Least square spectral collocation method for nonlinear heat transfer in moving porous plate with convective and radiative boundary conditions

Abstract

In this article, the least square spectral collocation method (LSSCM) is proposed to predict temperature distribution and heat transfer efficiency of moving porous plate. In this moving porous plate, heat is dissipated to ambient flow by radiation and convection, and generated by non-linear internal heat source. Two types of boundary conditions of this moving porous plate, constant temperature boundary condition, and combined convective and radiative boundary conditions are taken into account. Otherwise, radiation heat transfer in moving porous plate is also considered and assumed by Rosseland approximation. Different with traditional porous heat transfer, heat transfer equation of moving porous plate can be considered as a special kind of convective-diffusive equation with strong convection features. The convection term may cause non-physical oscillation of solutions. To overcome this non-physical oscillation, the least square scheme is adopted. Lagrange interpolation polynomials and Chebyshev collocation points are employed for spectral discretization. In order to validate LSSCM for this nonlinear heat transfer process, a test case is examined. The computational results by LSSCM agree well with analytical solutions, which shows that the present model is high accuracy and good flexibility to simulate nonlinear heat transfer in moving porous plate. Then, effects of thermo-physical parameters on dimensionless temperature and heat transfer efficiency are comprehensively investigated.