Unsteady heat transfer in non-axisymmetric Homann stagnation-point flows towards a stretching /shrinking sheet

Abstract

Abstract We have studied the unsteady non-axisymmetric Homann’s stagnation point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet in the presence of time dependent free stream. In a very recent paper Mahapatra and Sidui (2017) show a modification of Homann’s stagnation point flow over a rigid plate. Now if the plate is not rigid but linearly stretched as well as shrunk with velocities in x and y -directions, then there is a new family of asymmetric viscous stagnation-point flows depending on the unsteadiness parameter δ ( = σ ∕ | c | ) and the ratios of shear to the rate of linear stretching/shrinking of the sheet γ ( = b ∕ | c | ) , the strain-rate to the rate of linear stretching/shrinking of the sheet λ ( = a ∕ | c | ) in the range − ∞ γ , λ ∞ . Here a and b are the strain rate and shear rate of the stagnation-point flow respectively, σ is a positive constant whose dimension is t i m e − 1 and c is the rate of linear stretching/shrinking of the sheet along x - and y -axes at unit distance from origin when time, t = 0 . We have also studied the heat transfer in the flow. The temperature of the sheet is assumed to be higher than the ambient fluid temperature. The governing momentum equations are solved numerically using fourth order Runge–Kutta method with shooting technique. The effect of the various parameters on wall shear stress parameters, dimensionless velocities, displacement thicknesses and temperature distributions are analysed. A good agreement is found when we compare our numerical results of wall shear stress, displacement thickness and temperature distributions with their corresponding asymptotic value behaviours. For the flow past a shrinking sheet dual solutions are found to exist. Here we have made a stability analysis in the case of non-unique solutions to identify the stable solution.