Heat and mass transfer characteristics in MHD Casson fluid flow over a cylinder in a wavy channel: Higher-order FEM computations

In this paper, an extensive analysis of heat and mass transfer characteristics of a Casson fluid flow past a cylinder in a wavy channel has been performed. Due to the non-availability of analytical solution the model represented by coupled non-linear partial differential equations has been simulated by implementing higher-order Finite Element Method (FEM). For the approximation of velocity, temperature, and concentration profiles, a finite element space involving the cubic polynomial (P3) is selected whereas the pressure estimation is accomplished through a space of quadratic polynomial (P2). Such a choice gives rise to 10 degrees of freedom for each of the velocity components, temperature, and concentration profile while 6 degrees of freedom for the pressure. The Newton's method is used to linearize the systems of equations. The linearized inner system of equations are solved with a direct solver PARDISO. Computational results are demonstrated in the form of velocity, isotherms, isoconcentrations, and for several quantities of interest including the drag and lift coefficients. It has been observed that both drag and lift coefficients show a decreasing trend with Magnetic parater M. In addition, for all values of Bn, the drag coefficient has a linear growth profile as a result of fluid forces dominating at higher values of Bn. Furthermore, the concentration is high in the center of the channel and has a decreasing trend as we move towards the walls.