Interaction of surface radiation with combined conduction and convection from a discretely heated L-corner

Prominent results pertaining to the problem of multi-mode heat transfer from an L-corner equipped with three identical flush-mounted discrete heat sources in its left leg are given here. The heat generated in the heat sources is conducted along the two legs of the device before being dissipated by combined convection and radiation into air that is considered to be the cooling agent. The governing equations for temperature distribution along the L-corner are obtained by making appropriate energy balance between the heat generated, conducted, convected and radiated. The non-linear partial differential equations thus obtained are converted into algebraic form using a finite-difference formulation. The resulting equations are solved simultaneously by Gauss–Seidel iterative solver. A computer code is specifically written to solve the problem. The computational domain is discretised using 101 grids along the left leg, with 15 grids taken per heat source, and 21 grids along the bottom leg. The effects of surface emissivity, convection heat transfer coefficient, thermal conductivity and aspect ratio on local temperature distribution, peak device temperature and relative contributions of convection and radiation to heat dissipation from the L-corner are studied in detail. The point that one cannot overlook radiation in problems of this class has been clearly elucidated.     

Conjugate mixed convection with surface radiation from a vertical electronic board with multiple discrete heat sources

The problem of combined conduction-mixed convection-surface radiation from a vertical electronic board provided with three identical flush-mounted discrete heat sources is solved numerically. The cooling medium is air that is considered to be radiatively transparent. The governing equations for fluid flow and heat transfer are converted from primitive variable form to stream function-vorticity formulation. The equations, thus obtained, are normalised and then are converted into algebraic form using a finite volume based finite difference method. The resulting algebraic equations are then solved using Gauss–Seidel iterative method. An optimum grid system comprising 151 grids along the board and 111 grids across the board is chosen. The effects of various parameters, such as modified Richardson number, surface emissivity and thermal conductivity on temperature distribution along the board, maximum board temperature and relative contributions of mixed convection and radiation to heat dissipation are studied in detail. Further, the contributions of free and forced convection components of mixed convection to board temperature distribution and peak board temperature are brought out. The exclusive roles played by surface radiation and buoyancy in the present problem are clearly elucidated.     

Combined radiation and natural convection in a rectangular cavity with a transparent wall and containing a non-participating fluid

This paper describes a numerical method for the study of combined natural convection and radiation in a rectangular, two-dimensional cavity containing a non-participating (i.e. transparent) fluid. One wall of the cavity is isothermal, being heated either by solar radiation or independently. The opposite wall is partially transparent, permitting radiation exchanges between the cavity and its surroundings and/or the Sun; that wall also exchanges heat by convection from its external surface to the surroundings. The other two walls are adiabatic: convection and radiation there are balanced, so that there is no heat transfer through those walls. The equations of motion and energy are solved by finite difference methods. Coupled to these equations are the radiative flux boundary conditions which are used to determine the temperature distribution along the non-isothermal walls. A two-band radiation model has been employed. Results are presented for a square cavity with a vertical hot wall at 150 °C, the ambient at 20 °C and 10⁴ ? Ra ? 3 × 10⁵, in the absence of direct insolation. The effects on the flow and heat transfer in the cavity of radiation and external convection have been examined. More extensive results will be presented in subsequent papers.     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

Natural convection due to solar radiation over a non-absorbing plate with and without heat losses

Natural convection over a non-reflecting, non-absorbing, ideally transparent semi-infinite vertical flat plate due to absorption of incident radiation (solar radiation) is considered. The absorbed radiation acts as a distributed source which initiates buoyancy-driven flow and convection in the absorbing layer. The plate when heated by the absorbing fluid loses heat to the surroundings from its external side. Solution of the governing equations of the flow under these circumstances is non-similar because of both the heat source term in the energy equation and the temperature boundary condition at the plate. A local non-similar technique is used to obtain solutions for a wide range of the dimensionless distance along the plate and of the dimensionless loss coefficient to the surroundings. The results show that the temperature distribution has a maximum temperature in the depth of the fluid rather than on the plate. A new definition for a local heat transfer coefficient between the plate and the absorbing fluid is introduced which is based on the local maximum temperature rise in the fluid. A formula to calculate this heat transfer coefficient is given for the anticipated range of the loss coefficient.     

Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature,and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.     

A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity

This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.     

A numerical simulation of combined radiation and natural convection heat transfer in a square enclosure heated by a centric circular cylinder

A numerical simulation of combined natural convection and radiation in a square enclosure heated by a centric circular cylinder and filled with absorbing-emitting medium is presented. The ideal gas law and the discrete ordinates method are used to model the density changes due to temperature differences and the radiation heat transfer correspondingly. The influence of Rayleigh number, optical thickness and temperature difference on flow and temperature fields along with the natural convection, radiation and total Nusselt number at the source surfaces is studied. The results reveal that the radiation heat transfer as well as the optical thickness of the fluid has a distinct effect on the fluid flow phenomena, especially at high Rayleigh number. The heat transfer and so the Nusselt number decreases with increase in optical thickness, while increases greatly with increase in temperature difference. The variation in radiation heat transfer with optical thickness and temperature difference is much more obvious as comparison with convection heat transfer.     

An analytical treatment for combined heat transfer by radiation,convection and conduction within a heat insulating wall structure

An analytical procedure has been proposed to attack a highly conjugate thermal problem associated with radiation, convection and conduction within a heat insulating wall structure. Firstly, an analytical solution is derived for fully-developed mixed convective flow through parallel plates. Secondly, the resulting expressions for convection are coupled with radiation and conduction equations to form a set of heat balance equations for each heat transfer surface. Illustrative calculations are conducted to estimate heat transfer rates through a heat insulating roof structure with an aluminum partition with high reflectivity, subject to solar radiation in summer. The effect of an aluminum partition on the heat insulation is elucidated.     

Magnetohydrodynamic effects on natural convection flow of a nanofluid in the presence of heat source due to solar energy

The objective of the present work is to investigate theoretically the MHD convective flow and heat transfer of an incompressible viscous nanofluid past a porous vertical stretching sheet in the presence of variable stream condition due to solar radiation (incident radiation). The governing equations are derived using the usual boundary-layer and Boussinesq approximations and accounting for the presence of an applied magnetic field and incident radiation flux. The absorbed radiation acts as a distributed source which initiates buoyancy-driven flow and convection in the absorbed layer. The partial differential equations governing the problem under consideration are transformed by a special form of Lie symmetry group transformations viz. one-parameter group of transformation into a system of ordinary differential equations which are solved numerically using Runge Kutta Gill based shooting method. The conclusion is drawn that the flow field and temperature are significantly influenced by radiation, heat source and magnetic field.     

Radiation effects on Marangoni convection boundary layer over a permeable surface

The problem of Marangoni convection boundary layer flow that can be formed along the interface of two immiscible fluids when the wall is permeable, where there is suction or injection effect, is considered. Similarity equations are obtained through the application of similarity transformation techniques. The effects of suction/injection and radiation parameters on the heat transfer characteristics are numerically studied using the shooting method for a fixed value of the Prandtl number (Pr=0.7). Numerical results are obtained for the surface temperature gradient or the heat transfer rate as well as the temperature profiles for some values of the governing parameters. Comparisons with known results from the open literature show very good agreements. The results indicate that the heat transfer rate at the surface decreases as the radiation parameter increases. Further, results show that multiple (dual) solutions exist for a certain range of the governing parameters.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

Influence of magnetic field and thermal radiation by natural convection past vertical cone subjected to variable surface heat flux

A numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation.The surface of the cone is subjected to a variable surface heat flux.The fluid considered is a gray,absorbing-emitting radiation but a non-scattering medium.With approximate transformations,the boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime.The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent,accurate,and unconditionally stable.Numerical results are obtained and presented for velocity,temperature,local and average wall shear stress,and local and average Nusselt number in air and water.The present results are compared with the previous published work and are found to be in excellent agreement.     

Numerical simulation of three-dimensional natural convection inside a heat generating anisotropic porous medium

Natural convection in anisotropic heat generating porous medium enclosed inside a rectangular cavity has been studied. A 3D finite volume based code is developed using the Darcy approximation and validated using experimental results of natural convection around an enclosed rod bundle. Subsequently, detailed simulation is carried out for a cavity, filled with orthotropic porous medium. The effects of heat generation, geometry and anisotropy are studied. Anisotropy is found to be of significant importance for both maximum value and distribution of temperature.     

Conjugate heat exchange and hydrodynamics for a viscous incompressible fluid moving in a rectangular cavity

Numerical simulation was performed of the motion of a viscous incompressible nonisothermal fluid in an open rectangular cavity under conditions of forced convection and conjugate heat exchange. The effect of the jet dynamic parameter (Reynolds number) and fluid flow conditions on the character of motion and heat exchange of viscous incompressible nonisothermal fluids in rectangular cavities is studied. A hydrodynamic pattern of viscous flow in an open cavity under forced convection conditions (in the conjugate and nonconjugate formulations of the problem) is obtained. The effect of parameters of the model on the character of motion is studied. Temperature profiles for the solid and fluid phases are obtained. The effect of parameters of the model on the character of temperature distribution in both phases is studied.     

Mixed convection in non-Newtonian fluids along a vertical plate with variable surface heat flux in a porous medium

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along a vertical plate with power-law surface heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate. Received on 13 October 1998     

Natural convection and conduction heat transfer in open shallow cavities with bounding walls

A numerical study has been carried out on inclined open shallow cavities, which are formed by a wall and horizontal fins. Constant heat flux is applied on the surface of the wall inside the cavity while its other surface was kept isothermal. The wall and the fins are conductive. Conjugate heat transfer by natural convection and conduction is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁶ to 10¹², conductivity ratio from 1 to 60, open cavity aspect ratio from 1 to 0.125, dimensionless end wall thickness from 0.05 to 0.20, horizontal walls from 0.01 to 0.15 and inclination of the end wall from 90° to 45°. It is found that the volume flow rate and Nusselt number are a decreasing function of the cavity aspect ratio, horizontal fin thickness and conductivity ratio. They are an increasing function of end wall thickness and inclination angle, except in the latter case optima exist at high Rayleigh numbers.     

Resolving the stratification discrepancy of turbulent natural convection in differentially heated air-filled cavities. Part III: A full convection–conduction–surface radiation coupling

The present study concerns an air-filled differentially heated cavity of 1 m × 0.32 m × 1 m (width × depth × height) subject to a temperature difference of 15 K and is motivated by the need to understand the persistent discrepancy observed between numerical and experimental results on thermal stratification in the cavity core. An improved experiment with enhanced metrology was set up and experimental data have been obtained along with the characteristics of the surfaces and materials used. Experimental temperature distributions on the passive walls have been introduced in numerical simulations in order to provide a faithful prediction of experimental data. By means of DNS using spectral methods, heat conduction in the insulating material is first coupled with natural convection in the cavity. As heat conduction influences only the temperature distribution on the top and bottom surfaces and in the near wall regions, surface radiation is added to the coupling of natural convection with heat conduction. The temperature distribution in the cavity is strongly affected by the polycarbonate front and rear walls of the cavity, which are almost black surfaces for low temperature radiation, and also other low emissivity walls. The thermal stratification is considerably weakened by surface radiation. Good agreement between numerical simulations and experiments is observed on both time-averaged fields and turbulent statistics. Treating the full conduction–convection–radiation coupling allowed to confirm that experimental wall temperatures resulted from the coupled phenomena and this is another way to predict correctly the experimental results in the cavity.     

Conjugate mixed convection heat and mass transfer in brick drying

 In this study, a numerical methodology for the solution of conjugate heat and mass transfer problem is presented. Fluid flow, heat and mass transfer over a rectangular brick due to transient laminar mixed convection has been numerically simulated. The coupled non-linear partial differential equations, for both gas phase and solid are solved using finite element procedure. Flow is assumed to be incompressible, two-dimensional, laminar. Analysis has been carried out at a Reynolds number of 200 with Pr = 0.71. The effect of buoyancy on the brick drying has been investigated. Velocity vectors, streamlines in the flow field and temperature and moisture contours and temperature distribution along the solid surface are presented. It is observed that there is considerable effect of buoyancy during drying. The results indicate a non-uniform drying of the brick with the leading edge drying faster than the rest of the brick. Received on 9 December 1998