Thermal performance of continuously moving radiative-convective fin of complex cross-section with multiple nonlinearities

Spectral collocation method (SCM) is adopted to predict the temperature distribution in the fin with temperature dependent thermal conductivity, heat transfer coefficient and surface emissivity. These temperature dependent properties or parameters cause multiple nonlinearities of energy equation. In order to reduce these multiple nonlinearities, a local linearization approach is adopted. The spatial distribution of dimensionless temperature is discretized by Lagrange interpolation polynomials. Accordingly, the differential form of energy equation is transformed to the matrix form of algebraic equation. The accuracy of the SCM model is verified by comparing SCM results with available data in references. Meanwhile, compared with analytical solutions, it can be found that the convergence rate of SCM approximately follows exponential law. In addition, effects of various physical parameters, such as Peclet number, thermal conductivity parameter, emissivity parameter, parameter of heat transfer coefficient, convective-conductive parameter and radiative-conductive parameter on the dimensionless temperature, the dimensionless fin-tip temperature and the volume adjusted fin efficiency are comprehensively analyzed.