Unique Analysis for Cascaded Rectangular–Triangular Fins with Convection–Radiation Transport

Abstract

A double-differential transform method has been used to analyze a cascaded rectangular–triangular fin losing heat by simultaneous convection and radiation to its surroundings. The base of the fin is heated by convection by a hot fluid at a uniform temperature. The thermal conductivity of the fin material assumed to be a linear function of temperature. An exact analytical solution is developed for a pure convection cascaded rectangular–triangular fin of constant thermal conductivity. Results are presented for the temperature distribution for a range of dimensionless parameters governing the problem. Both single- and two-material cascaded rectangular–triangular fins are analyzed. An optimization study has been performed to establish data for optimum heat transfer rate, cold fluid Biot number, fin efficiency, and fin effectiveness. If properly designed, a cascaded rectangular–triangular fin can be more effective than a rectangular or a triangular fin.