ANALYTICAL INVESTIGATION FOR FREE CONVECTIVE FLOW OF NON-NEWTONIAN NANOFLUIDS FLOW IN POROUS MEDIA WITH GYROTACTIC MICROORGANISMS

An approximate analytical investigation for free convection of non-Newtonian nanofluids over an isothermal impermeable horizontal flat plate, which is placed in a porous quiescent medium filled with non-Newtonian power law nanofluids, is carried out in this paper. A further assumption is also made that the medium contains both nanoparticles and gyrotactic microorganisms. The horizontal plate is deemed to have uniform surface temperature, solute, nanoparticles concentration, and density of motile microorganisms. The governing equations are transformed into a system of non-linear ordinary differential equation using suitable similarity transformations. Approximate analytical solutions for the dimensionless velocity, temperature, nanoparticle concentration, and density of the motile microorganisms are obtained using the optimal homotopy asymptotic method (OHAM). The effects of important control parameters on the dimensionless velocity, temperature, nanoparticles concentration, and density of motile microorganisms, as well as on the local Nusselt, Sherwood, and motile microorganism numbers, are obtained and analyzed. It is found that nanofluid and bioconvection parameters have strong effects on local Nusselt, Sherwood, and density numbers.