# SOLVING TRANSIENT CONDUCTION AND RADIATION USING FINITE VOLUME METHOD

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2 transfer, the finite volume method (FVM) is extensively used to compute the radiative information. This method is a variant of the DOM. It does not suffer from the false-scattering as in DOM and the ray-effect is also less pronounced as compared to other methods. Since the FVM for the radiative heat transfer utilizes the same theory as that of the FVM of the CFD its computational grids are compatible with the FVMgrids that are utilized in the solution of the momentum and energy equations. The objective of the present work is to establish the compatibility of the FVM for the solution of the radiative transfer equation and for the determination of radiative information. The radiative transfer equation is solved using the FVM of the CFD and the conduction term is computed using error function. Here a Transient conduction and radiation heat transfer problem in one dimensional slab is being considered. For various parameters like heat flux, incident radiation energy, the conduction radiation parameter, results of the FVM have been computed. The number of iterations and CPU times for the converged solutions has also been reported. II. MATHEMATICAL FORMULATION The radiative transfer equation at any direction s and at any location for an absorbing, emitting and scattering gray medium is governed by The first term on the RHS in eq. (1) represents an attenuation of radiation intensity due to absorption and out-scattering, while the last term accounts for an augmentation of intensity due to gas emission as well as in-scattering. 83

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