Non-Darcy Natural Convection Boundary Layer Flow Over a Vertical Cone in Porous Media Saturated with a Nanofluid Containing Gyrotactic Microorganisms with a Convective Boundary Condition

This article presents a numerical study of a natural convection about a vertical cone embedded in a non Darcian nanofluid containing gyrotactic microorganisms saturated porous medium. In addition, a convective boundary condition is considered into the model for nanofluid. The set of governing equations is transformed into a set of nonlinear ordinary differential equations by using unique similarity transformations. Runge-Kutta method of fourth order is used to solve these equations. The Brownian motion and thermophoresis effects are incorporated in the nanofluid model. The effects of convective parameter Bi (Biot number) (1 <= Bi <= infinity), thermophoresis parameter Nt (0.1 <= Nt <= 0.6), Brownian motion parameter Nb (0.1 <= Nb <= 1) and non-Darcy parameter ND (0 <= ND <= 1) with fixed values of other parameters Le = 10, Nr = 0.5, Pe = 0.2, Lb = 6, Rb = 0.1 and sigma = 0.3 on the dimensionless velocity and temperature are illustrated graphically. It is found that an increase in convective parameter leads to increasing both the dimensionless velocity and temperature. Also with an increase in non Darcy parameter, the dimensionless temperature increases, whereas velocity decreases. In addition, the dependency of the reduced Nusselt numbers and density number of the motion microorganisms on the governing parameters is discussed. It is found that the density number of the motion microorganisms decreases as the non-Darcy parameter and Rayleigh number increase, whereas it increases with increasing the convective parameter and buoyancy ratio parameter.