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.
The mathematical model responsible for fully developed laminar transient flow formation between the gaps of two stationary concentric porous tubes due to the imposition of azimuthal pressure gradient (Dean flow) is solved semi-analytically. The tubes walls are porous so that a radial flow can be superimposed. The solution of the momentum and continuity equations are obtained semi-analytically by using the combination of Laplace transform technique and a Laplace inversion method called Riemann sum approximation method. The solutions for skin friction at [Formula: see text] (outer surface of the inner porous tube) and [Formula: see text] (inner surface of the outer porous tube) are presented. The impact of suction/injection parameter and the ratio of the radii of the tubes are examined for the velocity profile and skin friction. Results show that the velocity profile decreases with increase in suction/injection parameter for various values of time, [Formula: see text] and at large value of time, ([Formula: see text]), the velocity and the skin friction attain a steady state.
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.
ARTICLE HISTORY
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.