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

Abstract

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 condition $Pr=1$. 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 temperature 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 ($\lambda \to \infty$). Nevertheless, in all the above-mentioned cases, the skin friction coefficient ($f″\left(0\right)$) and the heat transfer rate ($\theta \prime \left(0\right)$) 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.