Transient generalized Taylor-Couette flow: a semi-analytical approach

Abstract

Semi-analytical solution of transient generalized Taylor-Couette flow of a viscous, incompressible fluid between the gaps of concentric rotating cylinders under applied azimuthal pressure gradient ispresented. The dimensionless governing equations are transformed into standard Bessel equation with the aid of Laplace transformation technique and by a suitable transformation. Analytical solution of the Besselequation is obtained and the Riemann-sum-approximation method of Laplace inversion is utilized. The solution obtained is validated by comparing the Riemann-sum-approximation solution with the exact steady-statesolutions obtained separately. The velocity profile and skin frictions on both surfaces of cylinders are depicted graphically and discussed. The present study reveals that the velocity profile of the fluid is enhanced withincrease in time, and angular velocity,. The velocity profile attains fully developed state at large values of. In addition, increase in pressure gradient, increases the velocity profile of the fluid. Furthermore, back flow occursfor adverse pressure gradient.

Keywords

• transient
• generalized taylor-couette flow
• riemann-sum approximation
• annulus
• azimuthal pressure gradient