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Computation of flow of viscoelastic fluids by parameter differentiation
Author(s) -
Ariel P. D.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650151105
Subject(s) - viscoelasticity , boundary value problem , computation , flow (mathematics) , mechanics , mathematics , rotational symmetry , perturbation (astronomy) , mathematical analysis , physics , thermodynamics , algorithm , quantum mechanics
A technique combining the features of parameter differentiation and finite differences is presented to compute the flow of viscoelastic fluids. Two 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.