Transient Combined Convective Heat Transfer over a Stretching Surface in a Non-Newtonian Nanofluid Using Buongiorno’s Model

The present paper investigates the transient mixed convective boundary layer flow of an incompressible non-Newtonian quiescent nanofluid adjacent to a vertical stretching surface. The effects of the Brownian motion and thermophoresis are included for the nanofluid. Using appropriate non-similarity transformations the non-dimensional, coupled and highly non-linear system of equations is solved numerically using the efficient Keller-box implicit finite difference method for the whole transient from 0 t = (initial state) to t → ∞ (final steady-state flow). The box method is unconditionally stable. Numerical results for dimensionless velocity ( ′ f ), micro-rotation (g), temperature (θ), nanoparticle volume fraction (φ) at final steady state flow, skin friction function ( f x C Re 1 2 ), Nusselt number function ( x x Nu Re 1 2 ) and Sherwood number function ( x x Sh Re 1 2 ) have been presented on various parameters inform of tables and graphs. The results indicate that as Nb and Nt increase, the Nusselt number decreases whereas Sherwood number increases at initial and early state time but decreases at the final steady state time. As the K increases, the friction factor decreases whereas surface mass transfer rate and the surface heat transfer rates slightly increase. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work. The study has many practical applications such as extrusion of plastic sheets, paper production, glass blowing, metal spinning and drawing plastic films.