Exact solutions to heat transfer in straight fins of varying exponential shape having temperature dependent properties

This paper is concerned with the exact solutions for thermal diffusion in a straight fin with varying exponential shape when the thermal conductivity and heat transfer coefficients are temperature dependent. The conduction and heat transfer terms constitute the strong nonlinearity given by power laws. Explicit analytical solutions are derived for the relevant parameters in terms of special functions of advanced mathematics. The effects of parameters of physical interest such as the fin tip temperature, the fin efficiency and the fin base heat transfer rate can be better captured from the presented formulas. Moreover, with the help of the analysis here, the best shape of the straight fin is identified under a variety of operating conditions. Analysis further shows that the efficiency and base heat transfer rate of the exponential profiles are higher than those of the rectangular fin.

► Exact solutions for thermal diffusion in a straight fin with varying exponential shape are derived. ► Particular solutions are obtained where closed-form explicit forms are feasible. ► The fin tip temperature, the fin efficiency and the fin base heat transfer rate are mathematically formulated. ► The precise shape of the straight fin can be determined for the industrial applications. ► The efficiency and base heat transfer rate of the exponential profiles are higher than those of the rectangular fin.