Abstract
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 t=0 (initial state) to (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 (), Nusselt number function () and Sherwood number function () 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.
Highlights
Mixed convection heat transfer problems in the boundary layer flows adjacent to the surface have many important applications in production and manufacturing processes
A detailed parametric study has been performed for the influence of Material parameter (K), buoyancy parameter (λ), Brownian motion parameter (Nb), buoyancy ratio parameter (Nr), Thermophoretic parameter (Nt), Prandtl number (Pr), and Schmidt number (Sc) on dimensionless velocity ( f ′ ), micro-rotation (g), temperature (θ), nanoparticle volume fraction (φ) at final steady state, skin friction function ( C f Re1x 2 ), Nusselt number function ( Nux Re1x 2 ) and Sherwood number function ( Shx Re1x 2 )
We have studied the problem of the unsteady mixed convection boundary layer flow of a non-Newtonian nanofluid over a stretching surface
Summary
Mixed convection heat transfer problems in the boundary layer flows adjacent to the surface have many important applications in production and manufacturing processes. [27] studied the unsteady free convection flow over a continuous moving vertical surface in an ambient fluid, and [28] [29] investigated theoretically various stretching problems in micropolar fluids. [32] studied the coupled heat and mass transfer intransient flow by mixed convection past a vertical stretching sheet embedded in a fluid-saturated porous medium in the presence of a chemical reaction effect. Motivated by the above-mentioned investigations and applications, in this present paper the main objective is to investigate the unsteady mixed convective boundary layer flow of an incompressible non-Newtonian nanofluid over a stretching vertical surface in a quiescent viscous and incompressible fluid. Such a study has to the authors’ knowledge far not appeared in the scientific literature
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