A numerical study of new fractional model for convective straight fin using fractional-order Legendre functions

Abstract

The Fractional-order model of fin problem in the presence of a temperature-dependent rate of internal heat generation in fin material has been studied in the proposed paper. Fractional-order Legendre functions (F-OLFs) with the Galerkin approach has been used to compute the result of the proposed fin problem. The exact solution is also calculated in a particular case of our fractional-order fin problem. The proposed fin problem has been presented in the non-dimension form. Temperature distribution in the straight fin is calculated for different values of used variables or parameters along space coordinate. The impact of different parameters such as fractional order, fin parameter, internal heat generation, generation number, etc. on the temperature profile in the fin is described in detail. The cooling process is faster in fractional order fin problem than the integer-order.