Analysing flow and heat transfer of a viscoelastic fluid over a semi-infinite horizontal moving flat plate

Abstract

This paper presents a numerical study of the flow and heat transfer of an incompressible homogeneous second grade type fluid above a flat plate moving with constant velocity U. Such a viscoelastic fluid is at rest and the motion is created by the sheet. The effects of the non-Newtonian nature of the fluid are governed by the local Deborah number K (the ratio between the relaxation time of the fluid and the characteristic time of the flow). When K = ( 33 - 1 ) / 8 , a new analytical solution for this flow is presented and the effects of fluid's elasticity on flow characteristics, dimensionless stream function and its derivatives are analysed in a wide domain of K. A novel result of the analysis is that a change in the flow solution's behaviour occurs when the dimensionless stream function at the edge of the boundary layer, f ∞ , equals 1.0. It is found that velocity at a point decreases with increase in the elasticity of the fluid and, as expected, the amount of fluid entrained diminishes when the effects of fluid's elasticity are augmented. In our heat transfer analyses we assume that the surface temperature has a power-law variation. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Local similarity heat-transfer solutions are given for PST case when s = 2 (the wall temperature parameter) whereas when s = - 1 2 a similarity solution takes place in the case of prescribed wall heat flux. The numerical results obtained are fairly in good agreement with the aforementioned analytical ones.