Wavelets and the discrete ordinate method for the solution of radiative heat transfer through a participating medium

Wavelet method is applied to the study of radiative heat transfer and combined conductive-radiative heat transfer through the gray and nongray participating medium in one- and two-dimensional (1-D and 2-D) geometries. The participating medium is assumed to have an index of refraction of unity and to be absorbing, emitting, and nonscattering. The surfaces of 1-D infinite parallel plates and 2-D rectangular enclosure are assumed to be black and isothermal. The governing equations are the radiative transfer equation (RTE) and energy equation. The wavelet expansion is used to evaluate the spectral dependence of radiative intensity in RTE. And a set of differential equations about the expansion coefficients are developed by applying Galerkin method and discrete ordinates method (DOM). For 1-D problem, these equations are solved by finite difference method, and for 2-D problem, they are solved by finite volume method. The energy equation is solved simultaneously by applying the modified quasi-linearization algorithm (MQA) to obtain the temperature distribution and heat flux. The results for the cases of radiative equilibrium, uniform internal heat generation, and combined conductive-radiative heat transfer with gray and nongray medium are given and compared with those obtained by other methods. The optical thickness of the medium ranges from optical thin to optical thick. The conduction-radiation parameter varies from radiation-dominated to conduction-dominated situations. The method is proved to be a powerful tool in analyzing the radiative heat transfer through the nongray participating media. The results of 2-D nongray problems are first presented