source terms. terms. The Ϗ-epsilon model assumes that the flow is fully turbulent, and the effects of molecular terms.The Ϗ-epsilon TheThe Ϗ-epsilon -epsilonϏ model-epsilon modelassumes model model assumes assumes assumesthat the that thatflow that the thetheis flowfully flowflow isturbulent, isisfully fullyfully turbulent, turbulent, and the and effects and and the the the effectsof effects molecular effects of of molecular of molecular viscosity are negligible [65,69]. molecularviscosityviscosity viscosityare viscosity negligible are are arenegligible negligible negligible[65,69]. [65,69]. [65,69]. [65,69 ].

2.3. Heat Sink Models 2.3.2.3. HeatHeat2.3. Sink2.3.Sink Heat Heat ModelsModels Sink Sink Models Models The statistical design of experimentsTheThe (DOE) statistical statisticalThe wasThe statistical designstatisticalused design to of designdesignof experimentsdesign experiments ofthe of experiments setsexperiments (DOE) of(DOE) experi- was (DOE)was used(DOE) used towas designwas to used designused the to to sets designthe design of sets experiments the ofthe setsexperi- sets of of experi- experi- ments run in this work for fins and pinsrunments heat in thisrunments sinks,ments in work thisrun in run orderforworkin in this fins this tofor work andoptimize workfins pinsfor and for fins heatthepinsfins and main and sinks,heat pins pinsgeomet- sinks, inheat heat order in sinks, ordersinks, to in optimize toin order optimizeorder to theto optimize optimize the main main geometricthe thegeomet- main main geomet- geomet- ric parameters (pins/fins diameter/thickness and pins/fins spacing). Figure 3. Temperature contours vs. time for each type of heat sink. parametersric parametersricric parameters (pins/fins parameters (pins/fins diameter/thickness(pins/fins (pins/fins diameter diameter diameter/thickness/thickness and/thickness and pins/fins pins/fins and and pins/fins spacing). pins/finsspacing). spacing). spacing). As boundary conditions, the temperatureAsAs boundaryboundary ofAs theAs boundary heat boundary conditions,conditions, source conditions, conditions, (at the the the temperature temperature bottom the the temperature oftemperature the of of theheat the heat heat of of the source sourcethe heat heat (at source(at source the the bottom bottom(at (at the the ofbottom of bottom the the heat heat of of the the heat heat ◦ ◦ ◦ sink) varied between 80 °C and 100 °C,sink)sink) with variedvariedsink) 10sink) °C between variedbetween intervals, varied between 80 between80 and °CC and andinlet 80 80 100 °C100 air°C and °C,C,velocityand 100 withwith 100 °C, 1010took°C, with °C Cwith the intervals,intervals, 10 10 °C °C intervals, intervals, andand inletinlet and airandair inlet velocityvelocity inlet air air velocity took tookvelocity the the took took the the 2.2. CFD Governing Equations ◦ values 0.7 m/s, 2.1 m/s and 3.5 m/svalues (at 20 0.7°C),values m/s, leading 0.7 2.1 m/s, m/sto Reynolds2.1 and m/s 3.5 and m/snumbers 3.5 (at m/s 20 from (atC), 20 leading2500 °C), leading to Reynolds to Reynolds numbers numbers from 2500 from 2500 Computational Fluid Dynamics (CFD) consists of predictingvalues fluid 0.7values flow,m/s, 2.10.7heat, m/sm/s, and and2.1 m/s3.5 m/sand (at3.5 20 m/s °C), (at leading 20 °C), toleading Reynolds to Reynolds numbers numbers from 2500 from 2500 (laminar-turbulent transition) to 12,500(laminar-turbulent (very(laminar-turbulent turbulent transition)flow). transition) to 12,500 to (very 12,500 turbulent (very turbulent flow). flow). mass transfer and related phenomena by solving numerically a(laminar-turbulent set of governing(laminar-turbulent mathe- transition) transition) to 12,500 to(very 12,500 turbulent (very turbulent flow). flow). For fins heat sinks, DOE analyses wereFor finsperformedFor heat fins sinks, heatusing DOE sinks, fin analysesthickness, DOE analyses were fin spacing, performed were performed using fin using thickness, fin thickness, fin spacing, fin spacing, matical equations. CFD analysis complements testing and experimentationFor fins heatbyFor reducing finssinks, heat DOE sinks, analyses DOE analyseswere performed were performed using fin using thickness, fin thickness, fin spacing, fin spacing, inlet velocity, and heat source temperatureinlet velocity,inlet as factors velocity, and heatand and pressure source heat temperaturesource drop andtemperature heat as factors sink as andfactors pressure and pressure drop and drop heat and sink heat sink total effort and cost required for experimentation and data acquisition.inlet velocity, Thereinlet velocity, andare aheat num- and source heat temperature source temperature as factors as and factors pressure and pressuredrop and drop heat and sink heat sink temperature after 15 s as responses.temperature Each factortemperature afterwas considered 15 after s as responses. 15 swith as responses. three Each levels factor Each (Table was factor considered was considered with three with levels three (Table levels2) (Table ber of commercial CFD software packages available for applicationtemperature in thermaltemperature after design. 15 sOneafter as responses. 15 s as responses. Each factor Each was factor considered was considered with three with levels three (Table levels (Table 2) and an L9 matrix was constructed.and an L92) and matrix an L9 was matrix constructed. was constructed. of them is ANSYS. Based on the finite volume method, ANSYS2) andsolvers an2) L9 discretisedand matrix an L9 was matrix the constructed. was constructed. Table 2. Levels and factors for DOE matrix for fins heat sinks. Table 2. Levels and factors for DOE matrixTable for fins2.Table LevelsTable heat 2. sinks. and2.Levels Levels factors and and forfactors factors DOE for matrix for DOE DOE formatrix matrix fins forheat for fins sinks. fins heat heat sinks. sinks. Level Fin Thickness (mm) Fin Spacing (mm) Inlet Velocity (m/s) Heat Source Temperature (◦C) Level Fin Thickness (mm) FinLevel Spacing LevelLevel (mm) Fin Thickness Fin Inlet Fin Thickness ThicknessVelocity (mm) (mm)(m/s) Fin (mm) Spac Fin Fining HeatSpac Spac(mm) Sourceinging (mm) Inlet(mm) Temperature Velocity Inlet Inlet Velocity Velocity(m/s) (°C) (m/s) (m/s) Heat Source Heat Heat Source Temperature Source Temperature Temperature (°C) (°C) (°C) 1 1.5 11 2.0 1 1 1.5 1.51.5 0.71.5 2.0 2.0 2.0 2.0 80 0.7 0.7 0.7 80 80 80 80 2 2.5 3.5 2.1 90 2 2.5 3.5 2 2 2.5 2.12.5 3.5 3.5 90 2.1 2.1 90 90 23 2.5 3.5 3.5 5.0 2.1 3.5 90 100 3 3.5 3 5.0 3 3 3.5 3.5 3.53.5 5.0 5.0 5.0 100 3.5 3.5 3.5 100 100 100 For pins heat sinks, the arrangement factor (in-line or staggered) was added to com- For pins heat sinks, the arrangement factor For(in-lineFor pins pins or heat staggered)heat sinks, sinks, the wasthe arra arra addedngementngement to com- factor factor (in-line (in-line or or staggered) staggered) was was added added to to com- com- pose anFor L18 pins DOE heat matrix. sinks, the Level arra andngement factors factor are shown (in-line in Tableor staggered)3. was added to com- pose an L18 DOE matrix. Level and factorspose an arepose L18pose shown anDOE an L18 L18 inmatrix. DOE Table DOE matrix. Level 3.matrix. and Level Level factors and and factorsare factors shown are are shownin shown Table in 3.in Table Table 3. 3. Table 3. Levels and factors for DOE matrix for pins heat sinks.

Level Pin Diameter (mm) Pins Spacing (mm) Inlet Velocity(m/s) Heat Source Temperature (◦C) Arrangement 1 1.5 2.0 0.7 80 In-line (1) 2 2.5 3.5 2.1 90 Staggered (2) 3 3.5 5.0 3.5 100 -

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Table 3. Levels and factors for DOE matrix for pins heat sinks. Table 3. Levels and factors for DOE matrix for pins heat sinks. Level Pin Diameter (mm) Pins Spacing (mm) Inlet Velocity(m/s) Heat Source Temperature (°C) Arrangement Level Pin Diameter (mm) Pins Spacing (mm) Inlet Velocity(m/s) Heat Source Temperature (°C) Arrangement 1 1.5 2.0 0.7 80 In-line (1) 1 1.5 2.0 0.7 80 In-line (1) 2 2.5 3.5 2.1 90 Staggered (2) 2 2.5 3.5 2.1 90 Staggered (2) Materials 2021, 14, 2041 3 3.5 5.0 3.5 100 7 of 19 - 3 3.5 5.0 3.5 100 - Based on DOE results, the shape of fins or pins was varied according to some previ- BasedBased on onDOE DOE results, results, the the shape shape of offins fins or or pins pins was was varied varied according according to to some some previ- previous ous studies that showed good results [32,38–46,70] considering the same boundary pa- ousstudies studies that that showed showed good good results results [32 ,[32,38–38–46,7046,70]] considering considering the samethe same boundary boundary parameters. parameters. For fins heat sinks (Figure 4), the same number of fins was considered. For pins rameters.For fins For heat fins sinks heat (Figure sinks (Figure4), the same 4), the number same number of fins was of fins considered. was considered. For pins For heat pins sinks heat sinks (Figure 5), the same hydraulic diameter and pin spacing was maintained. heat(Figure sinks 5(Figure), the same 5), the hydraulic same hydraulic diameter diameter and pin spacingand pin wasspacing maintained. was maintained.

Figure 4. DifferentFigure ﬁns heat 4. Different sink models. fins heat sink models. Figure 4. Different fins heat sink models.

Figure 5. Different pins shapesFigure under 5. Different study. pins shapes under study. InFigure order to5. Different conﬁrm thepins advantages shapes under of study. additive manufacturing for thermal management components, lattice sinks with X, Hexagon, and Snow Flake (Figure6) unit cells were studied. Cell size and thickness were ﬁxed as well as boundary conditions.

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In order to confirm the advantages of additive manufacturing for thermal manage- mentIn order components, to confirm lattice the sinks advantages with X, ofHexagon, additive and manufacturing Snow Flake (Figure for thermal 6) unit manage- cells were Materials 2021, 14, 2041 mentstudied. components, Cell size lattice and thickness sinks with were X, Hexagon, fixed as welland Snowas boundary Flake (Figure conditions. 6) unit cells were 8 of 19 studied. Cell size and thickness were fixed as well as boundary conditions.

Figure 6. Different lattice heat sinks models. Figure 6. Different lattice heat sinks models. Figure3. Results 6. Different and lattice Discussion heat sinks models. 3. Results and Discussion 3.1. Fins Heat Sinks 3. Results3.1. Fins and Heat Discussion Sinks 3.1. FinsUsing HeatUsing Sinks analysis analysis of variance of variance (ANOVA), (ANOVA), the effects the of effectsvariables of and variables their interactions and their interactions on eachonUsing each response responseanalysis wereof were variance determined. determined. (ANOVA), For fins Forthe heat effects fins sinks, heatof it variables was sinks, found and it that, was their either found interactions for a that, lower either for a lower on heatheateach sinkresponse sink temperature temperature were determined. (Figure (Figure 7, top)For fins 7or, top)for heat a lowersinks, or for pressureit awas lower found drop pressure that, (Figure either 7, drop forbottom), a lower (Figure the 7, bottom), the heatthicknessthickness sink temperature of ofthe the fins fins(Figureshould should be7, top)as small beor asfor as smallapossible. lower as pressure The possible. same drop was The (Figure not sametrue 7, for bottom), was the spacing. not the true for the spacing. On the one hand, if it is as small as possible, it increases the density of the fins and there- thicknessOn the of one the fins hand, should if it be is as as small small as aspossible. possible, The same it increases was not true the for density the spacing. of the fins and therefore Onfore the onecauses hand, better if it thermalis as small efficiency. as possible, On itth increasese other hand, the density the smaller of the finsthe spacing,and there- the causes better thermal efficiency. On the other hand, the smaller the spacing, the higher forehigher causes pressure better drops.thermal In efficiency. agreement On between the other both hand,parameters, the smaller and since the thespacing, influence the is higherpressuremuch pressure higher drops. drops.for the InIn pressure agreement drop, between the between bigger both fins bothparameters, spacing parameters, (5and mm) since was andthe considered influence since the isfor influence is much muchhigherfurther higher studies for for the therelated pressurepressure to the drop, shape drop, the of the thebigger fins bigger fins(Figure spacing fins 4). spacing (5 mm) (5was mm) considered was considered for for further furtherstudies studies related related to to the the shape of of the the fins fins (Figure (Figure 4). 4).

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FigureFigure 7. Main 7. effectsMain for effects heat sink for temperature heat sink temperature(top) and pressure (top drop) and (bottom pressure) for fins drop heat ( bottomsinks. ) for ﬁns heat sinks.

Regarding boundary conditions, as expected, the effect of inlet velocity on pressure drop and heat source temperature on heat sink temperature after 15 s was linear. How- ever, an inlet velocity of 2.11 m/s (Re = 7500) caused a minimum heat sink temperature and a heat source temperature of 90 °C caused a minimum pressure drop. These conclusions are related with the geometric parameters (number of fins and fins spacing), according to Tables 4 and 5, respectively.

Table 4. Correlation between heat sink temperature and geometrical parameters.

Number of Heat Source Temperature Velocity HS Temperature Simulation Fins (°C) (m/s) after 15 s (°C) #1 14 80 0.7 52.2 #2 6 80 2.11 56.4 #3 8 80 3.51 54.1 #4 7 90 0.7 61.9 #5 11 90 2.11 57.7 #6 8 90 3.51 60.5 #7 7 100 0.7 68.6 #8 10 100 2.11 63.5 #9 9 100 3.51 65.3

Table 5. Correlation between pressure drop and DOE factors.

Spacing Velocity Pressure Drop Simulation Heat Source Temperature (°C) (mm) (m/s) (Pa) #1 2 80 0.7 13.8 #2 3.5 90 0.7 10.5 #3 5 100 0.7 4.4 #4 5 80 2.11 40.3 #5 2 90 2.11 108.4 #6 3.5 100 2.11 22.3 #7 3.5 80 3.51 105.1 #8 5 90 3.51 32.6 #9 2 100 3.51 380.1

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Regarding boundary conditions, as expected, the effect of inlet velocity on pressure drop and heat source temperature on heat sink temperature after 15 s was linear. However, an inlet velocity of 2.11 m/s (Re = 7500) caused a minimum heat sink temperature and a heat source temperature of 90 ◦C caused a minimum pressure drop. These conclusions are related with the geometric parameters (number of ﬁns and ﬁns spacing), according to Tables4 and5, respectively.

Table 4. Correlation between heat sink temperature and geometrical parameters.

Number of Heat Source Velocity HS Temperature Simulation Fins Temperature (◦C) (m/s) after 15 s (◦C) #1 14 80 0.7 52.2 #2 6 80 2.11 56.4 #3 8 80 3.51 54.1 #4 7 90 0.7 61.9 #5 11 90 2.11 57.7 #6 8 90 3.51 60.5 #7 7 100 0.7 68.6 #8 10 100 2.11 63.5 #9 9 100 3.51 65.3

Table 5. Correlation between pressure drop and DOE factors.

Heat Source Pressure Drop Simulation Spacing (mm) Velocity (m/s) Temperature (◦C) (Pa) #1 2 80 0.7 13.8 #2 3.5 90 0.7 10.5 #3 5 100 0.7 4.4 #4 5 80 2.11 40.3 #5 2 90 2.11 108.4 #6 3.5 100 2.11 22.3 #7 3.5 80 3.51 105.1 #8 5 90 3.51 32.6 #9 2 100 3.51 380.1

As boundary conditions, an inlet velocity of 2.11 m/s and a heat source temperature of 90 ◦C were considered for further studies with ﬁns.

Fins Shape In all ﬁns heat sinks variants (Figure4), the same number of ﬁns (8) and boundary parameters were considered. Results for each model are shown in Table6.

Table 6. Temperature and pressure drop for each ﬁn heat sink model.

Total Area Front Area Volume HS Temperature Pressure Drop Model (cm2) (cm2) (cm3) after 15 sec (◦C) (Pa) A 408.9 7.7 38.6 60.6 13.4 B 260.7 7.7 27.0 40.0 30.6 C 389.4 7.7 34.2 52.4 25.1 D 397.3 20.2 35.1 53.9 52.6 E 414.5 7.7 38.6 55.2 22.4 F 682.1 7.7 38.6 52.0 31.5 G 682.1 7.7 38.6 54.5 24.5

It was found that the incorporation of ﬁllets or chamfers did not bring any advantage, contrarily to all design variations shown in Figure4 and Table6. Fins with trapezoidal and inverted trapezoidal shape (Figure4B) were considered, the latter being an advantageous Materials 2021, 14, x FOR PEER REVIEW 10 of 19

As boundary conditions, an inlet velocity of 2.11 m/s and a heat source temperature of 90 °C were considered for further studies with fins.

Fins Shape In all fins heat sinks variants (Figure 4), the same number of fins (8) and boundary parameters were considered. Results for each model are shown in Table 6.

Table 6. Temperature and pressure drop for each fin heat sink model.

Total Area Front Area Volume HS Temperature Pressure Drop Model (cm2) (cm2) (cm3) after 15 sec (°C) (Pa) A 408.9 7.7 38.6 60.6 13.4 B 260.7 7.7 27.0 40.0 30.6 C 389.4 7.7 34.2 52.4 25.1 D 397.3 20.2 35.1 53.9 52.6 E 414.5 7.7 38.6 55.2 22.4 F 682.1 7.7 38.6 52.0 31.5 G 682.1 7.7 38.6 54.5 24.5

Materials 2021, 14, 2041 It was found that the incorporation of fillets or chamfers did not bring any advantage,10 of 19 contrarily to all design variations shown in Figure 4 and Table 6. Fins with trapezoidal and inverted trapezoidal shape (Figure 4B) were considered, the latter being an advanta- geousoption option due to due its wideto its part wide exposed part exposed to ambient to ambient air [27]. air Moreover, [27]. Moreover, the higher the the higher inverted the invertedtrapezoid trapezoid angle, the angle, better the the better performance the performance (Figure8 ).(Figure 8).

FigureFigure 8. 8. ModelModel B B variants. variants.

TheThe incorporation incorporation of of holes holes in inthe the fins ﬁns (model (model C) has C) hasbeen been studied studied by other by other authors au- [30,31]thors [30and,31 both] and agreed both agreed that it thatwas itan was advantageous an advantageous approach approach due to due theto higher the higher heat Materials 2021, 14, x FOR PEER REVIEW 11 of 19 transferheat transfer coefficient. coefﬁcient. Furthermore, Furthermore, for larger for larger holes holes diameter, diameter, maintaining maintaining holes holes spacing spacing (5 mm)(5 mm) resulted resulted in better in better heat heat sink sink performance performance (Figure (Figure 9).9 ).

Figure 9. Model C variants. Regarding model E, the lower the spacing between the fins at the bottom, keeping Regarding model E, the lower the spacing between the fins at the bottom, keeping the top spacing equal to 5 mm, the better the heat sink performance (Figure 10, I and II). the top spacing equal to 5 mm, the better the heat sink performance (Figure 10, I and II). This happens because airflow towards radial fins tends to quicken as the gap between two This happens because airflow towards radial fins tends to quicken as the gap between two consecutive fins reduces (EI to EII) [71]. These advantages of model E fins have also been consecutive fins reduces (EI to EII) [71]. These advantages of model E fins have also been confirmed experimentally by other authors [71,72]. However, the incorporation of more confirmed experimentally by other authors [71,72]. However, the incorporation of more material in the heat sink base (Figure 10, III), close to the fins, did not bring any advantage. material in the heat sink base (Figure 10, III), close to the fins, did not bring any advantage. With this, the properties of models B, C, and E have been combined and, among the studied, the heat sink design with the best performance was attained (Figure 11). Following some design rules for additive manufacturing, elliptical holes were considered instead of circular ones.

Figure 10. Model E variants.

With this, the properties of models B, C, and E have been combined and, among the studied, the heat sink design with the best performance was attained (Figure 11). Follow- ing some design rules for additive manufacturing, elliptical holes were considered instead of circular ones.

Figure 11. Best fin heat sink (among those studied).

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Figure 9. Model C variants.

Regarding model E, the lower the spacing between the fins at the bottom, keeping the top spacing equal to 5 mm, the better the heat sink performance (Figure 10, I and II). Figure 9. ModelThis C variants. happens because airflow towards radial fins tends to quicken as the gap between two consecutive fins reduces (EI to EII) [71]. These advantages of model E fins have also been Regardingconfirmed model E, experimentally the lower the spacingby other between authors [7the1,72]. fins However,at the bottom, the incorporation keeping of more the top spacingmaterial equal to in 5the mm, heat the sink better base the (Figure heat 10,sink III), performance close to the fi(Figurens, did 10,not Ibring and II).any advantage. This happens because airflow towards radial fins tends to quicken as the gap between two consecutive fins reduces (EI to EII) [71]. These advantages of model E fins have also been Materials 2021, 14, 2041 confirmed experimentally by other authors [71,72]. However, the incorporation of11 more of 19 material in the heat sink base (Figure 10, III), close to the fins, did not bring any advantage.

Figure 10. Model E variants.

With this, the properties of models B, C, and E have been combined and, among the studied, the heat sink design with the best performance was attained (Figure 11). Follow- Figure 10. Modeling E variants.some design rules for additive manufacturing, elliptical holes were considered instead Figure 10. Modelof E circular variants. ones.

Materials 2021, 14, x FOR PEER REVIEW 12 of 19

Figure 11. Best ﬁn heat sink (among those studied). Figure 11. Best fin heat sink (among those studied). 3.2.3.2. PinsPins HeatHeat SinksSinks ForFor pins heat heat sinks, sinks, the the arra arrangementngement factor factor was was added: added: in-line in-line or staggered or staggered pins pins(Fig-

(Figureure 12). 12For). staggered For staggered pins, there pins, are there two are possi twoble possible orientations orientations (1 and 2). (1 From and orientation 2). From orientation 1 to orientation 2, heat sink temperature increased by a maximum of 1.4% but 1 to orientationFigure 11. Best2, heat fin heatsink sink temperature (among those increased studied). by a maximum of 1.4% but pressure pressuredrop decreased drop decreased by about by25%. about Although 25%. Although the heat sink the heat temperature sink temperature after 15 s after is the 15 most s is thepertinent most pertinent response responseparameter, parameter, the decrease the in decrease pressure in drop pressure was dropmuch was higher, much causing higher, a causingbetter performance a better performance for orientation for orientation 2 (Figure 212c). (Figure For 12thisc). reason, For this the reason, staggered the staggered arrange-

arrangementment was considered was considered with orientation with orientation 2. 2.

Figure 12. Results for the possible pin heat sinks arrangements and orientations. Figure 12. Results for the possible pin heat sinks arrangements and orientations. Taking this into account, it was found that, either for a lower heat sink temperature or for a lowerTaking pressure this into drop, account, the staggered it was found arrangement that, either (2) for is more a lower advantageous heat sink temperature (Figure 13). Regardingor for a lower pins pressure diameter, drop, for a the lower staggered heat sink arrangement temperature (2) (Figure is more 13 advantageous, top), it should (Figure be as small13). Regarding as possible. pins The diameter, same was for not a lower true for heat the sink pressure temperature drop (Figure (Figure 13 13,, bottom), top), it should where therebe as issmall an ideal as possible. diameter The of same 2.5 mm. was In not agreement true for the between pressure both drop parameters, (Figure 13, and bottom), since where there is an ideal diameter of 2.5 mm. In agreement between both parameters, and since the heat sink temperature is the most relevant response parameter and the influence is more accentuated, the lower pins diameter (1.5 mm) will be considered for further studies related to the shape of the pins. With a smaller diameter, there is also a smaller building volume to be created by additive manufacturing. Respecting pins spacing, if, on the one hand, there was no influence on the heat sink temperature, on the other hand, the influence on the pressure drop is quite noticeable. For this reason, the upper spacing (5 mm) was considered the best choice. These conclusions about geometric parameters are in agreement with the fin heat sinks. As explained for fins heat sinks, a temperature of 90 °C caused a lower pressure drop (almost irrelevant) also due to some geometrical parameters (pins spacing and heat sink front area) given in Table 7. For this reason, this temperature was selected for further studies with pins. Regarding the inlet velocity, its influence was linear and as expected. There- fore, a velocity of 3.51 m/s was considered because it resulted in a lower heat sink temperature.

Table 7. Correlation between pressure drop and geometrical parameters for an inlet air velocity of 3.51 m/s.

Arrangement Simulation Spacing (mm) Front Area (mm2) Heat Source Temperature (°C) Pressure Drop (Pa) #1 3.5 13.4 80 289.7 In line #2 5 10.2 90 167.1 #3 2 16.6 100 776.9 #4 3.5 11.4 80 170.7 Staggered #5 5 7.7 90 116.0 #6 2 11.8 100 441.1

Materials 2021, 14, 2041 12 of 19

the heat sink temperature is the most relevant response parameter and the inﬂuence is more accentuated, the lower pins diameter (1.5 mm) will be considered for further studies Materials 2021, 14, x FOR PEER REVIEW 13 of 19 related to the shape of the pins. With a smaller diameter, there is also a smaller building volume to be created by additive manufacturing.

FigureFigure 13. Main effects forfor heatheat sinksink temperature temperature (top (top) and) and pressure pressure drop drop (bottom (bottom) for) for pins pins heat heat sinks. sinks. Respecting pins spacing, if, on the one hand, there was no influence on the heat sink temperature, on the other hand, the influence on the pressure drop is quite noticeable. For Pins Shape this reason, the upper spacing (5 mm) was considered the best choice. These conclusions aboutIn geometric all pins shapes parameters studies are (Figure in agreement 5), the same with thehydraulic fin heat diameter sinks. (1.5 mm) and pin spacingAs explained(5 mm) were for maintained, fins heat sinks, as awell temperature as boundary of 90 parameters.◦C caused aResults lower pressureare shown drop in Table(almost 8. irrelevant) also due to some geometrical parameters (pins spacing and heat sink front area) given in Table7. For this reason, this temperature was selected for further studies Tablewith 8. pins.Temperature Regarding and thepressure inlet velocity,drop for each its influence pin heat sink was model. linear and as expected. Therefore, a velocity of 3.51 m/s was considered because it resulted in a lower heat sink temperature.Pressure Model Nr of Pins Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (°C) Table 7. Correlation between pressure drop and geometrical parameters for an inlet air velocity of 3.51 m/s.Drop (Pa) H 60 162.7 7.7 16.1 36.0 116.0 2 ◦ IArrangement 52 Simulation 165.8 Spacing (mm) 6.4 Front Area 16.2 (mm ) Heat Source Temperature 38.4 ( C) Pressure Drop 57.2(Pa) J 53 #1 168.4 3.5 9.6 13.4 16.3 80 38.0 289.7 203.8 In line #2 5 10.2 90 167.1 K 52 #3 178.1 2 8.1 16.6 16.7 100 39.1 776.9 60.4 L 52 #4 178.1 3.5 8.1 11.4 16.7 80 42.9 170.7 95.1 M Staggered46 #5 159.6 5 9.0 16.07.7 90 50.4 116.0 96.9 #6 2 11.8 100 441.1 N 46 159.6 9.0 16.0 44.1 91.5 O 52 185.4 6.6 16.9 49.3 56.2

Materials 2021, 14, 2041 13 of 19

Pins Shape In all pins shapes studies (Figure5), the same hydraulic diameter (1.5 mm) and pin spacing (5 mm) were maintained, as well as boundary parameters. Results are shown in Table8.

Table 8. Temperature and pressure drop for each pin heat sink model.

Model Nr of Pins Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (◦C) Pressure Drop (Pa) H 60 162.7 7.7 16.1 36.0 116.0 I 52 165.8 6.4 16.2 38.4 57.2 J 53 168.4 9.6 16.3 38.0 203.8 K 52 178.1 8.1 16.7 39.1 60.4 L 52 178.1 8.1 16.7 42.9 95.1 MaterialsM 2021, 14, x 46FOR PEER REVIEW 159.6 9.0 16.0 50.4 96.9 14 of 19 N 46 159.6 9.0 16.0 44.1 91.5 O 52 185.4 6.6 16.9 49.3 56.2

ConventionalConventional heat heat sinks, sinks, with with circular circular pins, pins, continue continue to be to the be thebest best choice choice among among the manythe many options options of pin of shapes, pin shapes, even eventhough though the pressure the pressure drop dropis high. is high.For these For thesepins, con- pins, sideringconsidering drawing drawing outwards outwards (Figure (Figure 14), only 14), possible only possible to be produced to be produced by additive by additive manufacturing,manufacturing, was not was advantageous—a not advantageous—a higher higher temperature temperature and a andhigher-pressure a higher-pressure drop dropwas obtained.was obtained.

FigureFigure 14. 14. ComparisonComparison between between circular circular pins pins (A (A)) and and circular circular pins pins outwards outwards (A1). (A1). Figure 15 shows pins heat sinks with 1 mm frontal elliptical holes (H2) and side Figure 15 shows pins heat sinks with 1 mm frontal elliptical holes (H2) and side el- elliptical holes (H3) as well as a radial pins heat sink also with frontal elliptical holes (H4), liptical holes (H3) as well as a radial pins heat sink also with frontal elliptical holes (H4), spaced 5 mm apart. In all cases, holes were advantageous and the results were quite similar. spaced 5 mm apart. In all cases, holes were advantageous and the results were quite sim- For the same heat sink temperature obtained, the one with the lowest pressure drop was ilar. For the same heat sink temperature obtained, the one with the lowest pressure drop considered as the best option for pins heat sinks (H2). was considered as the best option for pins heat sinks (H2). For the case of ellipse pins (the second-best pins shape), differences were observed between maintaining the spacing (Model I) or maintaining the number of pins (Model I1), concerning the reference heat sink (Model H). According to Table9, there were no signiﬁcant differences, i.e., opting for ellipse pins, the choice should be Model I once it has a smaller building volume.

Table 9. Temperature and pressure drop for each pin heat sink model.

Model Nr of Pins Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (◦C) Pressure Drop (Pa) H 60 162.7 7.7 16.1 36.0 116.0 I 52 165.8 6.4 16.2 38.4 57.2 I1 60 186.1 6.4 16.9 38.3 59.1 J 53 168.4 9.6 16.3 38.0 203.8

Figure 15. Pins heat sinks with frontal (H2) and side (H3) holes and radial pins heat sink with frontal holes (H4).

For the case of ellipse pins (the second-best pins shape), differences were observed between maintaining the spacing (Model I) or maintaining the number of pins (Model I1), concerning the reference heat sink (Model H). According to Table 9, there were no signif- icant differences, i.e., opting for ellipse pins, the choice should be Model I once it has a smaller building volume.

Materials 2021, 14, x FOR PEER REVIEW 14 of 19

Conventional heat sinks, with circular pins, continue to be the best choice among the many options of pin shapes, even though the pressure drop is high. For these pins, considering drawing outwards (Figure 14), only possible to be produced by additive manufacturing, was not advantageous—a higher temperature and a higher-pressure drop was obtained.

Figure 14. Comparison between circular pins (A) and circular pins outwards (A1).

Figure 15 shows pins heat sinks with 1 mm frontal elliptical holes (H2) and side elliptical holes (H3) as well as a radial pins heat sink also with frontal elliptical holes (H4), spaced 5 mm apart. In all cases, holes were advantageous and the results were quite similar. For the same heat sink temperature obtained, the one with the lowest pressure drop Materials 2021, 14, 2041 14 of 19 was considered as the best option for pins heat sinks (H2).

Materials 2021, 14, x FOR PEER REVIEW 15 of 19

Table 9. Temperature and pressure drop for each pin heat sink model.

Pressure Drop Model Nr of Pins Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (°C) (Pa) H 60 162.7 7.7 16.1 36.0 116.0 I 52 165.8 6.4 16.2 38.4 57.2

I1 60 186.1 6.4 16.9 38.3 59.1 FigureFigure 15. 15. PinsPins heat heat sinks sinks with with frontal frontal (H2) (H2) and and side side (H3) (H3) holes and radial pins heatheat sinksink withwith frontal J 53 168.4 9.6 16.3 38.0 203.8 frontalholes (H4).holes (H4).

ForTherefore, the case theof ellipse best option pins (the contemplated second-best circularci pinsrcular shape), pins inin differences combinationcombination were withwith observed frontalfrontal betweenholes in maintaining their structure the (Figure spacing 1616). (Model). I) or maintaining the number of pins (Model I1), concerning the reference heat sink (Model H). According to Table 9, there were no signif- icant differences, i.e., opting for ellipse pins, the choice should be Model I once it has a smaller building volume.

Figure 16. Best pin heat sink (among those studied). Figure 16. Best pin heat sink (among those studied). 3.3. Lattice Heat Sinks 3.3. Lattice Heat Sinks Lattice sinks with X, Hexagon, and Snow Flake (Figure6) unit cells were studied. Cell size andLattice thickness sinks with were X, fixedHexagon, at 15 and× 15 Snow× 15 Flake mm3 (Figureand 1.5 6) mm, unit respectively,cells were studied. as well Cell as boundarysize and thickness conditions were (heat fixed source at 15 temperature × 15 × 15 mm of 903 and◦C and1.5 mm, air inlet respectively, velocity of as 3.5 well m/s). as Theboundary results conditions are shown (heat in Table source 10. temperature of 90 °C and air inlet velocity of 3.5 m/s). The results are shown in Table 10. Table 10. Temperature and pressure drop for each pin heat sink model. Table 10. Temperature and pressure drop for each pin heat sink model. Model Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (◦C) Pressure Drop (Pa) ModelX-type Total Area 187.9 (cm2) Front Area 31.3(cm2) Volume (cm 16.83) HS Temperature after 39.2 15 s (°C) Pressure 108.1 Drop (Pa) X-typeHexagon 187.9 243.7 31.3 41.1 16.8 19.2 39.2 26.7 108.1 161.2 Snow Flake 283.9 41.0 20.6 33.7 137.2 Hexagon 243.7 41.1 19.2 26.7 161.2 Snow Flake 283.9 41.0 20.6 33.7 137.2 Among the three models studied, the heat sink with hexagon unit cell showed the lowest temperature, despite the higher pressure drop. This heat sink has the middle total Among the three models studied, the heat sink with hexagon unit cell showed the area to volume ratio. The advantages of this unit cell in thermal management applications lowest temperature, despite the higher pressure drop. This heat sink has the middle total were also confirmed by Gu et al. [73]. area to volume ratio. The advantages of this unit cell in thermal management applications 3.4.were Fins also vs. confirmed Pins vs. Lattice by Gu Heat et al. Sink [73]. In this subchapter, it is intended to directly compare the best fins, pins, and blades 3.4. Fins vs. Pins vs. Lattice Heat Sink heat sinks (Figure 17), under the same geometric and boundary parameters. In this subchapter, it is intended to directly compare the best fins, pins, and blades heat sinks (Figure 17), under the same geometric and boundary parameters.

Figure 17. Fins, pins, and lattice heat sinks, respectively.

Materials 2021, 14, x FOR PEER REVIEW 15 of 19

Table 9. Temperature and pressure drop for each pin heat sink model.

Pressure Drop Model Nr of Pins Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (°C) (Pa) H 60 162.7 7.7 16.1 36.0 116.0 I 52 165.8 6.4 16.2 38.4 57.2 I1 60 186.1 6.4 16.9 38.3 59.1 J 53 168.4 9.6 16.3 38.0 203.8

Therefore, the best option contemplated circular pins in combination with frontal holes in their structure (Figure 16).

Figure 16. Best pin heat sink (among those studied). 3.3. Lattice Heat Sinks Lattice sinks with X, Hexagon, and Snow Flake (Figure 6) unit cells were studied. Cell size and thickness were fixed at 15 × 15 × 15 mm3 and 1.5 mm, respectively, as well as boundary conditions (heat source temperature of 90 °C and air inlet velocity of 3.5 m/s). The results are shown in Table 10.

Table 10. Temperature and pressure drop for each pin heat sink model.

Model Total Area (cm2) Front Area (cm2) Volume (cm3) HS Temperature after 15 s (°C) Pressure Drop (Pa) X-type 187.9 31.3 16.8 39.2 108.1 Hexagon 243.7 41.1 19.2 26.7 161.2 Snow Flake 283.9 41.0 20.6 33.7 137.2

Among the three models studied, the heat sink with hexagon unit cell showed the lowest temperature, despite the higher pressure drop. This heat sink has the middle total area to volume ratio. The advantages of this unit cell in thermal management applications were also confirmed by Gu et al. [73].

3.4. Fins vs. Pins vs. Lattice Heat Sink Materials 2021, 14, 2041 In this subchapter, it is intended to directly compare the best fins, pins, and blades15 of 19 heat sinks (Figure 17), under the same geometric and boundary parameters.

FigureFigure 17. 17. Fins,Fins, pins, pins, and and lattice lattice he heatat sinks, sinks, respectively. respectively.

Table 11 shows that, under forced convection environments, better results were obtained for the lattice heat sink with hexagon unit cell. The pressure drop increased more than double for the same inlet velocity and Reynolds number, a consequence of the high frontal area. Even so, a decrease of about 28% and 9% in heat sink temperature was achieve, comparing with the best ﬁns and pins heat sink, respectively. As inlet velocity and heat source temperature are kept constant during the experiments, the best heat sink is the one whose temperature is minimal, which, according to Equation (3), translates into lower thermal resistance.

Table 11. Direct comparison between heat sinks with ﬁns, pins, and blades (Re = 12,500).

Model Total Are (cm2) Front Area (cm2) Volume (cm3) Total Area to Volume Ratio HS Temperature after 15 s (◦C) Pressure Drop (Pa) Fins 255.9 7.7 25.1 10.2 36.9 50.2 Pins 173.0 7.3 15.6 11.1 29.4 61.1 Lattice 243.7 41.1 19.2 12.7 26.7 161.2

Based on this study, there is a direct correlation between the total area to volume ratio and the heat sink performance. The lattice heat sink, the heat sink with the highest area to volume ratio and only possible to be produced by additive manufacturing, was considered the best option among the studied.

4. Conclusions The thermal performance of heat sinks design under forced convection, varying geometric and boundary parameters (inlet velocity and heat source temperature), was conducted by computational fluid dynamics simulation with ANSYS Fluent. Considering heat sinks with fins configuration, it was found out that the thickness of the fins should be as thin as possible and widely spaced. The optimal design is obtained by an agreement between both parameters. However, since the spacing has a greater impact on the pressure drop, the bigger fins spacing (5 mm) was considered for studies related to the shape of the fins. For this last iteration on the shape configuration, all geometric and boundary parameters were kept constant, varying only in heat sinks design. It was found that radial fins designed with an inverted trapezoidal shape and with holes have great advantages and the design (Figure 11) was the one with better performance. A similar study was done for pins heat sinks. It was found that the best solution would be to consider a pin diameter of 1.5 mm with a spacing of 5 mm and with a staggered arrangement. By varying the shape of the pins, it was also found that the incorporation of holes in circular pins was beneficial for thermal performance. Taking advantage of additive manufacturing freedom of design, three different lattice structures with the same cell size (15 × 15 × 15mm3) and thickness of 1.5 mm but different cell topology were compared. Among X, Hexagon, and Snow Flake unit cells, it was found that the Hexagon unit cell exhibited the best performance. Through a direct comparison of the thermal efficiency of three heat sinks (the best fins, pins and lattice heat sinks), under the same boundary conditions, it was concluded that, under forced convection environments, a lattice heat sink with a hexagon unit cell is the optimal choice. These results validated how advantageous additive manufacturing can Materials 2021, 14, 2041 16 of 19

be for components that require thermal management, such as electronic devices. Even so, more studies should be treated to reduce pressure drop and optimize the lattice heat sink in terms of cell size and thickness.

Author Contributions: Conceptualization, methodology, software, formal analysis, investigation, Materials 2021, 14, x FOR PEER REVIEW resources,5 of 19 writing—original draft preparation, E.C.S.; writing—review and editing, supervision, Á.M.S. and A.J.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Portuguese Fundação para a Ciência e a Tecnologia (FCT), for ﬁnancial support under the PhD scholarship SFRH/BD/144590/2019 and by European Structural and Investment Funds in the FEDER component, through the Operational Competitiveness and Internationalization Programme (COMPETE 2020) [Project No. 039334; Funding Reference: POCI-01- Materials 2021, 14, x FOR PEER REVIEW 0247-FEDER-039334].6 of 19

Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. domain into a finite set of control volumes in which general conservation equations for mass (Equation (2)), momentum (Equation (3)) and energy (EquationData (4)) Availability are solved Statement: [67]. Not applicable. ∇∙(𝜌𝑢⃗) =0 Conﬂicts of Interest: The(2) authors declare no conﬂict of interest.

(𝑢⃗ ∙∇)(𝜌𝑢⃗) =∇P+∇∙(μ∇𝑢⃗) Nomenclature (3)

𝑢⃗ ∙∇𝜌𝐶 𝑇 = ∇ ∙ (𝑘∇𝑇 ) (4) q Heat Flux Density (W·m2) ρ air density (kg·m−e) Figure 2. LatticeNote thatheat 𝜌sink and mesh. 𝜇 are the fluid density and viscosity and 𝑢⃗ is the velocity vector. The ∂T −1 energy equation for solid regions [68] can be written as: ∂n thermal gradient in direction n (K·m ) t time (s) As initial values, the system was considered at a room𝑘 ∇𝑇=0 temperature of 20 °C. The (5) A heat transfer area (m2) outlet vent condition was used for the outlet boundary and the wind tunnel wall →considered adiabatic. TheThese remaining equations boundary are solved conditions with the presumption(heat source temperature that radiation and heat inletu transfer airvelocity is negligible. vector (m/s) The standard Ϗ-Epsilon viscous model used in this study is aP semi-empiricalair pressure model (Pa) velocity) were established according to each specific case. − R Ϗ thermal resistance (K·W 1) During computebased onsolution, model the transport discretised equations conservation for the turbulenceequations (Equations kinetic energy (4)–(6)) ( ) and its dissipation rate (ε), obtained from the following transport equations: Tf fluid temperature (K) are solved iteratively until convergence, i.e., when changes in solution variables fromµ oneair viscosity (kg·m−1·s−1) −6 −1 −1 iteration to the next are negligible𝜕 (residual𝜕 response𝜕 less 𝜇than 𝜕Ϗ 10 × 10 ). As theCp mostSpecific Heat Capacity (J·kg ·K ) (𝜌Ϗ) + (𝜌Ϗ𝑢) = 𝜇 + +𝐺Ϗ +𝐺 −𝜌𝜀−𝑌 +𝑆Ϗ (6) widely-used engineering turbulence𝜕𝑡 𝜕𝑥 model for industrial𝜕𝑥 applications,𝜎Ϗ 𝜕𝑥 standard Ϗ -Epsi-turbulence kinetic energy (J·kg) lon viscous model (Equations (6) and (7)) was selected. The pressure-velocity coupling∆T difference between the minimum temperature of the HS and the fluid temperature 𝜕 𝜕 𝜕 𝜇 𝜕𝜀 𝜀 𝜀 was achieved through the SIMPLE scheme [64] and the Least Squares Cell Based gradientsat the inlet (K) (𝜌𝜀) + (𝜌𝜀𝑢) = 𝜇 + +𝐶 (𝐺 +𝐶𝐺) −𝐶 +𝑆 (7) were choose as the spatial𝜕𝑡 discretization𝜕𝑥 scheme𝜕𝑥 [65]. 𝜎 𝜕𝑥 𝑘 Qheat total𝑘 heat applied at the base of the HS (W) −2 −1 Pressure drop across the heat sink and its temperature were reported after h15 s onconvective heat transfer coefficient (W·m ·K ) In these equations, GϏ represents the generation of turbulence kinetic energy due to −1 −1 the respective sensors (Figure 1). The temperature sensor was located where, as kgeneralthermal conductivity (W·m ·K ) the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoy- rule, the heat sink temperature was the minimum [66]. Considering a time step sizeT sof oneHS surface temperature (K) ancy, YM represents the contribution of the fluctuating dilatation Tin compressibleinlet air temperature turbu- (K) second with 10 maximum iterations per time step, the 15 s were found to be a good balancei lence to the overall dissipation rate, C1ε, C2ε and C3ε are constants, σϏ and σturbulentε are the Prandtl turbu- number for between good results and computational effort (Figure 3) once, in most cases, the temper- lent Prandtl numbers for Ϗ and ε, respectively. SϏ and Sε are user-definedσε turbulent source Prandtl terms. numbers for ε ature reached theThe steady-state Ϗ-epsilon model condition. assumes that the flow is fully turbulent, and Acronymsthe effects of molecular viscosity are negligible [65,69]. CFD Computational Fluid Dynamics DOE Design of experiments 2.3. Heat Sink Models HS Heat sink

The statistical design of experimentsReferences (DOE) was used to design the sets of experiments run in this work for fins and pins heat sinks, in order to optimize the main geomet- 1. Dede, E.M.; Joshi, S.N.; Zhou, F. Topology Optimization, Additive Layer Manufacturing, and Experimental Testing of an ric parameters (pins/fins diameter/thicknessAir-Cooled and pins/fins Heat Sink. spacing).J. Mech. Des. Trans. ASME 2015, 137, 11. [CrossRef] As boundary conditions, the temperature2. Brindley, of the K. Newnes heat source Electronics (at the Assembly bottom Handbook of the heat, 1st ed.; Heinemann Newnes: Manchester, UK, 1990; ISBN 0 434 90203 9. sink) varied between 80 °C and 100 °C,3. withFowler, 10 °C K.R.; intervals, Silver, and C.L. inletDeveloping air velocity and Managing took the Embedded Systems and Products: Methods, Techniques, Tools, Processes, and values 0.7 m/s, 2.1 m/s and 3.5 m/s (at 20Teamwork °C), leading, 1st ed.; to Fowler, Reynolds K., Ed.; numbers Newnes: from Boston, 2500 MA, USA, 2014; ISBN 9780124058637. (laminar-turbulent transition) to 12,5004. (veryWilson, turbulent P. The Circuit flow). Designer’s Companion, 4th ed.; Elsevier Ltd.: London, UK, 2017; ISBN 9780081017647. For fins heat sinks, DOE analyses5. were Otake, performed S.; Tateishi, using Y.; Gohara, fin thickness, H.; Kato, fin R.; Ikeda,spacing, Y.; Parque, V.; Faiz, M.K.; Yoshida, M.; Miyashita, T. Heatsink design using Figure 3. Temperatureinlet contoursvelocity, vs. and time heat for eachsource type temperature of heat sink.spiral-ﬁns as factors considering and pressure additive drop manufacturing. and heat Insink Proceedings of the 2019 International Conference on Electronics Packaging temperature after 15 s as responses. Each(ICEP), factor Niigata, was considered Japan, 17–20 with April three 2019; levels Volume (Table 175, pp. 46–51. 2.2. CFD Governing2) and Equations an L9 matrix was constructed. Computational Fluid Dynamics (CFD) consists of predicting fluid flow, heat, and mass transfer andTable related 2. Levels phenomena and factors by solvingfor DOE numericallymatrix for fins a heat set sinks.of governing mathematical equations. CFD analysis complements testing and experimentation by reducing Level Fin Thickness (mm) Fin Spacing (mm) Inlet Velocity (m/s) Heat Source Temperature (°C) total effort and cost required for experimentation and data acquisition. There are a num- 1 1.5 2.0 0.7 80 ber of commercial CFD software packages available for application in thermal design. One 2 2.5 3.5 2.1 90 of them is ANSYS. Based on the finite volume method, ANSYS solvers discretised the 3 3.5 5.0 3.5 100

For pins heat sinks, the arrangement factor (in-line or staggered) was added to com- pose an L18 DOE matrix. Level and factors are shown in Table 3.

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