Insight into the dynamics of electro-magneto-hydrodynamic fluid flow past a sheet using the Galerkin finite element method: Effects of variable magnetic and electric fields

The aim of this work is to investigate the influence of Arrhenius activation energy and variable thermal conductivity with EMHD fluid flow over a nonlinearly radiating stretching sheet in a porous medium. The main objective of this research is to study the effects of variable electromagnetohydrodynamic (EMHD) on fluid flow motion. The significance of the combined effects of electric and magnetic fields is useful where one can create a strong Lorentz force for industry applications. The fundamental laws, that is, conservation of mass, momentum, and energy equations, are given in the form of partial differential equations (PDEs). The current fluid flow problem is not similar, which means that the presented solution is local. The introduction of nonsimilarity variables transforms PDEs into a set of coupled ODEs. The resultant ODEs are not only solved computationally by MATLAB built-in solver bvp4c but the solution is also obtained with other numerical schemes that include the shooting method and the finite element method (FEM). In applying FEM, we choose the Galerkin method in which the weight function is equal to the shape function. The aforementioned numerical methods are implemented and programmed in MATLAB. Graphs illustrate the effects of various parameters on the velocity, temperature, concentration, and microorganism profiles. Physical parameters measure the roughness of the sheet (skin friction coefficient), heat transfer rate at the sheet (local Nusselt number), the mass transfer rate of the concentration gradient (local Sherwood number), and transfer rate of microorganisms at the sheet (density of motile microorganism). The skin friction coefficient increases for higher values of (K p ) and magnetic parameters (M). The local Sherwood number decreases for different values of activation energy. An excellent agreement of FEM results with other numerical methods, shooting method, and bvp4c has been achieved. Moreover, for particular cases, the current results have a good agreement with the published work.