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.
