Exact and analytical solutions for self-similar thermal boundary layer flows over a moving wedge

This article aims to achieve exact and analytical solutions for the classical Falkner-Skan equation with heat transfer (FSE-HT). Specifically, when the pressure gradient parameter beta = -1, there already exists a closed-form solution in the literature for the Falkner-Skan flow equation. The main purpose here is to extend this case to obtain a closed-form solution to the heat transport equation with the solubility condi-tion Pr = 1. An algorithm is presented and is found to be new to the literature that enriches the physical properties of FSE-HT. It is shown that for the moving wedge parameter lambda > 1, the momentum and tempera -ture equations show multiple solutions analytically. The skin friction coefficient and the heat transfer rate are also obtained in analytical form. The thus-obtained solution is then adapted to derive an analytical solution applicable to a wide range of pressure gradient parameters beta and Prandtl numbers Pr. Furthermore, an asymptotic analysis is conducted, focusing on scenarios where the moving wedge parameter becomes significantly large (lambda -> infinity). Nevertheless, in all the above-mentioned cases, the skin friction coefficient (f ''(0)) and the heat transfer rate (theta '(0)) are compared with the direct numerical solutions of the boundary layer equations, and it is found that the results are in good agreement. These solutions provide a benchmark and shed light on further studies on the families of FSE-HT.