Stretching/shrinking impact on the transient heat transfer in a radial moving porous fin of a longitudinal trapezoidal structure

The prime goal of the current pagination is to scrutinize the transient thermal response in a radial porous moving fin of a longitudinal trapezoidal structure. The solution of the constructed problem is heeded by a pdepe solver in Matlab, which works on the centered-finite difference technique. Darcy's model is utilized to investigate porous nature. A stretching/shrinking mechanism has been incorporated to improve the fin efficiency. Stretching reduces efficiency, whereas shrinking improves fin efficiency indicating major benefits of fin design consideration. The relevant temperature results are shown visually and discussed quantitatively in detail to evaluate the competence of the suggested fin. With a rise in the Peclet number, temperature distribution decreases. A similar nature is noted with respect to the power index of convective heat transfer coefficient, convection and radiation parameters, porous parameter, stretching/shrinking parameter, and thermal conductivity gradient with temperature. The graphical outcomes also show that the fin temperature amplifies with the ambient temperature parameter. Also, it is noticed that thermal distribution is a decreasing function of the power index of the convective heat transfer coefficient such that there is a decrease of 1.64% in temperature distribution as the power index increases. To support the validity of the solutions, a comparison was made with notable results from the existing literature for the specific case of this study. The novelty of the work is to study highly nonlinear boundary value problems and such nonlinearities are more relevant in the system that describes the thermal processing of materials. It is also noted that initial transient heat transfer vanishes quickly under steady-state conditions when the material is exposed to the ambient temperature.