| Summary: | Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and air conditioning. Because of this impetus, we investigated non-Newtonian fluid flow regimes from the perspectives of both heat and mass transfer aspects. In this study, heat transfer of electrical MHD non-Newtonian flow of Casson nanofluid over the flat plate is investigated under the effects of variable thermal conductivity and mass diffusivity. Emerging problems occur as nonlinear partial differential equations (NPDEs) in opposition to the conservation laws of mass, momentum, heat, and species transportation. The shown problem can be recast as a set of ordinary differential equations by making the necessary changes. A modified finite element method is adopted to solve the obtained set of ODEs. The numerical method is based on Galerkin weighted residual approach, and Gauss–Legendre numerical integration is adopted in the modified finite element method application procedure. To clarify the obtained results, another numerical technique is employed to solve the reduced ODEs. With the help of error tables and the flowing behavior of complicated physical parameters on estimated solutions, this study graphically and tabulatively explains the convergence of analytic solutions. Comparing some of the obtained results with those given in past research is also done. From the obtained results, it is observed that the velocity profile escalates by improving the electric parameter. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures.
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