Thermal transport and bio-convection transport phenomenon in non-Newtonian couple stress model via OHAM through Darcy-Forchheimer porous medium

Throughout a Darcy-Forchheimer porous medium, the Optimal Homotopy Analysis Method (OHAM) is utilized in this work to investigate the combined impacts of heat transport and bio-convection in a non-Newtonian pair stress fluid. Enhancing efficiency in biomedical and engineering applications, the discoveries are important for comprehending heat and mass transport in intricate biological and industrial systems. By using a similarity transformation, the complex governing equations are transformed into nonlinear ordinary differential equations. The bioconvection microbe, temperature, velocity, and concentration are all displayed both analytically and visually. Variable thermal conductivity, diffusion coefficients, and a bio convection equation are also used to improve modeling accuracy. As the temperature exponent, time relaxation, and Prandtl number increase, the temperature field decreases. The concentration field is increased by the temperature exponent and enhanced thermophoresis.