Unsteady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface

The unsteady mixed convection boundary-layer flow of a micropolar fluid near the region of the stagnation point on a double-infinite vertical flat plate is studied. It is assumed that the unsteadiness is caused by the impulsive motion of the free stream velocity and by sudden increase or sudden decrease in the surface temperature from the uniform ambient temperature. The problem is reduced to a system of non-dimensional partial differential equations, which is solved numerically using the Keller-box method. This method may present well-behaved solutions for the transient (small time) solution and those of the steady-state flow (large time) solution. It was found that there is a smooth transition from the small-time solution (initial unsteady-state flow) to the large-time solution (final steady-state flow). Further, it is shown that for both assisting and opposing cases and a fixed value of the Prandtl number, the reduced steady-state skin friction and the steady-state heat transfer from the wall (or Nusselt number) decrease with the increase of the material parameter. On the other hand, it is shown that with the increase of the Prandtl number and a fixed value of the material parameter, the reduced steady-state skin friction decreases when the flow is assisting and it increases when the flow is opposing.