BUOYANCY-AIDED MIXED CONVECTION WITH CONDUCTION AND SURFACE RADIATION FROM A VERTICAL ELECTRONIC BOARD WITH A TRAVERSABLE DISCRETE HEAT SOURCE

This article presents the results of a comprehensive fundamental numerical study of the problem of buoyancy-aided mixed convection with conduction and surface radiation from a vertical electronic board provided with a traversable, flush-mounted, discrete heat source. Air, a radiatively transparent medium, is considered to be the cooling agent. The governing equations in primitive variables for fluid flow and heat transfer are first converted into stream function–vorticity form, and are later converted into algebraic form using the finite-volume method. The resulting finite-difference equations are solved by Gauss-Seidel iterative technique. The governing equation for temperature distribution along the electronic board is obtained by appropriate energy balance. The effects of pertinent parameters, viz., location of the discrete heat source, surface emissivity of the board, and modifiedRichardson number, on various results, including local temperature distribution along the board, maximum board temperature, and contributions of convection and surface radiation to heat dissipation from the board, are studied in great detail. The fact that any design calculation that ignores surface radiation in problems of this kind would be error-prone is clearly highlighted.     

Simulation Studies on Buoyancy-Aided Conjugate Mixed Convection With Radiation From a Vertical Plate With Multiple Nonidentical Heat Sources

This paper documents certain salient results of the simulation studies performed on conjugate mixed convection with surface radiation from a vertical electronic board equipped with multiple nonidentical flush-mounted discrete heat sources. Air that is assumed to be radiatively transparent with constant thermophysical properties subjected to the Boussinesq approximation is considered to be the cooling agent. The governing fluid flow and heat transfer equations without the boundary-layer approximations are initially transformed into vorticity-stream function form and are later appropriately normalized. The resulting equations, along with pertinent boundary conditions, are subsequently solved using a finite-volume-based finite-difference method coupled with Gauss–Seidel iterative technique. An extended computational domain has been used to capture the fluid flow and heat transfer adequately employing optimum combination of finer and coarser grids. A computer code is specifically written for the job. Effects of modified Richardson number, surface emissivity, and thermal conductivity on local temperature distribution, peak board temperature, and contributions of mixed convection and radiation in heat dissipation have been clearly elucidated. Two correlations that help in calculation of maximum and average nondimensional plate temperatures have also been developed.     

Effects of Thermal Radiation for Electronic Cooling on Modified PCB Geometry under Natural Convection

In this study, the discrete ordinates method (DOM) model is employed to estimate the effect of thermal radiation from multiple heat sources in a natural-convection flow field. It is found that the flow field around the chips can be altered by natural convection as induced by radiative heat transfer. The influence of thermal radiation is higher than 65% when the chipboard is in a vertical orientation. Furthermore, even if the chip surface temperature is only 317 K, the influence of radiative heat transfer is still up to 18%. Therefore, radiative heat transfer cannot be ignored for electronic component computational fluid dynamics simulation under natural convection.     

Natural Convection in a Vertical Annuli with Discrete Heat Sources

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.     

Heat and Moisture Transfer in a Rectangular Cavity Partially Filled with Hygroscopic Porous Media

Abstract

This work deals with turbulent natural convection heat and moisture transfer with thermal radiation in a rectangular cavity partially filled with hygroscopic porous medium. The governing equations for the momentum and heat transfer in both free fluid and hygroscopic porous media and moisture content transfer in hygroscopic porous medium were solved by the finite element method. Comparisons with experimental and numerical results in the literature have been carried out. Effects of thermal radiation, Rayleigh number on natural convection and heat transfer in both free fluid and porous medium and moisture content transfer in porous medium were analyzed. It was found that surface thermal radiation can significantly change the temperature and moisture content fields in the regions of free flow and hygroscopic porous medium. With the increase in Rayleigh number, the temperature of porous medium at the interface increased slightly, and the magnitude of moisture change becomes smaller.     

Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels

Combined effect of laminar flow mixed convection and surface radiation heat transfer for thermally developing airflow in a vertical channel heated from a side has been experimentally examined with different thermal and geometric parameters. The channel boundary is made of two isothermal walls and two adiabatic walls, the isothermal parallel wall is heated uniformly and the opposite cold wall temperature is maintained equal to the inlet conditions. The heated wall temperature ranged from 55 to 100°C, Reynolds number ranged from 800 to 2900 and the heat flux was varied from 250 to 870 W/m². To cover the wide range of Reynolds numbers, two aspect ratios of square and rectangular section were used. Surface radiation from the internal walls is considered through two emissivities i.e. 0.05 and 0.85, to represent weak and strong radiation effects, respectively. From the experiments, surface temperature and Nusselt number distributions of convection and radiation heat transfer are obtained for different heat flux values. Flow structure inside the channel is visualized to observe the flow pattern. The results show the combined effect of laminar flow mixed convection and surface radiation on the total heat transfer rate within the channel. The accumulating buoyancy force and airflow moves together vertically in the upward direction to give significant heat transfer enhancement in the vertical orientation of the channel.     

EFFECTS OF ADAPTIVITY ON FINITE ELEMENT SCHEMES FOR TURBULENT HEAT TRANSFER AND FLOW PREDICTIONS

This article reports convection heat transfer in a short and tall annular enclosure with two discrete isoflux heat sources of different lengths. The discrete heat sources are mounted at the inner wall and the outer wall is maintained at a lower temperature, whereas the top and bottom walls and the unheated portions of the inner wall are kept at adiabatic. An implicit finite-difference method is employed to solve the vorticity–stream function formulations of the governing equations. The significant influence of the discrete heaters on the flow and heat transfer is analyzed for a wide range of modified Rayleigh numbers, aspect ratio, and length ratio (?) of heat sources. Our numerical results reveal that the average Nusselt number decreases with aspect ratio, whereas the magnitude of maximum temperature increases with the aspect ratio. For most of the parametric cases considered in the present study, the heat transfer rate is found to be higher at the bottom heater than at the top heater except for ? = 0.5. The effect of heater length ratio on the heat transfer rate is noticeable for unit aspect ratio, whereas its effect is insignificant as the aspect ratio increases. Furthermore, it was found that the maximum temperature is found generally at the top heater except for the case ? = 0.5, where the maximum temperature is found at the bottom heater.     

Effect of Thermal Conductivity on Cooling of Square Heat Source Array under Natural Convection in a Vertical Channel

Abstract

This article presents experimental and numerical investigation on natural convection air-cooling of discrete square heat source array in a vertical channel. Conjugate heat transfer for three-dimensional laminar developing flows over an array of square heat sources representing integrated circuit components for electronic cooling has been studied. Experiments are conducted using three-substrate board materials viz. FR4, Bakelite, and copper clad board having thermal conductivities of 0.3, 1.4, and 8.8?W/m K to study the effects of substrate thermal conductivity on fluid flow and heat transfer. A finite element-based software is used to solve the coupling between heat transfer in solids and fluid region. Incompressible flow over discrete square heat sources is modeled using Navier–Stokes equations under Boussinesq approximation. Air-cooling of circuit boards populated with heat sources is modeled and simulated to present heat transport in combination with the fluid flow resulting from the natural air circulation at constant heat fluxes of 1,000, 2,000, and 3,000?W/m². Multilayer copper clad board of thermal conductivity of 40.5?W/m K have been studied numerically. The results show that single sided copper clad board is the preferred candidate. Experiments indicate a deviation of under 5% with simulations.     

Interaction of Surface Radiation With Laminar and Turbulent Natural Convection in Tall Vertical Cavities: Analysis and Heat Transfer Correlations

The interaction of surface radiation with laminar and turbulent natural convection in differentially heated vertical cavities, filled with air and of large aspect ratio (greater than 10), is analyzed in this study. The k ? ωSST turbulence model is used for the formulation of the convection fluid flow and heat transfer, while the governing equations are discretized by the finite-volume method. As an extension of the scarce previous studies, more realistic conditions with a wide range of parameters are considered in the performed simulations. The presented results show the effect of surface radiation on streamlines, isotherms, turbulent kinetic energy, and temperature and vertical velocity profiles, as well as on local and on average convective and radiative heat transfer. Globally, it is found that surface radiation has a weak effect on the dynamic and thermal fields in the major part of the cavity; however, some influence in the upper and lower zones of the cavity is observed. For design purposes, accurate correlations are developed for average convective and radiative Nusselt numbers that cover emissivity of surfaces between 0 and 1, cold wall temperature ranging from 263 K to 303 K, temperature difference between vertical walls ranging from 5 K to 40 K, width of the cavity between 2.5 cm and 7.5 cm, and height of the cavity between 0.25 m and 6 m (this leads to a Rayleigh number ranging from 10³ to 2 × 10⁶ and an aspect ratio between 10 and 80).     

Numerical Method on Natural Convection and Radiation Heat Transfer with an Isotropic Scattering Medium

The finite-volume method (FVM) for radiation heat transfer with a nonscattering medium is extended to an isotropic scattering medium, and this method is implemented in the fluid flow solver GTEA on hybrid grids. For comparison and validation, three test cases, a semicircle enclosure with a hole, a rhombic enclosure, and a square cavity, are chosen. All the results obtained by the present FVM agree very well with the numerical solutions in the references. Furthermore, the effects of the extinction coefficient and scattering albedo on the flow and temperature distribution are studied numerically in the cavity based on present approach. As the extinction coefficient increases from 0.2 to 5, the temperature gradient adjacent to the hot and cold walls gradually decreases at Ra = 10⁵, however, the temperature profiles become similar at Ra = 10⁶. For Ra = 10⁵, 10⁶, the scattering albedo affects the structures of the isotherm and streamline to some extent. As the scattering albedo increases, the convection heat transfer in the middle region of the hot wall increases, but the radiation heat transfer and the total radiation heat transfer along the hot wall decrease.     

Effect of Radiative Heat Transfer on Three-Dimensional Double Diffusive Natural Convection

This work presents a numerical study of the effect of the radiative heat transfer on the three-dimensional double diffusive convection in a differentially heated cubic cavity for different optical parameters of the medium. This numerical study is conducted for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10⁵, Le = 2, and buoyancy ratio N in the range [–2, 0]. The natural convection equations, using the Boussinesq approximation for the treatment of buoyancy term in the momentum equation, are expressed using the vorticity–stream function formulation. These equations and the radiative transfer equation are discretized, respectively, with the control volume finite difference method and the FTn finite volume method. The influences of the optical thickness and the conduction–radiation parameter of the semitransparent fluid on heat and mass transfer are depicted. Results show different transitions of the structure of the main flow when varying the conduction–radiation parameter and the optical thickness.     

Heat transfer study of a hermetic refrigeration compressor

This paper presents an analytical study on heat transfer and temperature distribution for a hermetic reciprocating refrigeration compressor using the lumped thermal conductance approach. In this analysis, the intricate components of a hermetic compressor were divided into 46 geometrically simplified discrete elements and each was assumed to be at a uniform temperature. The lumped thermal conductance method was then applied to all the components of the compressor to form 46 simultaneous equations, which were then solved to get the components’ temperatures. The results obtained were in good agreement with measurement. The discrepancies in the prediction lie in the assumptions made in assigning various heat transfer correlations to model the convection heat transfer effects of the fluid and solid surface boundaries, and the simplification made in distributing the various components of the compressor into discrete parts. The results of this study have been applied to actual compressor design in industry and have resulted in improved compressor performance.     

Numerical simulation of coupled radiation‐convection heat transfer of high‐temperature developing flow in tube

By combining the discrete ordinate method with the control volume method, the coupled radiation‐convection heat transfer of high‐temperature developing laminar flow in a tube is investigated numerically. The radiative transfer is solved by the discrete ordinate method and its contribution to thermal balance is dealt with as a source term in the energy equation, which is solved, as well as the momentum equation, by the control volume method. The effects of medium optical thickness and tube wall temperature on the temperature distribution in medium as well as the heat flux and local Nusselt number on wall are analyzed. The results show that the radiation heat transfer of high‐temperature medium influences the temperature distribution and convection heat transfer greatly, and plays an important role in the heat transfer of developing laminar flow in a tube. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 53–63, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10135     

Study of the Thermal Behavior of Multi Tube Tank in Heat Recovery from Chimney—Analysis and Optimization

This work discusses the utilization of multi tube tank heat exchanger for waste heat recovery. The thermal behavior of the system is studied in order to understand the contribution of the different heat transfer modes governing the system. As application, heating water in residential application from chimney heat recovery is considered. A prototype illustrating the suggested system is implemented and tested. Different waste heat scenarios by varying the quantity of burned firewood (heat input) are experimented. The temperature at different parts of the system and the gas flow rates of the exhaust pipes are measured. Measurements showed that the temperature of 95 L tank of water can be increased by 68°C within one hour. Obtained results show that the convection and radiation exchanges at the bottom surface of the tank have a considerable impact on the total heat transfer rate of the water (as high as 70%). Moreover, the proposed system allows saving 9.8 L of gasoline, 10.6 L of diesel or 15 kg of wood for 12 hours of chimney operation.     

Heat transfer modelling of spherical particles subject to heating in a fluidized bed

This paper presents an analytical model for analyzing transient heat transfer between a brick particle and air flow during heating in a fluidized bed combustor. Both experimental and theoretical studies were carried out. The experimental investigation provided the temperature distributions at the centers of the spherical particles during heating. These data were presented in the dimensionless form and were compared with the results of the present analytical model. The theoretical investigation included two cases: e.g. Case 1 considered that the surface heat transfer coefficient is only the convection heat transfer coefficient; Case 2 also considered that the surface heat transfer coefficient is the sum of the convection and radiation heat transfer coefficients. Better agreement was found between the experimental data and the theoretical Case 2. The results of this study show that there is a dominant effect of the radiation heat transfer on the temperature distribution.     

Some New Solutions for Extended Surface Heat Transfer Using Symbolic Algebra

The paper reports some new solutions for heat transfer through extended surfaces or fins using the symbolic algebra package Maple 8, which is widely available. The four specific problems chosen for the present study are: (a) a rectangular convection fin with the heat transfer coefficient varying either linearly or exponentially with the distance from the base, (b) a truncated conical spine with convection at both ends, (c) a heat-generating annular fin with a constant base heat flux and an adiabatic tip, and (d) a convection fin array made of a rectangular fin and two triangular fins. Each problem is formulated in a manner that makes its solution novel and distinct from what is available in the literature. Solutions are provided in symbolic forms. Using the numerical and graphical capabilities of Maple, the results are presented in the form of numerical data as well as graphical displays. The paper demonstrates that Maple provides an effective and convenient tool for the analysis of extended surface heat transfer problems that otherwise demand tedious algebraic manipulations.     

Natural convection and radiation heat transfer in a vertical porous layer with a hexagonal honeycomb core (Part 1: numerical analysis)

Combined heat transfer characteristics were obtained numerically for three-dimensional natural convection and thermal radiation in a long and wide vertical porous layer with a hexagonal honeycomb core. We assumed that the porous layer was both homogeneous and isotropic. The pure Darcy law for fluid flow and Rosseland's approximation for radiation were used. The numerical methodology was based on an algebraic coordinate transformation technique and the transformed governing equations were solved using the SIMPLE algorithm. The effect of radiation on the heat transfer characteristics was investigated over a wide range of radiation numbers and temperature ratios for two Darcy-Rayleigh number values (Ra^* = 100 and 1000) and for a fixed aspect ratio of H/L = 1. The results are presented in the form of combined radiation and convection heat transfer coefficients and are compared with the corresponding values for pure natural convection. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 278–294, 1999     

Analysis of combined mode heat transfer in a porous medium using the lattice Boltzmann method

ABSTRACT

Application of the lattice Boltzmann method (LBM) in solving a combined mode conduction, convection, and radiation heat transfer problem in a porous medium is extended. Consideration is given to a 1-D planar porous medium with a localized volumetric heat generation zone. Three particle distribution functions, one each for the solid temperature, the gas temperature, and the intensity of radiation, are simultaneously used to solve the gas- and the solid-phase energy equations. The volumetric radiation source term appears in the solid-phase energy equation, and it is also computed using the LBM. To check the accuracy of the LBM results, the same problem is also solved using the finite volume method (FVM). Effects of convective coupling, flow enthalpy, solid-phase conductivity, scattering albedo porosity, and emissivity on axial temperature distribution are studied and compared with the FVM results. Effects of flow enthalpy, solid-phase conductivity, and emissivity are also studied on radiative output. LBM results are in excellent agreement with those of the FVM.     

RADIATION-CONDUCTION INTERACTION IN A PLANAR,ANISOTROPICALLY SCATTERING MEDIUM WITH FLUX BOUNDARY

Steady, combined radiation and conduction heat transfer in an absorbing, emitting, and anisotropically scattering planar medium is investigated theoretically. The problem is considered with a constant net heat flux imposed at one boundary and a constant temperature at the other. Both specular and diffuse reflectivities are included. The influence of radiation heat transfer is obtained by solving the exact integral equations of radiative transfer with the nodal approximation technique. The technique reduces the integral equations into a discrete system of algebraic equations and permits obtaining exact numerical solutions for any scattering-phase function. Temperatures are obtained from the energy equation with an iterative procedure. The effects of scattering anisotropy as well as radiation parameters such as albedo and wall reflectivities on temperatures are analyzed.     

Combined heat transfer of radiation and natural convection in a square cavity containing participating gases

This article deals with analyzing the effect of radiative heat transfer on natural convection heat transfer in a square cavity under normal room conditions. The governing equations of natural convection and radiative transfer are solved simultaneously to obtain the temperature, velocity and heat flux distributions inside the participating medium. The finite volume method has been adopted to solve the governing equations and the discrete ordinates method (DOM) is used to model the radiative transfer in absorbing-emitting media. The radiative–convective model is validated by comparison with test cases solutions from the literature. Then, the effects of Rayleigh number from 10² to 10⁶ and optical thickness in a broad range from 0 to 100 on temperature and velocity distributions and Nusselt numbers are investigated. The results show that even under normal room conditions with a low temperature difference, the radiation plays a significant role on temperature distribution and flow pattern in the cavity. Also, several interesting effects of radiation are observed such as a sweep behavior on the isotherms, streamlines and velocity distributions of the cavity along the optical thickness and a reverse behavior on maximum stream function and convective Nusselt number at different Rayleigh numbers.