Abstract
In this work, we investigate the time-dependent MHD free convection of Casson fluid across a vertical semi-infinite plate fitted inside a permeable medium, along with viscous dissipation, radiation absorption, and Soret effect by using several non-dimensional variables. The characteristics of a variety of elements influencing the flow phenomenon are examined using the Casson fluid model. The governing dimensional partial differential equations are transformed into an ordinary differential equation set by introducing the similarity variables. The reduced model is numerically solved via the Galerkin finite element method. The non-dimensional equations with suitable boundary conditions can be mathematically simplified using the efficient Galerkin finite element approach. The restrictions are shown numerically and graphically, and their effects on temperature, velocity, species concentration, and rate coefficients are all shown. This study is to present the influence of radiation absorption along with viscous dissipation on the heat transfer phenomenon. For different flow parameter estimations, graphs are generated for various flow profiles as well as skin friction coefficients. The Nusselt (Nu) and Sherwood (Sh) quantities are also demonstrated via graphs.