Analytical Modelling of Free Convection of non-Newtonian Nanofluids Flow in Porous Media with Gyrotactic Microorganisms Using OHAM

In this paper, free convection of non-Newtonian nanofluids over an impermeable vertical flat plate in a porous medium is studied. The medium contains both nanoparticles and gyrotactic microorganisms. The vertical plate is deemed to have prescribed temperature, nanoparticle concentration and density of motile microorganisms. Approximate analytical solutions for the dimensionless velocity, temperature, nanoparticle concentration, and density of the motile microorganisms are obtained using optimal homotopy asymptotic method (OHAM) and the effects of controlling parameters on dimensionless quantities such as velocity, temperature, nanoparticles concentration and density of motile microorganisms, as well as on dimensionless numbers such as local Nusselt, Sherwood and motile microorganism numbers are analyzed.