Impact of Cattaneo-Christov heat and surface temperature on viscoelastic non-newtonian micropolar nanofluids: Darcy exponential sheet flow with planktonic microorganisms

This paper investigates the influence of chemical reactions and variable magnetic field on three dimensional Oldroyd B micropolar nanofluids subjected to exponentially stretching sheet in the presence of motile microbes. The study incorporates several significant physical phenomena, including Cattaneo-Christov heat$,$ thermal radiation$,$ chemical reaction kinetics$,$ and Darcy-Forchheimer effects. A particularly novel aspect of PST (prescribed surface temperature) and PHF (prescribed heat flux) are taken into account. The governing nonlinear PDEs of Oldroyd B fluids with thermophoretic diffusion and Brownian motion are transformed in to nonlinear ODEs via similarity functions. The resulting set of nonlinear ODEs are solved numerically via MATLAB platform and compared the results with published literature through bvp4c built-in code for better agreement. The results of on different parameters like Peclet number, Forchheimer number, thermal relaxation time, chemical reaction, Prandtl number, Schmidt number, porosity parameter, heat source coefficient and magnetic parameter on Skin friction, Nusselt number, Sherwood number and motile density number are discussed in detail through graphs, tables and literature. It is declared that Skin friction coefficients decline for developed values of magnetic parameter$M$, porosity parameter$K_1$.and viscoelastic parameter$K_2$. The thermal boundary layer thickness decreases with growing value of Prandtl number. The findings have significant implications for industrial and engineering processes where heat transfer is major issue.