Computation of flow of viscoelastic fluids by parameter differentiation

Abstract

SUMMARYA technique combining the features of parameter differentiation and finite differences is presented to compute the flow of viscoelastic fluids. Twe flow problems are considered: (i) three-dimensional flow near a stagnation point and (ii) axisymmetric flow due to stretching of a sheet. Both flows are characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. The exact numerical solutions are obtained using the technique described in the paper. Also, the first-order perturbation solutions (in terms of the viscoelastic fluid parameter) are derived. A comparison of the results shows that the perturbation method is inadequate in predicting some of the vital characteristic features of the flows, which can possibly be revealed only by the exact numerical solution.

On the second solution of flow of viscoelastic fluid over a stretching sheet

“…The BVP (1) and (2) accordingly was integrated numerically starting with Chang's solution for k = 0.5 using the technique of parameter differentiation (Ariel [7]), in which k was incremented by 0.01. It was confirmed that Chang's solution could be extended to k -1 where /"(0) became zero.…”