The heat transfer and fluid flow of a partially heated microchannel heat sink

Numerical modeling of the conjugate heat transfer in microchannel heat sink is presented. As the most of the cooling applications deals with the partial heated sections, the influence of the heating position on the thermal and hydrodynamic behavior is analyzed. The laminar fluid flow regime and the water as a working fluid are considered. It is observed that partial heating together with variable viscosity has a strong influence on thermal and hydrodynamic characteristics of the micro-heat sink.     

Three-dimensional numerical computation for magnetic convection of air inside a cylinder heated and cooled isothermally from a side wall

Three-dimensional convection of air in a vertical cylinder isothermally heated and cooled from a side wall was numerically computed both in magnetic and gravity fields. A single electric coil was placed around a cylinder to generate a magnetic field. Convection was calculated for various coil levels and magnetic strengths. The gravity field, magnetic strength and Rayleigh number are shown to have substantial effect. Convection modes and heat transfer rates are also presented.     

Numerical study of mixed convective cooling in a square cavity ventilated and partially heated from the below utilizing nanofluid

A numerical investigation of mixed convection flows through a copper–water nanofluid in a square cavity with inlet and outlet ports has been executed. The natural convection effect is attained by heating from the constant flux heat source which is symmetrical located at the bottom wall and cooling from the injected flow. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Reynolds number in the range 50 ≤ Re ≤ 1000, with Richardson numbers 0 ≤ Ri ≤ 10 and for solid volume fraction 0 ≤ ? ≤ 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. Results are presented in the form of streamlines, isotherms, average Nusselt number and average bulk temperature. In addition, the effects of solid volume fraction of nanofluids on the hydrodynamic and thermal characteristics have been investigated and discussed. The results indicate that increase in solid concentration leads to increase in the average Nusselt number at the heat source surface and decrease in the average bulk temperature.     

Convective heat transfer of horizontal spherical particle layer heated from below and cooled from above Part II: Effect of thickness of particle layer

Convection heat transfer and pressure drop measurements were performed with a rectangular duct, having a cooled upper and a heated lower surface, which was packed with spherical particles. Air was used as the test fluid and four kinds of spherical particles having different diameters and thermal conductivities were used as the packing materials. The ratio of the diameter of the spherical particle to the distance between the cooled and heated surfaces, d/H, was varied from 0.173 to 1. The thermal conductivity of the particle layer was also measured under the still air condition. The thermal conductivity of the particle layer was not affected by the value of d/H. In the case of the one-stage arrangement of spherical particles (d/H = 1), the flow resistance took on a remarkably small value compared with the flow resistance of a homogeneous spherical particle layer. Moreover, the flow resistance of the particle layer formed with some layers of particles could be predicted by combining the flow characteristics of the one-stage particle layer and that of the homogeneous spherical particle layer. The heat transfer coefficient of the particle layer was larger than that of turbulent air flow on a flat plate. At a constant superficial air velocity, there existed a value of d/H which gave a maximum value of the average heat transfer coefficient. Nondimensional heat transfer correlation equations were derived in terms of parameters expressing the average characteristics of the spherical particle layers. © 1998 Scripta Technica, Heat Trans Jpn Res, 26(3): 176–192, 1997     

Numerical studies on heat and fluid flow of nanofluid in a partially heated vertical annulus

A numerical investigation on natural convective heat transfer of nanofluid (Al₂O₃+water) inside a partially heated vertical annulus of high aspect ratio (352) has been carried out. The computational fluid dynamics solver Ansys Fluent is used for simulation and results are presented for various volume fraction of nanoparticles (0‐0.04) at different heat flux values (3‐12 kW/m²). Two well‐known correlations for evaluating thermal conductivity and viscosity have been used. Thus different combinations of the available correlations have been set to form four models (I, II, III, and IV). Therefore, a detailed analysis has been executed to identify effects of thermophysical properties on heat transfer and fluid flow of nanofluids using different models. The results show enhancement in heat transfer coefficient with volume fraction of nanoparticles. Highest enhancement achieved is found to be 14.17% based on model III, while the minimum is around 7.27% based on model II. Dispersion of nanoparticles in base fluid declines the Nusselt number and Reynolds number with different rates depending on various models. A generalized correlation is proposed for Nusselt number of nanofluids in the annulus in terms of volume fraction of nanoparticles, Rayleigh number, Reynolds number, and Prandtl number.     

Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method

The main purpose of this paper is to study, in a three-dimensional, differentially heated cavity, the phenomenon of radiation and natural convection in both transparent and participating media. The discrete ordinates method (DOM) is used to solve the radiative transfer equation. The Navier-Stokes equations (NSE), describing natural convection, are solved with a segregated SIMPLE-like algorithm. For non-participating media, the coupling between the radiative transfer and NSE is done via the radiative heat exchange between surfaces. For participating media, a source term is added in the energy equation. The local and mean heat flux as a function of the Rayleigh number is studied, for both transparent and participating media with different optical thicknesses. The effect of the Planck number on the heat flux is also analyzed for different values of the Rayleigh number. Also, a comparison between a purely two-dimensional case and the results obtained in the mid-plane of a long rectangular enclosure is presented.     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Three-dimensional flow of a viscous fluid with heat and mass transfer

Three-dimensional unsteady free convection and mass transfer flow of an incompressible, viscous liquid through a porous medium past an infinite vertical flat plate subjected to a time-dependent suction velocity normal to the plate is studied. The equations encountered into the problem are solved using perturbation technique to obtain the velocity, temperature and concentration fields considering as reference parameter. Expressions for the skin-friction, rate of heat and mass transfers are also obtained. Two cases of most common interest viz. cooling case (G_r > 0) and heating case (G_r < 0) are discussed.     

Experimental and numerical studies of natural convection from horizontal concrete cylinder heated with a cylindrical heat source

Natural convection heat transfer from horizontal concrete cylinder heated with cylindrical heat source was investigated experimentally and numerically. Bare cylinder having a diameter of 9.45 mm was buried in a cylindrical concrete cylinder and thermocouples located outside the copper tube and inside and outside of the concrete cylinder in axial, radial and angular directions. Experiments are conducted at 20 °C and 30 °C ambient temperatures in a conditioned room. Copper cylinder surface temperatures varied between 30–50 °C and 40–50 °C for 20 °C and 30 °C ambient temperatures respectively. In a numerical study, the measured temperatures in the experimental study were used for boundary conditions. Experimental and numerical results were compared and heat transfer enhancement was seen for concrete cylinder. Also the effect of the decrease in the temperature of the copper tube surface was investigated on an ideal Carnot refrigerator. It is found that the enhancement in the coefficient of performance of a Carnot refrigerator is about 35%.     

Experimental study on heat and fluid flow in LNG tank heated from the bottom and the sidewalls

Heat and fluid flow in a layer heated from the bottom and the sidewalls simulating an underground LNG tank is experimentally studied under high Rayleigh number (7.5×10¹⁰<Ra<1.5×10¹³) conditions by electrochemical mass transfer technique. The experiment yielded the following results. When sidewalls are heated, the heat transfer along the bottom surface is reduced. Heat transfer along sidewalls is independent of bottom heating, and is modeled by an equation for laminar natural convection flow even for Ra>10⁹. Convective flow pattern in the tank is visualized by the Schlieren technique. The results, combined with local mass transfer measurement, show that Sh of the bottom surface is reduced in the area where impinging downward flow exists. It is caused by the suppression of thermal plume formation by the downward flow. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 417–430, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20031     

The role of stably stratified fluid and anisotropy porous medium in modeling fluid flow through an asymmetrically heated/cooled vertical annulus

In this article, the natural convection of stratified fluid driven by the asymmetric heating and cooling of the surfaces of the concentric cylinders filled with an anisotropic porous matrix is investigated. The stratified fluid is confined between the outer surface of the inner cylinder and the inner surface of the outer cylinder while the onset transient natural convection is induced by the asymmetric heat heating/cooling of the inner surface of the outer cylinder while the outer surface of the inner cylinder is maintained at a constant temperature $T=1$. The present problem is governed by a pair of coupled second-order partial differential equations. To obtain the expressions for the temperature and velocity fields, the coupled mathematical equations describing the problem are systematically uncoupled such that their original orders remain unaltered. The research established that if the temperature of the outer surface of the inner cylinder equals the temperature of the inner surface of the outer cylinder, a symmetric flow occurs where two maxima velocities are observed close to the surfaces $Z=1$ and $\lambda$ of the annulus, respectively. Furthermore, for some constraints on certain values of some physical quantities in the flow solutions, the present work excellently compares with the research conducted by Jha and Oni.     

The onset of ferroconvection in a horizontal ferrofluid saturated porous layer heated from below and cooled from above with constant heat flux subject to MFD viscosity

The effect of magnetic field dependent (MFD) viscosity on the onset of ferroconvection in a ferrofluid saturated horizontal porous layer is investigated theoretically. The bounding surfaces of the porous medium are considered to be either rigid-ferromagnetic or stress free with constant heat flux conditions. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also analytically by regular perturbation technique. It is found that increase in porous parameter, MFD viscosity parameter and decrease in the magnetic number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.     

Investigation of fluid flow and heat transfer in a vertical channel heated from one side by PV elements, part I - Numerical Study

The impetus of this paper is to analyse numerically the fluid flow and heat transfer characteristics of buoyancy-driven convection between two vertical parallel walls, heated from one side. Both convection and radiation heat exchanges are considered as the heat transfer mechanisms by which the thermal energy is transferred into the air. A steady-state two-dimensional model is used for the analysis. Numerical results are derived for a channel of 6.5 m in height and different widths of the channel. Various heat fluxes are considered in order to show the effect of the input heat on the heat transfer across the air layer. Detailed studies of the flow and thermal fields in the air are presented in order to explore the thermal behavior of air in the channel. Velocity and temperature profiles of the outlet air and the surface temperature of the heated and insulated wall are presented. In Part II of this paper the findings from an experimental study are reported.     

Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification

This work studies the coupled heat and mass transfer by natural convection near a vertical wavy surface in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the vertical wavy plate is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the important heat and mass transfer characteristics are studied. Results show that an increase in the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the vertical wavy surface. It is shown that an increase in the power-law index, the thermal stratification parameter, or the concentration stratification parameter leads to a smaller fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinate. Moreover, the total heat transfer rate and the total mass transfer rate of vertical wavy surfaces are higher than those of the corresponding smooth surfaces.     

Numerical study of natural convection from a heat generating element using a locally divergence free FEM and comparison with experiment

A locally divergence free numerical scheme based on a hybrid finite element-finite volume method together with a restricted domain approach is used for the numerical solution of laminar conjugate natural convection in a vertical channel containing a short planar heat generating element. Numerical simulations have been carried out for modified Rayleigh numbers in the range 1 × 10⁵–8.1 × 10⁷. The numerically evaluated temperature rise above the ambient of the heat generating element is found to agree well with experimental data. A correlation for dimensionless temperature rise as a function of dimensionless volumetric heat generation is presented. Natural convection, Hybrid FEM-FVM method, Restricted domain approach, Volumetric heat generation.