Unsteady Flow of a Nanofluid over a Sphere with Nonlinear Boussinesq Approximation

A theoretical study is presented for transient mixed convection flow of a nanofluid in the forward stagnation region of a heated sphere that is rotating with time-dependent angular velocity, taking nonlinear Boussinesq approximation into account. The nanofluid is treated as a two-component mixture (i.e., nanoparticles distributed homogenously in a base fluid). The effects of the Brownian motion and thermophoresis are included for the nanofluid flow. The first and second laws of thermodynamics are employed to study thermophysics as well as heat and mass transfer phenomena. The governing equations are transformed into a system of dimensionless, nonlinear, coupled, differential equations using suitable transformation, which are then solved numerically by applying the Keller box method. The accuracy of the obtained numerical results is validated via comparison to previously published results for special cases. Primary shear stress is boosted with increasing mixed convection parameter and Brownian motion effect, whereas secondary shear stress is depressed. Temperatures are suppressed with increasing nonlinear temperature parameter, whereas nanoparticle concentrations are elevated.