Unsteady mixed convection boundary layer flow due to a stretching vertical surface

الملخص EN

Unsteady mixed convection boundary layer flow adjacent to a vertical, stretching surface in a viscous and incompressible quiescent fluid is studied in this paper.

The stretching velocity and the surface temperature are assumed to vary linearly with the distance along the surface.

Two equal and opposite forces are impulsively applied along the x-axis so that the wall is stretched, keeping the origin fixed in a viscous fluid of constant ambient temperature T∞ .

The transformed unsteady boundary layer equations are solved numerically using the Keller-box method for the whole transient from t = 0 (initial state) to t →∞ (final steady-state flow).

The equations for the early unsteady flow (0 < t << 1) are also solved analytically.

It is found that there is a smooth transition from the small-time solution to the large-time solution.

Results for the local skin friction coefficient and the local Nusselt number, temperature profiles as well as velocity profiles are presented for different values of the governing parameters, namely, the buoyancy parameter, λ (= constant), and Prandtl number, Pr.