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Multi-Artery, Heat-Pipe Spreader

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Multi-Artery, Heat-Pipe Spreader International Journal of Heat and Mass Transfer 52 (2009) 629–635 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt Multi-artery, heat pipe spreader D.H. Min, G.S. Hwang, M. Kaviany * Department of Mechanical Engineering, University of Michigan, 2250 G.G. Brown, Ann Arbor, MI 48109-2125, USA article info abstract Article history: Multiple, columnar liquid vapor chamber allows for effective heat removal from finite, concentrated heat Received 20 March 2008 source by heat spreading via lateral vapor flow, while minimizing conduction resistance through thinner Received in revised form 11 July 2008 evaporator wick. The individual liquid arteries are designed by wick coated solid pillar. We optimize the Available online 31 August 2008 artery geometry, numbers, and distribution, for both liquid and air-cooled, finned condensers, and show that the overall thermal resistance is substantially lower than the uniform wick vapor chamber. Keywords: Ó 2008 Elsevier Ltd. All rights reserved. Multiple liquid artery Vapor chamber Heat pipe Optimal design Dry out Wick superheat 1. Introduction vapor flow paths, and this is similar to the multiple-artery heat pipe spreader proposed here. With smaller and faster microprocessors, heat removal from We design a multiple artery VC to supply liquid for evaporation such concentrated sources pose challenges [1]. Using single-phase and reduce the evaporator wick thickness (where its conduction gas or liquid cooling, this concentrated heat should be spread over resistance is dominating). The geometric parameters such as artery a sufficiently large area. Vapor chambers spread heat from concen- diameter, numbers, and spacings, are optimized based on three- trated sources to large condenser area, where it can be readily re- dimensional resistance network analyses for heat and fluid flows. moved with high single-phase coolant streams. Vapor chamber We use external, air or water cooled, finned condenser and com- (VC) is particularly effective in absence of any solid heat spreader pare the overall thermal resistance with the uniform artery VC. added to the heat source (called internal heat spreader), where VC reduces the external coolant thermal resistance (due to the 2. Multi-artery heat pipe spreader large area). The internal resistance of VC should be small enough such the overall thermal resistance RR is small compared with no The multi-artery heat pipe spreader (MAHPS) is a columnar va- VC present. por chamber heat pipe. An individual artery is designed by a solid The analysis of heat, vapor, and liquid flows in the asymmetric pillar covered with a uniform wick as the liquid artery. This capil- flat heat pipes are presented in [2] and a simplified conduction- lary artery draws the liquid from the condenser to the evaporator based model for VC is given in [3], including the effect of gravity. wick. Water is used as an operating fluid to achieve high capillary The uniform wick VC [4] is easy to fabricate since it has a single, pressure (surface tension) and heat of vaporization. Fig. 1(a) and uniform liquid wick artery; however, it has a large conduction wick (b) shows the geometric parameters of MAHPS, and heat flow path resistance. In [4] a centered, single wick column is placed above from the heating source to the external, coolant. MAHPS is placed the heater area to circulate the liquid and ensure the structural sta- between the heater area and this external heat sink. The heat bility VC. It decreases the distance of the liquid travels from con- source is a constant heat flux condition and the coolant is far-field denser to evaporator, thus the evaporator wick thickness is temperature and surface-convection resistance surface. Since the reduced. However, it is also important to secure enough evapora- two temperatures for the Th and Tc are predefined as constant, iso- tion area to increase the heat flux through the wick. In [5] the mea- thermal heat flux and constant coolant temperature boundary con- sured and predicted heat flux in various modulated-wick heat ditions, respectively, in this theoretical analysis, the saturation pipes are presented and compared. One of models depicted as an temperature depends on how much heat spreading occurs as the artery–evaporator system with completely separated liquid and heater area. Phase change occurs at the liquid–vapor interface in the evaporator and condenser wicks [6]. During the phase change, * Corresponding author. Tel.: +1 734 936 0402; fax: +1 734 615 6647. the generated vapor moves toward the condenser, where it is uni- E-mail address: [email protected] (M. Kaviany). formly condensed over a large area. Capillary pressure is used for 0017-9310/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2008.07.021 630 D.H. Min et al. / International Journal of Heat and Mass Transfer 52 (2009) 629–635 Nomenclature A (cross-section) area (m2) Subscripts cp specific heat (J/kg-K) atm atmosphere D diameter (m) b bare area d (fin or column) diameter (m) c capillary or column or condenser or coolant Dhlg enthalpy of vaporization (J/kg) c,c center to center K permeability (m2) e evaporator k thermal conductivity (W/m-K) eff effective L distance or height (m) ffin M_ mass flow rate (kg/s) g vapor N number h heater Nud Nusselt number for coolant stream, crossflow over cyl- hex hexagonal unit cell inder i, j node position p pressure (Pa) k conduction Pr Prandtl number ku surface-convection Q heat transfer rate (W) l liquid R resistance (K/W) lg phase change or saturation hRedi Reynolds number for coolant, crossflow over cylinder MA multi-artery heat pipe spreader r radius (m) max maximum T temperature (K) min minimum u velocity (m/s) p particle ps pillar spacing Greek symbols s surface or solid porosity sh superheat g efficiency R overall (thermal resistance) l viscosity (Pa-s) UA uniform-artery heat pipe spreader q density (kg/m3) vc vapor chamber r surface tension (N/m) w wick the liquid circulation in MAHPS [7,8]. The critical geometric param- lary pressure by reducing the effective meniscus radius there. Since eters of the baseline MAHPS are given in Table 1. For the baseline the condenser has the highest liquid pressure and we assume that model, the heater diameter is 1 cm, and the condenser diameter is in the outmost location on the condenser wick the capillary pres- 5 cm. The wick covers the entire internal surface, including the sure is zero (i.e., pl = plg). The radii difference between the evapora- evaporator wall and column walls, but different wick diameter, tor and condenser gives the capillary pressure difference Young– large sintered particles are used for the condenser and column, Laplace equation [8] and small particles for the evaporator. In the baseline, the con- denser-column and evaporator particle diameters are 200 and 2r 2r Dpc ¼ Dpl ¼ À ; ð1Þ 50 lm, respectively. A hexagonal unit cell is used to calculate the rc;e rc;c axial and lateral heat flows, as well as the liquid pressure distribu- tion. The thermophysical properties are evaluated at the saturation we have assumed uniform vapor pressure pg ¼ plg, where plg is the temperature of vapor which varies from 71.8 to 76.2 °C in the VC. saturation pressure. r is the surface tension, rc;e and rc;c are the The smaller the heater area, the lower the saturation temperature meniscus radii at evaporator and condenser wick surfaces. We as- is (because of heat spreading). The effect of liquid convection in the sume rc;c is infinity at the outmost corner of the condenser, and thermal network is neglected (assuming small Péclet number [9]). the maximum capillary pressure pc;max is [8] In [6] the liquid and heat flow network models are designed for the steady-state analysis of the modulated wick heat pipe, and similar 2r approach is used here. pc;max ¼ pg À pl;min ¼ cos hc; rc;min ¼ð0:41Þ0:5dp;e; ð2Þ rc;min 3. Analysis using resistance thermal/hydraulics networks where the hc is the contact angle and dp;e is the wick particle diam- eter for the evaporator wick. Here, rc;min is the minimum meniscus 3.1. Liquid flow resistance network radius in Eq. (1) for sintered-particle wicks [10]. The material prop- erties and relations are given in Table 2. Assuming that the liquid (l) _ _ For the liquid flow network, the mass flow rates, Ml;e and Ml;c and vapor (g) flow are incompressible (ii), the continuity equations are calculated for each hexagonal unit cell (Fig. 1(a)). Assumptions are for the network model are (i) liquid velocity is locally averaged, (ii) u 0 and u 0; 3 pressure drop by gravity is neglected, (iii) flow is Darcian and r Á l ¼ r Á g ¼ ð Þ incompressible, (iv) liquid–vapor interface is in thermal equilib- where ul and ug are the liquid and vapor velocity vectors. The liquid rium, (v) wick is isotropic, and (vi) condensation and evaporation mass flow rate is determined by heat flow from the constant, iso- occur on the wick surfaces [6]. Fig. 2(a) and (b) shows the ther- thermal area, using the heat of evaporation Dhlg mal–hydraulic resistance network models. The liquid moves be- Z Q tween the condenser wick and the evaporator wick. Evaporation M_ ¼ ¼ m_ dA; ð4Þ l Dh lg on the evaporator wick surface is sustained by adjusting the capil- lg Alg D.H. Min et al. / International Journal of Heat and Mass Transfer 52 (2009) 629–635 631 B Air or Water flow, uf , Tc D 2 Condenser A = c Tc , Cooler temperaure c 4 df Fin d + L Lc,c = c + 2 w,p ps Rku, f Rku, b Ts,c, Condenser temperaure Ts,c Ac L , sp dc Rk, 9 T3 Heater Rk, 6 Rk, 5 Rk, 7 T5 2 T2 Dh Tlg A A = R A h 4 k, 8 w,p R Ahex k, 3 Effective 2 Evaporation df Lhex, lat Fin A = Area, A f 4 eff T Lhex Rk, 2 lg T1 Ts, i Ts, j Rk, 1 (a) Top view of MAHPS Rk, 4 Th , Heater temperature Axis of Symmetry Air or Water flow, u ,T f c (a) Heat Flow Network A Dc /2 B Fin Uniform Air or Water flow, u , T d Lf Ac f c Temperature f Condensation Fin Ts,c Ls,c w,c L ,sp Column Lwall Condenser wall p Lc 1, j p 1, i dc w,e Vapor • Rl,1 • Rl, col pg = plg = pc M c, i M c, j Tlg(pv) L s,e Column R l,1-2 Th Q w,p Evaporation Adiabatic Surface • • M e, i M e, j Dh /2 Heater p Rl,2 p 2, i 2, j (b) Side view of MAHPS Evaporator wall Fig.
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