A Similarity Approach for an Unsteady Two-dimensional Forced Convective Heat Transfer Boundary Layer Flow along a Convergent Channel

Abstract

The unsteady flow in a converging channel (“wedge nozzle”) is analyzed in the present paper. A specific similarity approach is used, which leads to a model where the temporal and spatial variables are combined into a single parameter in the flow problem. In the second part of the paper the problem of convective heat transfer is analyzed. Considering a variable wall temperature, there are two possibilities identified, leading to similarity solutions, namely a linear or an inverse linear wall temperature. Only the second case produces physical solutions. Numerical results are given in terms of skin friction and Nusselt number variations along the wedge nozzle and velocity and temperature boundary layer distributions. The obtained numerical results show that the skin friction increases along the wedge nozzle for positive values of unsteadiness parameter while it decreases for negative values of unsteadiness parameter. Results also show sharp variations in the streamwise direction of the Nusselt number, for larger values of the unsteadiness parameter.

Keywords: Wedge nozzle, unsteady flow, forced convection, boundary
layer.