The objective of this work is to analyze the impact of magneto-hydrodynamics flow across a stretching layer in the existing magnetic sector. The classifying boundary layer equations are converted to a set of non-linear equations by taking advantage of similarity structures. The transformed scheme is mathematically resolved by the homotopy analysis method. Results are measured numerically and plotted graphically for velocity and temperature distribution. Furthermore, flow and heat transfer effects for different physical parameters such as the stretching parameter, mixed convection parameter, magnetic parameter, heat generation coefficient, and Prandtl number are analyzed. Some physical effects reveal that an increase in the Hartmann number raises the fluid’s boundary layer that shows the reverse phenomena of Lorentz force because the speed of the free stream transcends the stretching surface. Upon verifying the homology of the current study with some past investigations, a good harmony is revealed. The velocity of the fluid flow was initially considered to be an increasing function of heat generation, buoyancy parameter, and magnetic field strength, but it later revealed as a decreasing function of the Prandtl number.

The present investigation is related to the analysis of boundary layer (BL) flow of hydro-magnetic non-Newtonian Casson fluid (CF) which is fruitful for understanding the rheology of the fluid model for electrolyte application as a case study for Silicon Composite micro-porous electrode as sandwich channel with Soret-Dufour Effects for Lithium-Ion Batteries. The study of motile microorganisms (MMs) in the Casson flow field near the point of stagnation gives some insights over the porous stretchable heated surface to discuss the physical phenomenon and will be interesting to elucidate that how the movement of these microorganisms influence the flow field and how this phenomenon can be monitored by other pertinent factors. Viscosity is considered to be a linear function of temperature in which the fluid flow lodges or entertains the diffusion processes, due to the concentration gradients as well as temperature. The fascinating vivid features are presented to physically inspect the characteristics of flow; when the viscosity is a map of the change in temperature (or temp gradient), the velocity profile raises but it manages the temperature's fluid in the reverse direction. The approximate numerical values are combined for physical parameters. The integration of micro-porous electrodes made with silicon matrix to serve as sandwich channels experiencing Soret-Dufour phenomena alongside innovative micro-organism based electrolytes completes a breakthrough as far as lithium-ion battery technology is concerned. These enhancements pave the way for various high-demand applications opening up new frontiers in the field of energy storage.