Analytical and numerical solutions for the boundary layer flow and heat transfer over a moving wedge in Casson fluid

Abstract

This paper presents exact, analytical, and numerical solutions to the two-dimensional Casson fluid boundary layer flow over a moving wedge with varying wall temperature. The boundary layer flow of the Casson fluid with varying wall temperature is governed by a system of partial differential equations called Prandtl boundary layer equations modified by Casson fluid. By applying similarity transformations the governing system of partial differential equations is reduced to a system of nonlinear ordinary differential equations called as the Falkner–Skan equation modified by Casson fluid flow with heat transfer (C-FSEHT). In the beginning, an exact solution of the C-FSEHT is obtained for the particular values of physical parameters (i.e., $\beta =-1$, $\text{Pr}=\frac{c}{c+1}$, $N=0$, see nomenclature) in terms of two standard functions, namely error function and exponential function. Thus, obtained exact solution is then modified to obtain the analytical solution of C-FSEHT for general values of physical parameters, in terms of power series. The analysis of the asymptotic behavior of the problem, when the wedge velocity is very large ($\lambda \to \infty$), is performed using the Dirichlet series. A comparative analysis is performed using the Chebyshev collocation technique (CCT) to validate the obtained results in all the scenarios. The effect of governing parameters, which are the Casson parameter $c$, Hartree pressure gradient parameter $\beta$, moving wedge parameter $\lambda$, Prandtl number $Pr$, and wedge temperature parameter $N$ on the skin friction coefficient, temperature coefficient, velocity profiles, and temperature profiles is discussed in detail. Multiple solutions are found analytically for fixed values of governing parameters. The fact that an increase in the value of the Casson parameter ($c$) reduces the thickness of both velocity and temperature boundary layers, is also validated during the study.