Unsteady axial flows of upper-convected maxwell fluid in pipe

Abstract EN

The present research involves an analytical examination of the unsteady axial flow of an incompressible viscoelastic upper-convected Maxwell fluid through a straight tube of circular cross-section in the absence of external forces.

The flow is considered initially at rest and the flow pattern is investigated through the velocity profiles for four cases of pressure-gradient field: (i) Constant pressure-gradient, (ii) Exponentially rising pressure-gradient with time, (iii) Exponentially falling pressure-gradient with time, and (iv) Periodic pressure-gradient.

Fourier-Bessel series solution is assumed in a general form for the velocity field.

The integral-transforms and the inverse derivative technique are used to obtain the exact solution of the considered initial-boundary value problem.

The limiting flow of the Newtonian fluids is well described in this approach by removing the relaxation-time dependence.

The velocity profiles have been determined.