Dauda Gambo

This research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically explore the role of velocity of applied magnetic field. Here, our treatment of the governing momentum equations accountable for the flow is done using the classical Laplace transform technique and Riemann-Sum Approximation. The effects of the physical parameters such as time, relaxation time parameter, radii ratio, Hartmann number, variable mass parameter and velocity of applied magnetic field on the fluid phase velocity, dust phase velocity and skin friction have been illustrated pictorially. It is concluded that contrary to the known classical effect of boosting Hartmann number on velocity, both components of flow (fluid and dust phase) and skin friction are seen to be heightened with an overwhelming presence of velocity of applied magnetic field. For large time, it is anticipated that higher profiles for velocity and skin friction are seen with fluid phase and an accelerated moving wall.

Hydrodynamic behaviour of slip flow and radially applied exponential time-dependent pressure gradient in a curvilinear concentric cylinder is examined. A two-step method of solution has been utilized in resolving the governing momentum equation. Accordingly, the exact solution of the time-dependent partial differential equation is derived in terms of the Laplace parameter. Afterwards, the Laplace domain solution is then inverted to time domain using a numerical-based inverting scheme known as Riemann-sum approximation. The effect of various dimensionless parameters involved in the problem on the Dean velocity, shear stresses and Dean vortices is discussed with the aid of graphs. It is found that maximum Dean velocity is due to an exponentially growing time-dependent pressure gradient and slip wall coefficient. Stability of the Dean vortices is achieved by suppressing time, wall slippage and inducing an exponentially decaying time-dependent pressure gradient.

This investigation attempts to address heat and mass transfer behavior exhibited by a steady fully developed natural convective flow of a viscous, incompressible, and electrically conducting fluid in a vertical porous annulus in the presence of radially applied magnetic field and velocity slip. The motion of the fluid in the annular gap is triggered by the buoyancy forces due to temperature gradient of the inner and outer cylinders. The governing momentum and energy equations responsible for the flow are transformed into dimensionless forms using the appropriate dimensionless parameters. Accordingly, analytical solutions of the energy and momentum fields are derived with the appropriate boundary conditions. The effects of the controlling parameters involved in the flow on the temperature field, velocity field, and drag on the walls of the cylinders are illustrated graphically and with the aid of tables. Findings affirm that fluid temperature can be decreased/increased by increasing suction/injection on the porous wall. Furthermore, the fluid flow in the annular gap can be enhanced by increasing Grashof number, fluid injection, and velocity slip.

Our study probes the impact of an exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow in a curved concentric cylinder. A two-step method of solution has been employed in the treatment of the governing momentum equation. Accordingly, the exact solution of the time-dependent partial differential equation is derived in terms of the Laplace variable. The Laplace domain solution is then transformed to the time domain using a numerical inversing scheme known as Riemann-sum approximation. The effect of the various dimensionless parameters involved in the problem on the Dean velocity, skin drags and Dean vortex are illustrated graphically. It was established that maximum Dean velocity is due to an exponentially growing time-dependent pressure gradient. However, the instability of the Dean vortex is rendered less effective by reducing time and applying an exponentially decaying time-dependent pressure gradient.

This article deliberates fully developed natural convective flow of heat‐generating/absorbing fluid in open‐ended vertical concentric annulus under a magnetic field. The momentum and energy equations which arise from the definition of velocity and temperature are written in the dimensional form and then recast into the nondimensional form. Approximate solutions are obtained by using the semi‐analytical Adomian decomposition method. The solutions for the velocity, temperature, skin friction, mass flux and rate of heat transfer are obtained. The influence of physical parameters such as heat generation/absorption parameter and Hartmann number (M) are illustrated with the aid of graphs and tables. In the course of this investigation, it is found that an increase in the heat generation/absorption parameter increases the temperature. In addition, the magnitude of the temperature is higher for heat‐generating fluid in comparison to heat‐absorbing fluid. Furthermore, the temperature and velocity can be controlled by carefully selecting suitable values of the heat generation/absorption parameter and Hartmann number respectively.

Background: Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results: It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion: Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.