Abstract
This paper aims to examine the combined effects of Arrhenius activation and microorganisms on unsteady flow through a porous medium with thermophoresis and Brownian motion over an inclined stretching sheet. The governing partial differential equations are transformed into a set of non-linear ordinary differential equations using similarity analysis. The resultant non-linear coupled ordinary differential equations are solved numerically using the boundary value problem solver in MATLAB. The effects of the physical parameter such as magnetic field parameter ([Formula: see text]), thermal radiation parameter ([Formula: see text]), permeability parameter ([Formula: see text]), Eckert number ([Formula: see text]), thermophoresis parameter ([Formula: see text]) and Brownian motion parameter ([Formula: see text]) on the velocity, temperature, concentration profiles, skin friction coefficient, Nusselt number, and the local Sherwood number are presented and analysed graphically. The comparison has been made with previously published work, and there is a good agreement. These results may be helpful in geothermal engineering, energy conversation and disposal of nuclear waste material. Furthermore, scientists can employ this technique in medical fields such as gene therapy and the synthesis of drug delivery systems.