DOCSLIB.ORG

Free Convective Heat Transfer from an Object at Low Rayleigh Number 23

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Free Convective Heat Transfer from an Object at Low Rayleigh Number 23 Free Convective Heat Transfer From an Object at Low Rayleigh Number 23 FREE CONVECTIVE HEAT TRANSFER FROM AN OBJECT AT LOW RAYLEIGH NUMBER Md. Golam Kader and Khandkar Aftab Hossain* Department of Mechanical Engineering, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh. *Corresponding e-mail: [email protected],ac.bd Abstract: Free convective heat transfer from a heated object in very large enclosure is investigated in the present work. Numerical investigation is conducted to explore the fluid flow and heat transfer behavior in the very large enclosure with heated object at the bottom. Heat is released from the heated object by natural convection. Entrainment is coming from the surrounding. The two dimensional Continuity, Navier-Stokes equation and Energy equation have been solved by the finite difference method. Uniform grids are used in the axial direction and non-uniform grids are specified in the vertical direction. The differential equations are discretized using Central difference method and Forward difference method. The discritized equations with proper boundary conditions are sought by SUR method. It has been done on the basis of stream function and vorticity formulation. The flow field is investigated for fluid flowing with Rayleigh numbers in the range of 1.0 ≤ Ra ≤ 1.0×103 and Pr=0.71. It is observed that the distortion of flow started at Rayleigh number Ra=10. It is observed that the average heat transfer remains constant for higher values of Reyleigh number and heating efficiency varies with Ra upto the value of Ra=35 and beyond this value heating efficiency remains constant. Keywords: Free convection, enclosure, distortion, Rayliegh no., vorticity. INTRODUCTION al. [5], analyzed natural convection heat transfer in a Free convection heat transfer from a heated differentially heated enclosure, within which a body draws additional attention to the researchers, centered, circular, heat-conducting body generates because it does not require any external energy for heat. They concluded that for a constant Rayleigh transferring heat. Only the variation of density of number, the average Nusselt number at the hot and fluid plays important role to transfer heat from the cold walls varied linearly with temperature- body. The present work deals with free convection difference ratio. heat transfer from a heated body in a very large Sidik et al. [6], studied numerically, the fluid enclosure in quiescent atmospheric condition. flow behavior and heat transfer mechanism from a Buoyancy induced flow and heat transfer is an heated square cylinder located at various heights important phenomenon in engineering systems due inside a square enclosure by the numerical method to its wide applications in electronic cooling, heat in the range of 103≤Ra≤106. Their computational exchangers, double pane windows, molding and results proved that the flow pattern, number, size casting, nuclear and chemical reactors, flooding and formation of vorticies and also heat transfer protection for buried pipes, solidification processes, mechanism were critically dependent on Rayleigh growing crystals and solar collectors etc [1]. number and the position of heated square cylinder in Oh et al. [2], used a numerical simulation to enclosure. Hussain et al. [7], considered the problem study natural convection in a vertical square of natural convection in a square enclosure which enclosure containing heat generating conducting had an isothermal walls and was heated by a body, when a temperature difference existed across concentric internal circular isoflux boundary. They the enclosure. The streamlines, isotherms and concluded that vorticies down the bottom and up the average Nusselt number at the hot and cold walls top of the inner cylinder can be noticed as the inner are presented and discussed. Roychowdhury et al. cylinder moved upward and downward. However, a [3], analyzed the natural convective flow and heat very little literatures deal with natural convection transfer features for a heated cylinder kept in a problem when a conductive circular cylinder with square enclosure with different thermal boundary heat generation embedded inside a square enclosure conditions. Arnab et al. [4], performed an extensive and moves at different locations along the enclosure analysis of flow pattern and heat transfer from a diagonal. The objective of this study is to simulate heated rectangular cylinder enclosed inside an two-dimensional free convection heat transfer in a enclosure with three different aspect ratio. The cylinder within a square enclosure in order to effect of aspect ratio and two kinds of boundary investigate the effect of a hot conductive circular conditions (i.e, constant wall heat flux and constant cylinder location and its heat generation on the heat wall temperature) were studied. They concluded that transfer and fluid flow in an enclosure. R. T. Bailey the uniform wall temperature heating was greatly et al. [8], investigated the force convective heat different from the uniform wall flux heating. Jami et transfer relations for atmospheric flow over sparsely Journal of Mechanical Engineering, Vol. ME 43, No. 1, June 2013 Transaction of the Mech. Eng. Div., The Institution of Engineers, Bangladesh Free Convective Heat Transfer From an Object at Low Rayleigh Number 24 vegetated areas and compared to existing relations equation, the effects of compressibility and viscous for flow in rough ducts. Experimental convection dissipation is neglected. coefficients obtained are compared to the analytical relations. Convection coefficient is directly Continuity equation calculated by measuring the power dissipation and surface temperatures. The experimental heat transfer u v (1) results are correlated with micrometeorological 0. models from which a soil roughness height is x y calculated. A simplified heat transfer correlation is Navier-Stokes equations presented for desert surfaces. The Grashof no. is calculated from u u 1 p 2u 2u (2) 3 2 u v Gr gW / and Prandtl no. is calculated 2 2 x y x x y from Pr / . The Rayleigh no. Ra = GrPr 2 2 (3) 3 v v 1 p v v = gW / . The Nusselt number, Nu at the u v 2 2 hot surface is a measure of convective heat transfer x y y x y coefficient at the surface. Higher values of Nu g (T T ) indicate higher heat transfer rate from the hot obj surface. The local Nusselt number from the isothermal top face of the object is computed as, Energy equation Nu(Y ) d / dx and the average Nusselt TopFace T T 2T 2T (4) l2 u v 2 2 number is calculated as, Nu1/W Nu(Y) dY , x y x y l1 The above equations are converted into a non- where W=l2-l1 is the face width of the top face of the dimensional form considering the following object as in Figure 1. Similarly, the average Nusselt dimensionless quantities: number of left and right vertical sides of the object x y uW vW are computed. Now, taking the average of three X ; Y ; U ; V ; sides will give the average heat transfer from the W W T(x, y) T object. An index of the performance of the overall (x, y) heating process of fluid is defined in terms of the T T heating efficiency, [9], which is defined as the obj ratio of the net heat energy flux through the inlet Now, putting this value in equation (1), (2), (3) and and outlet to the heat energy influx, i.e., (4), we get the normalized forms of these equations are as follows, v.ndA / v.ndA where v is the velocity Ainout Ain u v (5) vector and n is the outward-drawn unit normal 0 vector. Defining the average inlet and outlet x y 2 2 (6) temperatures as, in v.ndA/ v.ndA and u u 1 p u u u v Pr 2 2 Ain Ain x y 2 x x y out v.ndA/ v.ndA and noting that for 2 2 Aout Aout v v 1 p v v (7) u v Pr 2 2 steady state v.ndA v.ndA the heating x y 2 y x y Ain Aout Ra.Pr and efficiency is given by [9], 1 out / in . 2 2 (8) u v x y x2 y2 NUMERICAL MODELING The conservation equations for mass, momentum, and energy for the two-dimensional, BOUNDARY CONDITIONS steady, and laminar flow. All the physical properties Boundary Conditions at the Bottom Wall of the fluid, μ, k, and Cp, are considered constant Since the Velocity Component, u and v both are except density, in the buoyancy term, which follows zero at the wall. We know that the velocity the Boussinesq approximation. In the energy components are: Journal of Mechanical Engineering, Vol. ME 43, No. 1, June 2013 Transaction of the Mech. Eng. Div., The Institution of Engineers, Bangladesh Free Convective Heat Transfer From an Object at Low Rayleigh Number 25 u and v Applying no-slip The length of the computational domain is y x L=12 and height H=5. The top face width of the conditions, u=0 and v=0, stream function object W=1.0 and the height of the object Hobj=0.34. =constant. The vorticity at the bottom wall is Uniform grid is specified in the axial direction and prescribed by the constant non-uniform grid is specified in the vertical 0.05Re direction. Grid independency test has been done, but and the bottom wall is assumed to be no improved result is obtained after more fine grids 2 than 50 × 50, which is shown in the Fig. 2. The heated one-third of the heated object, that is, =0.3. -6 maximum error is obtained as 10 based on stream Boundary Conditions at Left and Right function. Boundaries Gradients of variables are assumed to be zero at the left and right boundaries are as, u v 0; 0; 0; 0; 0; x x x x x Boundary Conditions at object At the object, for no-slip conditions, u=0 and v=0, Stream function = constant.
Load more

Recommended publications
  • Convection Heat Transfer
    Convection Heat Transfer Heat transfer from a solid to the surrounding fluid Consider fluid motion Recall flow of water in a pipe Thermal Boundary Layer • A temperature profile similar to velocity profile. Temperature of pipe surface is kept constant. At the end of the thermal entry region, the boundary layer extends to the center of the pipe. Therefore, two boundary layers: hydrodynamic boundary layer and a thermal boundary layer. Analytical treatment is beyond the scope of this course. Instead we will use an empirical approach. Drawback of empirical approach: need to collect large amount of data. Reynolds Number: Nusselt Number: it is the dimensionless form of convective heat transfer coefficient. Consider a layer of fluid as shown If the fluid is stationary, then And Dividing Replacing l with a more general term for dimension, called the characteristic dimension, dc, we get hd N ≡ c Nu k Nusselt number is the enhancement in the rate of heat transfer caused by convection over the conduction mode. If NNu =1, then there is no improvement of heat transfer by convection over conduction. On the other hand, if NNu =10, then rate of convective heat transfer is 10 times the rate of heat transfer if the fluid was stagnant. Prandtl Number: It describes the thickness of the hydrodynamic boundary layer compared with the thermal boundary layer. It is the ratio between the molecular diffusivity of momentum to the molecular diffusivity of heat. kinematic viscosity υ N == Pr thermal diffusivity α μcp N = Pr k If NPr =1 then the thickness of the hydrodynamic and thermal boundary layers will be the same.
    [Show full text]
  • The Influence of Magnetic Fields in Planetary Dynamo Models
    Earth and Planetary Science Letters 333–334 (2012) 9–20 Contents lists available at SciVerse ScienceDirect Earth and Planetary Science Letters journal homepage: www.elsevier.com/locate/epsl The influence of magnetic fields in planetary dynamo models Krista M. Soderlund a,n, Eric M. King b, Jonathan M. Aurnou a a Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, USA b Department of Earth and Planetary Science, University of California, Berkeley, CA 94720, USA article info abstract Article history: The magnetic fields of planets and stars are thought to play an important role in the fluid motions Received 7 November 2011 responsible for their field generation, as magnetic energy is ultimately derived from kinetic energy. We Received in revised form investigate the influence of magnetic fields on convective dynamo models by contrasting them with 27 March 2012 non-magnetic, but otherwise identical, simulations. This survey considers models with Prandtl number Accepted 29 March 2012 Pr¼1; magnetic Prandtl numbers up to Pm¼5; Ekman numbers in the range 10À3 ZEZ10À5; and Editor: T. Spohn Rayleigh numbers from near onset to more than 1000 times critical. Two major points are addressed in this letter. First, we find that the characteristics of convection, Keywords: including convective flow structures and speeds as well as heat transfer efficiency, are not strongly core convection affected by the presence of magnetic fields in most of our models. While Lorentz forces must alter the geodynamo flow to limit the amplitude of magnetic field growth, we find that dynamo action does not necessitate a planetary dynamos dynamo models significant change to the overall flow field.
    [Show full text]
  • Laws of Similarity in Fluid Mechanics 21
    Laws of similarity in fluid mechanics B. Weigand1 & V. Simon2 1Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart, Germany. 2Isringhausen GmbH & Co KG, Lemgo, Germany. Abstract All processes, in nature as well as in technical systems, can be described by fundamental equations—the conservation equations. These equations can be derived using conservation princi- ples and have to be solved for the situation under consideration. This can be done without explicitly investigating the dimensions of the quantities involved. However, an important consideration in all equations used in fluid mechanics and thermodynamics is dimensional homogeneity. One can use the idea of dimensional consistency in order to group variables together into dimensionless parameters which are less numerous than the original variables. This method is known as dimen- sional analysis. This paper starts with a discussion on dimensions and about the pi theorem of Buckingham. This theorem relates the number of quantities with dimensions to the number of dimensionless groups needed to describe a situation. After establishing this basic relationship between quantities with dimensions and dimensionless groups, the conservation equations for processes in fluid mechanics (Cauchy and Navier–Stokes equations, continuity equation, energy equation) are explained. By non-dimensionalizing these equations, certain dimensionless groups appear (e.g. Reynolds number, Froude number, Grashof number, Weber number, Prandtl number). The physical significance and importance of these groups are explained and the simplifications of the underlying equations for large or small dimensionless parameters are described. Finally, some examples for selected processes in nature and engineering are given to illustrate the method. 1 Introduction If we compare a small leaf with a large one, or a child with its parents, we have the feeling that a ‘similarity’ of some sort exists.
    [Show full text]
  • Chapter 5 Dimensional Analysis and Similarity
    Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences.
    [Show full text]
  • Turning up the Heat in Turbulent Thermal Convection COMMENTARY Charles R
    COMMENTARY Turning up the heat in turbulent thermal convection COMMENTARY Charles R. Doeringa,b,c,1 Convection is buoyancy-driven flow resulting from the fluid remains at rest and heat flows from the warm unstable density stratification in the presence of a to the cold boundary according Fourier’s law, is stable. gravitational field. Beyond convection’s central role in Beyond a critical threshold, however, steady flows in myriad engineering heat transfer applications, it un- the form of coherent convection rolls set in to enhance derlies many of nature’s dynamical designs on vertical heat flux. Convective turbulence, character- larger-than-human scales. For example, solar heating ized by thin thermal boundary layers and chaotic of Earth’s surface generates buoyancy forces that plume dynamics mixing in the core, appears and per- cause the winds to blow, which in turn drive the sists for larger ΔT (Fig. 1). oceans’ flow. Convection in Earth’s mantle on geolog- More precisely, Rayleigh employed the so-called ical timescales makes the continents drift, and Boussinesq approximation in the Navier–Stokes equa- thermal and compositional density differences induce tions which fixes the fluid density ρ in all but the buoyancy forces that drive a dynamo in Earth’s liquid temperature-dependent buoyancy force term and metal core—the dynamo that generates the magnetic presumes that the fluid’s material properties—its vis- field protecting us from solar wind that would other- cosity ν, specific heat c, and thermal diffusion and wise extinguish life as we know it on the surface. The expansion coefficients κ and α—are constant.
    [Show full text]
  • On the Inverse Cascade and Flow Speed Scaling Behavior in Rapidly Rotating Rayleigh-Bénard Convection
    This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics 1 On the inverse cascade and flow speed scaling behavior in rapidly rotating Rayleigh-B´enardconvection S. Maffei1;3y, M. J. Krouss1, K. Julien2 and M. A. Calkins1 1Department of Physics, University of Colorado, Boulder, USA 2Department of Applied Mathematics, University of Colorado, Boulder, USA 3School of Earth and Environment, University of Leeds, Leeds, UK (Received xx; revised xx; accepted xx) Rotating Rayleigh-B´enardconvection is investigated numerically with the use of an asymptotic model that captures the rapidly rotating, small Ekman number limit, Ek ! 0. The Prandtl number (P r) and the asymptotically scaled Rayleigh number (Raf = RaEk4=3, where Ra is the typical Rayleigh number) are varied systematically. For sufficiently vigorous convection, an inverse kinetic energy cascade leads to the formation of a depth-invariant large-scale vortex (LSV). With respect to the kinetic energy, we find a transition from convection dominated states to LSV dominated states at an asymptotically reduced (small-scale) Reynolds number of Ref ≈ 6 for all investigated values of P r. The ratio of the depth-averaged kinetic energy to the kinetic energy of the convection reaches a maximum at Ref ≈ 24, then decreases as Raf is increased. This decrease in the relative kinetic energy of the LSV is associated with a decrease in the convective correlations with increasing Rayleigh number. The scaling behavior of the convective flow speeds is studied; although a linear scaling of the form Ref ∼ Ra=Pf r is observed over a limited range in Rayleigh number and Prandtl number, a clear departure from this scaling is observed at the highest accessible values of Raf .
    [Show full text]
  • Rayleigh-Bernard Convection Without Rotation and Magnetic Field
    Nonlinear Convection of Electrically Conducting Fluid in a Rotating Magnetic System H.P. Rani Department of Mathematics, National Institute of Technology, Warangal. India. Y. Rameshwar Department of Mathematics, Osmania University, Hyderabad. India. J. Brestensky and Enrico Filippi Faculty of Mathematics, Physics, Informatics, Comenius University, Slovakia. Session: GD3.1 Core Dynamics Earth's core structure, dynamics and evolution: observations, models, experiments. Online EGU General Assembly May 2-8 2020 1 Abstract • Nonlinear analysis in a rotating Rayleigh-Bernard system of electrical conducting fluid is studied numerically in the presence of externally applied horizontal magnetic field with rigid-rigid boundary conditions. • This research model is also studied for stress free boundary conditions in the absence of Lorentz and Coriolis forces. • This DNS approach is carried near the onset of convection to study the flow behaviour in the limiting case of Prandtl number. • The fluid flow is visualized in terms of streamlines, limiting streamlines and isotherms. The dependence of Nusselt number on the Rayleigh number, Ekman number, Elasser number is examined. 2 Outline • Introduction • Physical model • Governing equations • Methodology • Validation – RBC – 2D – RBC – 3D • Results – RBC – RBC with magnetic field (MC) – Plane layer dynamo (RMC) 3 Introduction • Nonlinear interaction between convection and magnetic fields (Magnetoconvection) may explain certain prominent features on the solar surface. • Yet we are far from a real understanding of the dynamical coupling between convection and magnetic fields in stars and magnetically confined high-temperature plasmas etc. Therefore it is of great importance to understand how energy transport and convection are affected by an imposed magnetic field: i.e., how the Lorentz force affects convection patterns in sunspots and magnetically confined, high-temperature plasmas.
    [Show full text]
  • Arxiv:1903.08882V2 [Physics.Flu-Dyn] 6 Jun 2019
    Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number Ao Xua,∗, Le Shib, Heng-Dong Xia aSchool of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China bState Key Laboratory of Electrical Insulation and Power Equipment, Center of Nanomaterials for Renewable Energy, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China Abstract We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function ap- proach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-B´enardconvection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-B´enardconvection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106, 3×106, and 107, and Prandtl numbers of arXiv:1903.08882v2 [physics.flu-dyn] 6 Jun 2019 ∗Corresponding author Email address: [email protected] (Ao Xu) DOI: 10.1016/j.ijheatmasstransfer.2019.06.002 c 2019.
    [Show full text]
  • Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1
    Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1 We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically Nicolas G. and thermally fully developed conditions. Our investigation covers both the slip-flow Hadjiconstantinou regime 0рKnр0.1, and most of the transition regime 0.1ϽKnр10, where Kn, the Knud- sen number, is defined as the ratio between the molecular mean free path and the channel Olga Simek height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0рKnр0.2, and a stochastic molecular simulation technique Mechanical Engineering Department, known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in Massachusetts Institute of Technology, the range 0.02ϽKnϽ2. Inclusion of the effects of axial heat conduction in the continuum Cambridge, MA 02139 model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Knр0.1, but also remains a good approximation beyond its ex- pected range of applicability. We also show that the Nusselt number decreases monotoni- cally with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Knϭ0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.
    [Show full text]
  • Time-Periodic Cooling of Rayleigh–Bénard Convection
    fluids Article Time-Periodic Cooling of Rayleigh–Bénard Convection Lyes Nasseri 1 , Nabil Himrane 2, Djamel Eddine Ameziani 1 , Abderrahmane Bourada 3 and Rachid Bennacer 4,* 1 LTPMP (Laboratoire de Transports Polyphasiques et Milieux Poreux), Faculty of Mechanical and Proceeding Engineering, USTHB (Université des Sciences et de la Technologie Houari Boumedienne), Algiers 16111, Algeria; [email protected] (L.N.); [email protected] (D.E.A.) 2 Labo of Energy and Mechanical Engineering (LEMI), Faculty of Technology, UMBB (Université M’hamed Bougara-Boumerdes, Boumerdes 35000, Algeria; [email protected] 3 Laboratory of Transfer Phenomena, RSNE (Rhéologie et Simulation Numérique des Ecoulements) Team, FGMGP (Faculté de génie Mécaniques et de Génie des Procédés Engineering), USTHB (Université des Sciences et de la Technologie Houari Boumedienne), Bab Ezzouar, Algiers 16111, Algeria; [email protected] 4 CNRS (Centre National de la Recherche Scientifique), LMT (Laboratoire de Mécanique et Technologie—Labo. Méca. Tech.), Université Paris-Saclay, ENS (Ecole National Supérieure) Paris-Saclay, 91190 Gif-sur-Yvette, France * Correspondence: [email protected] Abstract: The problem of Rayleigh–Bénard’s natural convection subjected to a temporally periodic cooling condition is solved numerically by the Lattice Boltzmann method with multiple relaxation time (LBM-MRT). The study finds its interest in the field of thermal comfort where current knowledge has gaps in the fundamental phenomena requiring their exploration. The Boussinesq approximation is considered in the resolution of the physical problem studied for a Rayleigh number taken in the range 103 ≤ Ra ≤ 106 with a Prandtl number equal to 0.71 (air as working fluid).
    [Show full text]
  • Fluid Dynamics Analysis and Numerical Study of a Fluid Running Down a Flat Surface
    29TH DAAAM INTERNATIONAL SYMPOSIUM ON INTELLIGENT MANUFACTURING AND AUTOMATION DOI: 10.2507/29th.daaam.proceedings.116 FLUID DYNAMICS ANALYSIS AND NUMERICAL STUDY OF A FLUID RUNNING DOWN A FLAT SURFACE Juan Carlos Beltrán-Prieto & Karel Kolomazník This Publication has to be referred as: Beltran-Prieto, J[uan] C[arlos] & Kolomaznik, K[arel] (2018). Fluid Dynamics Analysis and Numerical Study of a Fluid Running Down a Flat Surface, Proceedings of the 29th DAAAM International Symposium, pp.0801-0810, B. Katalinic (Ed.), Published by DAAAM International, ISBN 978-3-902734- 20-4, ISSN 1726-9679, Vienna, Austria DOI: 10.2507/29th.daaam.proceedings.116 Abstract The case of fluid flowing down a plate is applied in several industrial, chemical and engineering systems and equipments. The mathematical modeling and simulation of this type of system is important from the process engineering point of view because an adequate understanding is required to control important parameters like falling film thickness, mass rate flow, velocity distribution and even suitable fluid selection. In this paper we address the numerical simulation and mathematical modeling of this process. We derived equations that allow us to understand the correlation between different physical chemical properties of the fluid and the system namely fluid mass flow, dynamic viscosity, thermal conductivity and specific heat and studied their influence on thermal diffusivity, kinematic viscosity, Prandtl number, flow velocity, fluid thickness, Reynolds number, Nusselt number, and heat transfer coefficient using numerical simulation. The results of this research can be applied in computational fluid dynamics to easily identify the expected behavior of a fluid that is flowing down a flat plate to determine the velocity distribution and values range of specific dimensionless parameters and to help in the decision-making process of pumping systems design, fluid selection, drainage of liquids, transport of fluids, condensation and in gas absorption experiments.
    [Show full text]
  • Forced Convection Heat Transfer Convection Is the Mechanism of Heat Transfer Through a Fluid in the Presence of Bulk Fluid Motion
    Forced Convection Heat Transfer Convection is the mechanism of heat transfer through a fluid in the presence of bulk fluid motion. Convection is classified as natural (or free) and forced convection depending on how the fluid motion is initiated. In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in forced convection, the fluid is forced to flow over a surface or in a tube by external means such as a pump or fan. Mechanism of Forced Convection Convection heat transfer is complicated since it involves fluid motion as well as heat conduction. The fluid motion enhances heat transfer (the higher the velocity the higher the heat transfer rate). The rate of convection heat transfer is expressed by Newton’s law of cooling: q hT T W / m 2 conv s Qconv hATs T W The convective heat transfer coefficient h strongly depends on the fluid properties and roughness of the solid surface, and the type of the fluid flow (laminar or turbulent). V∞ V∞ T∞ Zero velocity Qconv at the surface. Qcond Solid hot surface, Ts Fig. 1: Forced convection. It is assumed that the velocity of the fluid is zero at the wall, this assumption is called no‐ slip condition. As a result, the heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid is motionless. Thus, M. Bahrami ENSC 388 (F09) Forced Convection Heat Transfer 1 T T k fluid y qconv qcond k fluid y0 2 y h W / m .K y0 T T s qconv hTs T The convection heat transfer coefficient, in general, varies along the flow direction.
    [Show full text]