Magnetohydrodynamic bioconvective flow past an elongated surface with convective heat transport, and velocity slip in a non-Darcian porous regime

In recent times, bioconvection has numerous uses, like, biological and biotechnological problems. The present study describes the magnetic bioconvective Buongiorno's flow model with microorganisms in a stretchable area with convective heat transfer and second-order velocity slip in a non-Darcian porous regime. Here, the influence of variable viscosity, viscous dissipation, Joule heating, and heat source/sink are considered in the occurrence of higher-order chemical reactions. Employing proper similarity transformations leading equations are transformed to dimension-free form. The transformed equations are solved via MATLAB bvp4c problem solver. This study's main objective is to graphically analyze the effects of different pertinent factors on the density of motile microorganisms, velocity, concentration, temperature, number of motile microorganisms' density, skin friction, mass transport rate, and heat transport rate. The main findings drawn from this study are viscosity $\left(-5\le {\theta }_r\le -1\right)$ and magnetic parameter $\left(0.5\le M\le 3\right)$ lowers the fluid velocity. Biot number $\left(0.4\le B_i\le 0.6\right)$ increases fluid temperature, but reduces heat transport rates and skin friction. Schmidt $\left(0.5\le Sc\le 1\right)$ and Eckert numbers $\left(0.1\le E_c\le 3\right)$ reduce the fluid concentration. A rise of 0.3 in bioconvective Rayleigh number $\left(0.3\le R{a}_b\le 0.9\right)$ and 0.2 in buoyancy ratio number $\left(0.1\le N_r\le 0.5\right)$ causes a percentage drop in velocities of 8.79% and 3.91% (approximately), respectively, in the neighborhood of the sheet. Furthermore, the increase in Peclet number $\left(0.8\le P_e\le 1.5\right)$ by 0.2 lowers the density number of microorganisms by 28%. Additionally, the profile of motile microorganisms is improved by thermophoresis impact, while it is diminished by chemical reaction.