EFFECTS OF VARIABLE VISCOSITY AND CONVECTIVE HEATING ON MHD NANOFLUID FLOW CONTAINING GYROTACTIC MICROORGANISMS WITH NAVIER SLIP

Abstract

The problem of temperature-varying properties of fluid is more complex than that of con- stant properties. The different property ratio correlations of different fluids increase the complexity of the variable-temperature properties problem. In this study, the effects of variable viscosity and convective heating on magneto-hydro-dynamics (MHD) nanofluid flow containing gyrotactic microorganisms with Navier slip are examined. Reynold’s vis- cosity model and Vogel’s viscosity model cases are considered. The dimensional partial differential equations that govern the nanofluid flow are transformed to dimensionless equations via appropriate similarity transformation. Similarity variables are used to transform the partial differential equations to ordinary differential equations together with the reduced Nusselt, Sherwood and density number of motile microorganisms. The resulting nonlinear coupled ordinary differential equations are consequently reduced to a system of first order ordinary differential equations. This system of equations are solved numerically using shooting technique along with fourth order Runge-Kutta integration scheme subject to the boundary conditions. The results are compared with available records. Major highlights of the problems are analyzed and discussed thoroughly. The results are displayed graphically with respect to variation in the controlling parameters on dimensionless velocity, temperature, nanoparticle volume fraction and density of motile microorganisms. The findings reveal that increase in convective heat parameter increases the nanofluid velocity and temperature but decreases the nanoparticle volume fraction and density of motile microorganisms’ profiles for both cases under consideration. Fur- thermore, the nanoparticle volume fraction and density of motile microorganisms’ profiles reduce with increase in Reynold’s viscosity variation parameter but increase with rise in Vogel’s viscosity variation parameter. However, reverse is the case as the velocity of ivthe nanofluid accelerates by increasing the Reynold’s viscosity variation parameter but deccelerates with increase in Vogel’s viscosity variation parameter. Meanwhile, increase in viscosity variation parameter enhance the temperature profile in both cases.