Unsteady heat transfer in impulsive Falkner–Skan flows: constant wall heat flux case

Abstract

A theoretical study of the heat transfer in the unsteady thermal boundary layer associated with the forced convection flow past a sharp, semi-infinite wedge that is started impulsively from rest and for which the constant heat flux at the walls is suddenly changed is presented in this paper. The velocity far from the wedge is given by ue (x) = xm, where x is the coordinate measured along the wedge and m is a constant. Using appropriate non-dimensional transformations, the number of independent variables in the governing boundary-layer equations is reduced from three to two. These equations are then solved numerically for both small (initial) and large (steady-state) times. It is found that for the steady-state flow the Blasius-like solutions exist for each value of m in the range m* ≤ m < ∞, where m* is the value of the power law exponent m that corresponds to a self-similar solution profile with vanishing skin friction.