Thermal distribution through a moving longitudinal trapezoidal fin with variable temperature-dependent thermal properties using DTM-Pade approximant

The present inspection elaborates the thermal distribution through a convective-radiative longitudinal trapezoidal moving fin with an internal heat source by considering the linear and nonlinear temperature-dependent thermal conductivities and heat transfer coefficient. The non-dimensionalization of the energy equation is carried out using dimensionless terms, and the resulting nonlinear ordinary differential equation (ODE) is solved analytically using the differential transform method (DTM) with Pade approximant approach. Furthermore, the consequence of several non-dimensional parameters, namely thermal conductivity parameter, convection-conduction parameter, Peclet number, radiation-conduction parameter, fin taper ratio, temperature ratio parameter, and internal heat generation parameter on temperature gradient and fin efficiency is explained with the help of graphs. The significant primary results of the investigation illustrate that the thermal distribution through the fin gradually decreases as the magnitude of the convection-conduction parameter, temperature ratio parameter, and radiation-conduction parameter rise. In contrast, it upsurges for heat generation and thermal conductivity parameters.