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.     

Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source

Prominent results of a simulation study on conjugate convection with surface radiation from an open cavity with a traversable flush mounted discrete heat source in the left wall are presented in this paper. The open cavity is considered to be of fixed height but with varying spacing between the legs. The position of the heat source is varied along the left leg of the cavity. The governing equations for temperature distribution along the cavity are obtained by making energy balance between heat generated, conducted, convected and radiated. Radiation terms are tackled using radiosity-irradiation formulation, while the view factors, therein, are evaluated using the crossed-string method of Hottel. The resulting non-linear partial differential equations are converted into algebraic form using finite difference formulation and are subsequently solved by Gauss–Seidel iterative technique. An optimum grid system comprising 111 grids along the legs of the cavity, with 30 grids in the heat source and 31 grids across the cavity has been used. The effects of various parameters, such as surface emissivity, convection heat transfer coefficient, aspect ratio and thermal conductivity on the important results, including local temperature distribution along the cavity, peak temperature in the left and right legs of the cavity and relative contributions of convection and radiation to heat dissipation in the cavity, are studied in great detail.     

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.     

MHD non-Darcian flow through a non-isothermal vertical surface embedded in a porous medium with radiation

The effect of MHD on steady two-dimensional laminar mixed flow about a vertical porous surface is numerically analyzed. Also the effects of radiation and heat generation and absorption are considered. A power law variation of temperature along the vertical wall is assumed. The nonlinear boundary-layer equations were transformed and the resulting differential equations were solved by an implicit finite difference scheme (Keller box method). Numerical results for the velocity distribution and the temperature distribution are presented for various values of Prandtl number Pr, magnetic parameter, porous medium parameter and internal heat generation or absorption coefficient. Further validation with previous works is carried out.     

Combined radiation and natural convection effects on graetz problem in horizontal isothermal circular tubes

A numerical analysis is performed on the combined thermal radiation and mixed convection for a gray fluid flow in a horizontal isothermally-heated circular tube. The governing equations of vorticity-velocity form are employed and solved by DuFort-Frankel method. The contribution of radiation is formulated by integral expression and solved by finite element nodal approximation. The effects of radiation and convection on local Nusselt number and the developing of bulk temperature are presented. The result shows that the heat transfer can be significantly enhanced by the effects of radiation and secondary flow induced by buoyancy. Besides, the fluctuation in local Nusselt number curve which is caused by the existence of secondary flow is reduced by the effect of thermal radiation.     

Conjugate free convection of non-Newtonian fluids about a vertical cylindrical fin in porous media

Conjugate free convection along a vertical cylindrical fin in a non-Newtonian fluid-saturated porous medium has been investigated theoretically. The boundary layer equations based on the power lay model appropriate for the Darcy flows are solved numerically exploiting a very efficient finite difference method. Effects of the power-law index, conjugate convection-conduction parameter and the surface curvature parameter on the fin temperature distribution, local heat transfer-coefficient and local heat flux are studied and presented in graphical and tabular form.     

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.     

MHD mixed convection–radiation interaction along a permeable surface immersed in a porous medium in the presence of Soret and Dufour’s Effects

This work is focused on the numerical modeling of steady, laminar, heat and mass transfer by MHD mixed convection from a semi-infinite, isothermal, vertical and permeable surface immersed in a uniform porous medium in the presence of thermal radiation and Dufour and Soret effects. A mixed convection parameter for the entire range of free-forced-mixed convection is employed and the governing equations are transformed into non-similar equations. These equations are solved numerically by an efficient, implicit, iterative, finite-difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in excellent agreement. A parametric study illustrating the influence of the thermal radiation coefficient, magnetic field, porous medium inertia parameter, concentration to thermal buoyancy ratio, and the Dufour and Soret numbers on the fluid velocity, temperature and concentration as well as the local Nusselt and the Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.     

Mixed convection boundary layer flow along vertical moving thin needles with variable heat flux

The problem of steady laminar mixed convection boundary layer flow of an incompressible viscous fluid along vertical moving thin needles with variable heat flux for both assisting and opposing flow cases is theoretically considered in this paper. The governing boundary layer equations are first transformed into non-dimensional forms. The curvature effects are incorporated into the analysis whereas the pressure variation in the axial direction has been neglected. These equations are then transformed into similarity equations using the similarity variables, which are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for a blunt-nosed needle (m = 0). Numerical calculations are carried out for various values of the dimensionless parameters of the problem, which include the mixed convection parameter λ, the Prandtl number Pr and the parameter a representing the needle size. It is shown from the numerical results that the skin friction coefficient, the surface (wall) temperature and the velocity and temperature profiles are significantly influenced by these parameters. The results are presented in graphical form and are discussed in detail.     

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     

Dual solutions of a mixed convection flow near the stagnation point region over an exponentially stretching/shrinking sheet in nanofluids

The aim of this paper is to study the development of mixed convection flow near the stagnation point region over an exponentially stretching/shrinking sheet in nanofluids. The external flow, stretching velocity and wall temperature are assumed to vary as prescribed exponential functions. Using the local similarity method, it has been shown that dual solutions of velocity and temperature exist for certain values of suction/injection, mixed convection, nanoparticle volume fraction and stretching/shrinking parameters. The transformed non-linear ordinary differential equations along with the boundary conditions form a two point boundary value problem and are solved using Shooting method, by converting into an initial value problem. In this method, the system of equations is converted into a set of first order system which is solved by fourth-order Runge–Kutta method. Three different types of nanoparticles, namely copper (Cu), aluminum oxide (Al₂O₃) and titanium oxide (TiO₂) are considered by using water-based fluid with Prandtl number Pr = 6.2. It is also found that the skin friction coefficient and the heat transfer rate at the surface are highest for Copper–water nanofluids as compared to Al₂O₃. The effect of the solid volume fraction parameter φ of the nanofluids on the heat transfer characteristics is also investigated. The results indicate that dual solutions exist only for shrinking sheet. The effects of various parameters on the velocity and temperature profiles are also presented here.     

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     

Thermal radiation effect on mixed convection heat and mass transfer of a non-Newtonian fluid over a vertical surface embedded in a porous medium in the presence of thermal diffusion and diffusion-thermo effects

Thermal radiation, thermal diffusion, and diffusion-thermo effects on heat and mass transfer by mixed convection of non-Newtonian power-law fluids over a vertical permeable surface embedded in a saturated porous medium are investigated. The governing equations describing the problem are non-dimensionalized and transformed into a non-similar form. The transformed equations are solved by using the local non-similarity method combined with the shooting technique. The effects of the physical parameters of the problem on the fluid temperature and concentration are illustrated graphically and analyzed. Also, the effects of the pertinent parameters on the local Nusselt number and the local Sherwood number are presented.     

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.     

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.     

Radiation effect on mixed convection along a vertical plate with uniform surface temperature

This paper investigates the effect of radiation on the forced and free convection flow of an optically dense viscous incompressible fluid along a heated vertical flat plate with uniform free stream and uniform surface temperature with Rosseland diffusion approximation. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations valid in the forced convection regime as well as in the free convection regime. A group of transformation is, also, introduced to reduce the boundary layer equations to a set of local nonsimilarity equations valid in both the forced and free convection regimes. Solutions of the governing equations are obtained by employing the implicit finite difference methods together with Keller box scheme and are expressed in terms of local shear stress and local rate of heat transfer for a range of values of the pertinent parameters.     

Nonsimilar Solutions for Mixed Convection in Non-Newtonian Fluids Along Horizontal Surfaces in Porous Media

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along horizontal surfaces with variable 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.     

Transient mixed convection flow instabilities in a vertical pipe

The present paper investigates a numerical study of flow instabilities in transient mixed convection in a vertical pipe. At the entrance of the pipe, the flow is suddenly submitted to a temperature step. The convection heat transfer on the outer surface of the pipe is taken into account. The governing equations are solved using a finite difference explicit scheme. The numerical results show that the time development of streamlines and isotherms is strongly dependent on the inlet temperature steps. For positive temperature steps, the unsteady vortex is significant in the vicinity of the wall and the reversal flow appears below the wave instability. In the case of negative temperature steps and especially for the low Reynolds number, the reversal flow appears on top of the wave instability. During the transient, the apparition of the vortical structures along the wall leads to the wall boundary layer instability. This phenomenon is due to the transient mixed convection flows. The temperature step effects on the heat transfer of the flow are presented in our paper.     

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.     

Mixed convection in a vertical channel with discrete heat sources at the wall

The mixed convection in a vertical plane-parallel channel with two heat sources of finite dimensions located at the wall is analyzed on the basis of a two-dimensional numerical simulation. The effect of the distance between the heat sources on the flow pattern and the temperature field is studied. Calculations are performed on the Grashof and Reynolds number ranges from 0–10⁵ and 0–10, respectively, at a Prandtl number of 0.7. The mathematical model is based on the time-dependent Navier-Stokes equations in the Boussinesq approximation. The problem is solved by the finite element method.