Abstract
We study the analytical and numerical behaviour of adiabatic shearing flows of viscoelastic fluids with temperature dependent viscosity, under several types of boundary conditions and an ‘oscillatory’ inertial force. We consider the shearing adiabatic flow of an incompressible Newtonian fluid with temperature dependent viscosity, caused by two types of shearing forces and a time dependent ‘oscillatory’ body force. Our first objective is to study the analytical behaviour of the solution of this problem. We show that the velocity and the stress are well behaved, provided the rate of change of viscosity with temperature satisfy appropriate bounds, that correspond to the type of the fluid. Our second objective is to devise a numerical solution of the problem and study its behaviour. The numerical results obtained indicate an agreement between the analytical and numerical behaviour.
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