Numerical simulation of unsteady MHD bio-convective flow with Cattaneo-Christov heat flux over a stretching surface

The study explores the properties of mass and heat transfer in a time-dependent, unsteady magnetohydrodynamic (MHD) flow over a permeable, radiative, and expanded surface, incorporating bio-convection, nanoparticle suspension, and gyrotactic bacteria dynamics. The model considers the effects of emission, speed slip, and bio-thermal convection in the fluid system. The Cattaneo-Christov heat flux model is employed to account for the finite speed of thermal diffusion, and the fourth-order Runge-Kutta method with the shooting technique is utilized for numerical solutions. Additionally, the study investigates the influence of mass suction, heat source, and aligned magnetic field on the boundary layer. The local concentration of mobile microorganisms decreases as the stretching parameter and bio-convection Schmidt both improve. The concentration φ(η) gets stronger, and when Sc values increase, it decreases. The concentration of microorganism $h\left(\eta \right)$ is strengthened by increasing angle β, but it is diminished by increasing $Pe,Sb$ and Sc, respectively.Even if the rate of temperature transmission ($Nu$) is maximal for positive values of A relative to negative values, the friction drags ($C_f$) are more powerful for negative values of A than for positive values of $A$.