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Conductive and convective heat transfer with radiant heat flux boundary conditions Sikka, Satish

Abstract

Some conductive and convective heat transfer problems with radiative boundary conditions are analysed theoretically. Three specific problems have been analysed. The study has, therefore, been divided into three parts. In Part I the temperature distribution produced in-long, solid circular and rectangular cylinders and a solid sphere in interplanetary space is studied. The solid bodies receive parallel radiation flux on one side and emanate radiant energy to their surroundings at zero degree Rankine. Steady state, constant physical and surface properties, and no heat loss by convection are assumed. Solution of the linear conduction equation with nonlinear boundary conditions is obtained by two approximate, semi-analytical methods, (i) point matching and (ii) least-squares fitting. The results are compared with earlier results obtained by a variational method. The least-squares fit method appears to be most suitable regarding accuracy and simplicity in computation. Its accuracy does not appear to depend appreciably either on the radiation-conduction parameter or on the surface absorptivity. The effect of semi-grayness of the receiving surface is analysed. In Part II the heat transfer characteristics of a circular fin dissipating heat from its surface by convection and radiation are analysed. The temperature is assumed uniform along the base of the fin and constant physical and surface properties are assumed. There is radiant interaction between the fin and its base. Two separate situations are considered. In the first situation heat transfer from the end of the fin is neglected. Solution of the linear conduction equation with nonlinear boundary conditions has been obtained by the least-squares fit method. A solution has also been obtained by the finite difference method and the results compared. Results are presented for a wide range of environmental conditions and physical and surface properties of the fin. In the second situation heat transfer from the end of the fin is also included in the analysis. The solution is obtained by a finite difference procedure. It is shown that neglecting heat transfer from the end is a good approximation for long fins or for fins of high thermal conductivity material. In Part III the problem of laminar heat transfer in a circular tube under radiant heat flux boundary conditions has been analysed. Fully developed velocity profile is assumed and the tube is considered stationary. A steady radiant energy flux is being incident on one half of the tube circumference while the fluid emanates heat through the wall on all sides by radiation to a zero degree temperature environment. A solution by finite difference procedure has been obtained. The temperature distribution and the Nusselt number variation are presented for a wide range of the governing physical parameters.

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