CONVECTIVE-RADIATIVE FIN OF IRREGULAR PROFILE WITH MULTIPLE NONLINEARITIES BY THE COLLOCATION SPECTRAL METHOD
In this paper, a collocation spectral method (CSM) is used to analyze the thermal performance of the fin of irregular profile with temperature dependent thermal conductivity, heat transfer coefficient, surface emissivity and internal heat generation. In this physical model of fin heat transfer, ambient fluid temperature and radiative sink temperature are considered to be non-zero. The distribution of temperature in the fin is discretized by spectral collocation points and Chebyshev polynomials. Thus, the differential form of energy equation is transformed to the matrix form of algebraic equation. In order to test the efficiency of the developed method, five different fins of triangular, trapezoidal, exponential, concave parabolic and convex profiles are examined. Results obtained by the CSM are assessed by comparing available results in references. These comparisons indicate that the CSM can be recommended as a good option to simulate and predict thermal performance of the convective-radiative fin.