Impact of Variable Viscosity on Unsteady Couette Flow

Abstract

This research presents the effect of space-dependent and viscosity variation on the time-dependent flow of viscous, incompressible fluid in a finite channel (Couette flow). The viscosity of the fluids is assumed to grow exponentially. The governing equations and the boundary conditions are nondimensionalized with the aid of dimensionless parameters and solved semi-analytically using the Laplace transformation method and its numerical inversion approach called Riemann-sum approximation (RSA). Time-dependent velocity profiles, time-dependent skin frictions, and time-dependent mass flow rates of the fluids with variables viscosity and of the fluids with constant viscosity are obtained exactly in the Laplace domain in terms of modified Bessel functions of the first and second kinds. Due to the complexity of the solutions to the problem, the analytical procedure could not be obtained in the time domain, so the RSA is sought. For the validation of the method used, steady-state solutions of the velocity profiles, skin frictions, and the mass flow rates of the fluids with variable viscosity and constant viscosity are obtained analytically and compared with the numerical results. Graphs are plotted and tables are tabulated for the analysis of the effect of space-dependent and viscosity variation of the fluid flows. In the course of analysis, it is observed that the velocity profile is higher in the case where the fluid viscosity is constant compared with the variable viscosity.