Thermal Analysis of a Functionally Graded Conical Fin by Wavelets and Spectral Method

ABSTRACT Heat transfer by radiation with convection on a fully wet conical pin fin set in a uniform motion is considered. The pin fin is composed of a functionally graded material (FGM). As a result, thermal conductivity varies along its length, and three cases of such variations are examined: linear, quadratic, and exponential. The governing equation of the aforementioned model is nondimensionalized, and the resultant nonlinear differential equation is solved numerically using the Haar wavelet collocation method and validated using the spectral method. The advantage of using the quasilinearization technique in handling nonlinearity is demonstrated. The results obtained by these methods are in excellent agreement with each other. The influence of the critical dimensionless parameters on the temperature profile, tip temperature, base heat transfer rate, and efficiency of the conical fin in motion is analyzed graphically and quantitatively. Increasing the grading parameter enhances the thermal profile and efficiency in all three FGM cases. Maximum efficiency is achieved by scaling the grading parameter in the exponential FGM profile (36%) and minimizing the convective and radiative parameters. Peclet number positively influences the fin efficiency, unlike the wet parameter. The base heat transfer rate increases multifold with a controlled rise in the convection (127%), radiation (116%), and wet (200%) parameters.