Application of semi-analytical mathematical approach for thermal analysis of convective-radiative fin with variable specific heat

Abstract

Summary This research paper depicts the application of highly powerful and accurate semi-analytical methods, Differential transformation method (DTM) to portray the non linear temperature distribution of convective-radiative fin with variable specific heat. With the help of DTM, the nonlinear terms appeared in governing equations are reduced to recurrence relation with non-dimensional terms. A longitudinal fin of constant rectangular profile through which air flows in transverse direction at ambient temperature has been considered for present analysis. The governing differential equation and corresponding boundary conditions are decided based on the heat transfer in longitudinal fin. The governing equation is non-dimensionalised for successful application of DTM with generalised terms. The results of temperature distribution in fin have been obtained for a range of values of several parameters of DTM. The results have indicated that DTM is efficient and convenient tool for analysing nonlinear differential equations of several environments. Present results have been compared and analysed with other analytical methods available in literature.