Radiative Effects on Unsteady MHD Couette Flow through a Parallel Plate with Constant Pressure Gradient

In this paper, the unsteady MHD Couette flow through a porous medium of a viscous incompressible fluid bounded by two parallel porous plates under the influence of thermal radiation and chemical reaction is investigated. A uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to the constant pressure gradient. The transformed conservation equations are solved analytically subject to physically appropriate boundary conditions by using the Eigenfunction expansion technique. The influence of some emerging non-dimensional parameters namely, pressure gradient, suction parameter, radiation parameter, and Hartman number are examined in detail. It is observed that the primary velocity is increased with increasing pressure gradient while the increase in radiation parameter leads to adecrease in the thermal profile of the flow.

Role of Sudden Application or Withdrawal of Magnetic Field on MHD Couette Flow

This article investigates the impact of a sudden application or sudden withdrawal of a magnetic field on an unsteady MHD Couette flow formation in a parallel plate channel. The governing momentum equation is derived and solved exactly in Laplace domain using the Laplace transform technique with the necessary initial and boundary conditions to capture the present physical situation for the cases; sudden application or sudden withdrawal of a magnetic field. Due to the complexity of the solution obtained, the Riemann-sum approximation technique is used to transform the Laplace domain to time domain. During the course of graphical and tabular representations, results show that the Hartmann number, time and nature of application of a magnetic field play an important role in the transition from hydrodynamic to magnetohydrodynamic flow and vice-versa. Also, fluid velocity steady-state solution is independent on whether the magnetic field is fixed relative to the moving plate or to the fluid for sudden withdrawal of magnetic field. In addition, the application of a sudden magnetic field leads to a delay in the attainment of steady-state solution.

Novel numerical analysis of multi-term time fractional viscoelastic non-newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid

In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H1 norm and prove that their accuracy is of O(τ + h2) and O(τmin{3–γs,2–αq,2–β}+h2), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model.