Heat transfer analysis of fluid flow over a nonlinear porous radially moving sheet: Benchmark solutions

The mathematical study focuses on the exact solutions of Casson fluid flow on a radially stretching/shrinking porous sheet subject to the convective boundary condition. The findings of this study have the potential to be applied in a wide variety of biological systems, such as blood flow through arteries and veins, as well as in engineering processes, such as extrusion and spinning. It is possible to optimize the design and performance of these systems by understanding these phenomena. The physical situation governing the problem is modeled in the form of highly non-linear PDEs, which are simplified by employing a similarity variable and reduced to a system of ODEs so that the analytical solutions can be obtained. The vast majority of studies used numerical approaches. The research involves a number of phenomena, including Casson fluid flow, thermal radiation, heat source/sink, porous stretching/shrinking axisymmetric sheet, and convective boundary conditions. The energy equation was solved with the help of hypergeometric Kummer's function. Plots show the behavior of the suction/injection, Casson, stretching/shrinking, radiation, heat source/sink parameters, and Biot number on the velocity and temperature distributions. As part of this work, a table is provided to illustrate the variation of some parameters on the heat transfer rate and compare it to the numerical results. Also, the effects of the parameters on the heat transfer rate were depicted. The findings show that the Biot number directly affects the heat transfer rate in the shrinking case of a porous disk. Compared to the heat source/sink parameters, the suction/injection parameters affect the local Nusselt numbers to an increased extent.