Regression analysis of Cattaneo-Christov heat and thermal radiation on 3D Darcy flow of Non-Newtonian fluids induced by stretchable sheet

This study explores the influence of thermal radiation and heat source on magnetized flow micropolar nanofluid through a Stretchable Sheet in the presence of mobile microbes. The presence of microorganisms adds a biological dimension to the problem, affecting fluid dynamics and heat transfer, which are central to this investigation. To motivate the problem, the flow is induced by a Darcy porous exponentially stretching sheet with generalized boundary conditions. A regression analysis is conducted to analyze the interplay of various parameters on the flow and heat transfer characteristics. Additionally, similarity transformations are implemented to transform the set of partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). The resulting equations are solved numerically using the shooting approach via the bvp4c platform in Matlab. The regression model quantifies the impact of each parameter and their interactions on the flow field, temperature distribution, and Darcy effects. Furthermore, the impact of involved parameters on flow, energy, volumetric concentration, density of microbes, and micro-rotations distribution are analyzed and discussed through graphs, literature, and tables. The findings of this research are crucial for various engineering, industrial, and pharmaceutical applications, including biofilm formation, geothermal energy extraction, and wastewater treatment processes.