Transient generalized Taylor–Couette flow of a dusty fluid: A semi-analytical approach

Abstract

This paper discusses extensively the time-dependent flow of a dusty viscous, incompressible fluid in rotating horizontal annuli under the influence of an azimuthal pressure gradient. The momentum and continuity equations depicting the flow system alongside the initial and boundary conditions are non-dimensionalized and solved semi-analytically using Laplace transform and Riemann-sum approximation (RSA) method. The velocity, skin frictions, vorticity and mass flow rates are obtained in the Laplace domain and then inverted back to the time domain with the aid of RSA. Steady-state solutions for the velocity, skin frictions, vorticity and mass flow rates are presented analytically to check the validity of the method employed at large values of the time. The governing dimensionless parameters appearing in the flow phenomenon are examined with the aid of line graphs and tables for comparison. From the findings and numerical computations, it is found that at large values of time, t, the velocity, skin frictions, vorticity and mass flow rates reach steady-state. Physically, as the angular velocity of the dusty particles increases, so does the mass concentration of the dust particles, resulting in a reduction in the velocity of the dusty particles.

Keywords

• Transient
• Taylor–Couette flow
• Dusty particles
• Riemann-sum approximation
• Angular velocity