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.     

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.     

Heat transfer of a micropolar fluid by the presence of radiation

An analysis of the steady flow of a micropolar fluid past an unmoving plate by the presence of radiation is considered. Numerical solution for temperature field has been derived and the effect of the radiation parameter on the temperature field is discussed.     

Features of High-Viscosity Fluid Flow Through a Porous Medium Heated by Electromagnetic Radiation

Models describing the process of flow of a high- viscosity fluid through a porous medium heated by electromagnetic radiation are investigated analytically and numerically with allowance for the temperature dependence of the fluid viscosity and density. In addition to ordinary heating, the nonlinear electromagnetic heating regime associated with variation of the radiation absorption coefficient with temperature is considered.     

The quasi-stationary structure of radiating shock waves. II. The two-temperature fluid

We solve the equations of radiation hydrodynamics in the two-temperature fluid approximation on an adaptive grid. The temperature structure depends upon the electron-ion energy exchange length, , and the electron conduction length, . Three types of radiating shock structure are observed: subcritical, where preheating of the unshocked gas is negligible; electron supercritical, where radiation preheating raises the temperature of the unshocked electron fluid to be equal to the final electron temperature; supercritical, where preheating and electron-ion energy exchange raise the preshock to their final post shock values. No supercritical shock develops when is larger than the photospheric depth of the shocked gas because a negligible amount of the ion energy is transferred to the electrons and the shock is weakly radiating. Electron conduction smooths the profile on a length scale , reducing the radiation flux. Received 21 September 1998 / Accepted 15 January 1999     

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.     

Grey-body surface radiation coupled with conduction and convection for general geometries

This paper presents a numerical technique for the simulation of the effects of grey-diffuse surface radiation on the temperature field of fluid flows using FIDAP, a general purpose incompressible, viscous fluid code. The radiating surface relationships assume a non-participating medium, constant surface temperature and heat fluxes at the discretized elemental level. The technique involves the decoupling of energy and radiation exchange equations. A concept of macrosurfaces, each containing a number of radiating boundary surfaces, is introduced. These boundary macroelements then carry the information from the radiating boundary into the fluid regime. A number of simulations illustrating the algorithm are presented.     

Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition,thermal radiation,and mixed convection

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth-and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the nonlinear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.     

Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation,heat flux,and variable conductivity

A sophisticated theoretical and mathematical model is proposed. It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux, thermal radiation, and viscous dissipation. Despite the fact that some properties of the fluid do not depend on the temperature, the fluid thermal conductivity is assumed to depend on the temperature. Based on accelerating the fluid elements, some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena. The contribution in this study is that a similar solution is obtained, in spite of the high nonlinearity of the Carreau model,especially, with the heat flux, variable conductivity, and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number. Likewise, the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally, the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.     

Radiation effect on temperature distribution in three-dimensional Couette flow with suction or injection

A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidal one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the temperature distribution than the injection or radiation parameter.     

Forced convective flow and heat transfer over a?porous plate in a?Darcy-Forchheimer porous medium in presence of?radiation

A mathematical model is presented for analyzing the boundary layer forced convective flow and heat transfer of an incompressible fluid past a plate embedded in a Darcy-Forchheimer porous medium. Thermal radiation term is considered in the energy equation. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. It is noticed that the boundary layer decreases with an increase in the value of inertial parameter and in this case the temperature profile is found to decrease smoothly within the boundary layer. In case of porous plate, fluid velocity increases whereas non-dimensional temperature decreases for increasing values of suction parameter. The rate of heat transfer increases with the increasing values of Prandtl number. The effect of thermal radiation on temperature field is also analyzed.     

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.     

Thermal radiation effect on non-Darcy natural convection with lateral mass transfer

 A boundary layer analysis has been presented to study the influence of thermal radiation and lateral mass flux on non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. Forchheimer extension is considered in the flow equations, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Similarity solution for the transformed governing equations is obtained and the combined effect of thermal radiation and fluid suction/injection on the heat transfer rate is discussed. Numerical results for the details of the velocity and temperature profiles as well as Nusselt number have been presented. Received on 7 July 1999     

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.     

Radiation Effect on MHD Free Convection Flow of a Gas Past a Semi-infinite Vertical Plate with Variable Viscosity

The radiation effect in the presence of a uniform transverse magnetic field on steady free convection flow with variable viscosity is investigated. The fluid viscosity is assumed to vary as the reciprocal of a linear function of temperature. Boundary layer equations are derived. The resulting approximate non-linear ordinary differential equations are solved linearly and nonlinearly by shooting methods. The velocity and temperature profiles are shown, and the skin friction on the plate and heat transfer coefficient are presented and discussed. The results of the present study show that in the presence of magnetic field, as the radiation parameter increases the temperature increases, but the velocity decreases.     

The effect of radiation on mixed convection flow past a stretching surface

A boundary layer analysis is presented for a study of the influence of radiation and buoyancy on heat and mass transfer characteristics of continuous surfaces having a prescribed variable surface temperature and stretched with rapidly decreasing power law velocities. The effects of suction in the presence of a quiescent fluid medium of constant temperature are considered. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The transformed governing equations are solved numerically and the velocity and temperature profiles as well as the local Nusselt number and skin friction coefficient are presented. Results show that the effect of radiation is to keep the molten mass away from the slot warmer, reduces the friction factor and increases the heat transfer rate compared to the case with no radiation.     

The effects of temperature-dependent fluid properties on free convective flow along a semi-infinite vertical plate by the presence of radiation

The effects of temperature-dependent density, viscosity and thermal conductivity on the free convective steady laminar boundary layer flow by the presence of radiation for large temperature differences, are studied. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. The fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The usual Boussinesq approximation is neglected due to the large temperature difference between the plate and the fluid. The nonlinear boundary layer equations, governing the problem under consideration, are solved numerically by applying an efficient numerical technique based on the shooting method. The effects of the density/temperature parameter n, the thermal conductivity parameter , the viscosity/temperature parameter _r and the radiation parameter F are examined on the velocity and temperature fields as well as the coefficient of heat flux and the shearing stress at the plate.     

Heat transfer in a radiating fluid with slug flow in a parallel-plate channel

Summary As a step towards a better understanding of combined conduction, convection, and radiation, fully developed heat transfer in slug flow in a flat duct between two parallel plates is considered. The flat duct consists of two diffuse, nonblack, isothermal surfaces. The gray radiating fluid between them is capable of emitting and absorbing thermal radiation. The problem is formulated in terms of a nonlinear integrodifferential equation, and the solution is obtained by an approximate method. The differences between heating and cooling the fluid are examined. The effects of the optical thickness of the fluid, the ratio which determines the relative role of energy transport by conduction to that by radiation, and the emissivity of the duct surfaces on the temperature distribution and the heat transfer characteristics are investigated. An approximate method for calculating the radiant heat flux at the wall is presented, and the accuracy of the approximation is tested.Work done under the auspices of the U.S. Atomic Energy Commission.     

Radiation effect on forced convective flow and heat transfer over a porous plate in a porous medium

Heat transfer analysis has been presented for the boundary layer forced convective flow of an incompressible fluid past a plate embedded in a porous medium. The similarity solutions for the problem are obtained and the reduced nonlinear ordinary differential equations are solved numerically. In case of porous plate, fluid velocity increases for increasing values of suction parameter whereas due to injection, fluid velocity is noticed to decrease. The non-dimensional temperature increases with the increasing values of injection parameter. A novel result of this investigation is that the flow separation occurred due to suction/injection may be controlled by increasing the permeability parameter of the medium. The effect of thermal radiation on temperature field is also analyzed.     

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.