Multiscale finite element modeling and analysis of magnetically-influenced double diffusive Casson fluid flow in a complex domain

In this work, the development of a robust numerical scheme for solving the MHD mixed convective double diffusive Casson fluid flow in a doubly staggered cavity is presented. The mathematical model incorporates the effects of multiple forces arising from magnetic fields, double diffusive effects, non-Newtonian factors, and convective terms, among others. The stabilized scheme is derived using the algebraic subgrid scale variational multi-scale method, where the stabilization parameters are derived using Fourier analysis. This derivation follows the transformation of fine-scale terms into coarse-scale terms. Then we theoretically derive an a priori bound for the error between the computational solution and the exact solution and establish the convergence of the proposed scheme. After the code is validated against the benchmark results, simulations are carried out to trace the multiphysics associated with the flow and thermal fields because of several interacting forces in a two-staggered domain. The non-Newtonian behavior of the fluid is characterized by low β values. The flow characteristics for high Reynolds numbers, impact of Richardson number, Ri , Reynolds’ number, Re , Hartmann number, Ha have been studied. The highest rate of heat transfer is observed for the case with a Reynolds number of 4500, while the highest rate of mass transfer occurs for the case with a Richardson number of 10. The results provide fundamental insights into heat and species transport in confined geometries, with potential relevance to thermal management and contaminant dispersion in enclosed environments.