全谱方法求解平行平板间非线性各向异性散射介质内辐射换热

he full spectral method (FSM) is proposed to address the problem of radiation heat transfer in parallel planes with a nonlinear anisotropic scattering medium. In the solving process, the nonlinear anisotropic scattering phase function of radiation transfer equation is expressed by finite series of Legendre polynomials; the spatial differential term and the scattering integral term are expressed by finite series of Chebyshev polynomials; the spatial and angular distributions of radiation intensity are discretized by the spectral method. Then, the integral-differential form of radiation transfer equation can be converted into matrix form of algebraic equation. Taking radiation heat transfer in space-dependent scattering medium with semitransparent boundary as an example, we test the performance of FSM for solving radiation heat transfer in nonlinear anisotropic scattering medium. Comparisons of FSM results, analytic solutions, least square finite element solutions and spectral collocation method are performed based on discrete ordinates method (SCM-DOM) results. These comparisons indicate that FSM results are in good agreement with those results, and FSM has a good accuracy. Meanwhile, with the increase of collocation points, the computational error of FSM decreases with an exponential trend. FSM can also obtain satisfactory results even using a small number of nodes.