Abstract
Abstract The present study used analytical and numerical methods to conduction works in functional graded material fin that is exposed to progressive boundary cooling and heating. The fin length was chosen as a direction to vary thermal characteristic in functionally graded material, and the physical properties were ascertained by the linear model. In heat sink, two approximation analytical techniques are employed to evaluated the thermal performance: one based on a mean value problem and the other strategy based on principle of the equivalent qualities. ANSYS APD’s numerical solution was based on a stepwise modification of characteristics. The outcomes indicated that the thermal conductivity ratio significantly influences temperature levels, with the terminal temperature levels of the functionally graded fin varying exponentially in relation to the thermal conductivity ratio. The influence of material index begins with the length of functionally graded material-fin where the fin’s terminus experiences the largest effect. A 6.756% is the maximum absolute error between numerical and analytical findings, which indicating a strong concordance between the two analysis methods.