Unified Approach for Transient Heat Transfer in a Longitudinal Fin with Functional Grading

Abstract

A longitudinally finned fin composed of functionally graded materials (FGMs) with a constant cross-sectional area is the subject of this article, which aims to present its transient thermal behaviour. The transient thermal performance of the longitudinally finned fin made of FGMs is investigated assuming the fin has an adiabatic tip. The longitudinal variation in thermal conductivity in the FGM fin properties is adapted into four types of variations, namely linear, quadratic, exponential, and power, and this results in non-uniform and two-point linear boundary value problems that are numerically resolved. These problems are solved using the pseudospectral Chebyshev method. Two characteristics, the traditional fin parameter and the fin's thermal conductivity rating parameter, affect how well a fin transfers heat. Results from the study are shown for selected values of the fin parameter and thermal conductivity rating parameter, including dispersion of temporal temperatures, base heat flux, loss of convectional heat, the fin's energy reserve, and fin effectiveness. The results demonstrate that both transient and steady-state performing of the fin are significantly influenced by the functional grading of the fin materiel. The findings suggest that the pseudospectral Chebyshev method is highly accurate and easy to use, making it a suitable option for solving engineering problems. It can be easily applied to such problems without much difficulty.