Comprehensive Computational Study on Transient Heat Transfer in Functionally Graded Longitudinal Fins under Time-Varying Laser Heating

Abstract

The present study assumes that the material properties of the fin vary by a force rule in the axial direction, with the exception of the thermal relaxation coefficient, which is assumed to be constant. The temperature distribution in the longitudinal fin with homogeneous cross-section exposed to the laser heat source is numerically investigated. This is because these constraints lead to a linear differential equation with partial solutions that cannot be analytically resolved using conventional methods, except for a few elementary order functions. Consequently, a linear or nonlinear system of equations as a function of time is obtained by transforming a differential equation attained with one or more independent factors using the highly efficient, potent, and practical semianalytical method known as the Chebyshev pseudospectral method. Temperature distributions in the fin are then examined in terms of different homogeneity factors and time- varying heat source capacity. Furthermore, the numerical solutions' convergence is emphasised, and the results are confirmed using homogeneous solutions from the literature.