Spectral collocation method for transient thermal analysis of coupled conductive, convective and radiative heat transfer in the moving plate with temperature dependent properties and heat generation

Abstract

The spectral collocation method is developed and formulated to solve transient thermal process in the moving plate with temperature dependent properties and heat generation. In this moving plate, thermal conductivity and surface emissivity are assumed as linear functions of temperature; and heat transfer coefficient and heat generation are considered as power exponent functions of temperature. The time domain of energy equation is discretized by fully implicit Euler scheme; the spatial domain of energy equation is discretized by Chebyshev polynomials and Chebyshev collocation points. Numerical results by the spectral collocation method are compared with analytical solutions. This comparison indicates that the spectral collocation method can obtain very high accuracy even using few nodes. Meanwhile, the spectral collocation method can provide the exponential node convergence rate for this present problem. Moreover, the effects of various dimensionless parameters, such as Peclet number, heat generation parameters, thermal conductivity coefficient, surface emissivity coefficient, power exponent of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter and dimensionless ambient temperature on transient temperature, efficiency and effectiveness of the moving plate are comprehensively investigated.