Transient Dean flow in an annulus: a semi-analytical approach

Abstract

The mathematical model of a fully developed laminar transient flow formation between the gaps of two horizontally stationary concentric tubes forming concentric annulus due to the impact of sudden application of azimuthal pressure gradient is analysed. Analytical and numerical solutions of the momentum equations are obtained by the aid of two-step process. The first step is by solving the governing partial differential equation analytically by using Laplace transform technique in the Laplace domain. Using Riemann–sum approximation of Laplace inversion, the velocity and skin friction are then inverted to time domain. Expressions for steady-state velocity and skin friction are obtained for the validations of the method employed. In the course of numerical computations, it is observed that increase in dimensionless time $ (T ) $ leads to increase in velocity as well as skin friction at the surfaces of tubes. It is also found that at large values of dimensionless time $ (T ) $ , the velocity and skin friction reach steady state.

Keywords

• transient
• dean flow
• annulus
• riemann–sum approximation