Muhammad R. Mohyuddin

The flow of a non-Newtonian fluid induced due to the oscillations of a porous plate

An analytic solution of the flow of a third-grade fluid on a porous plate is constructed. The porous plate is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous plate is also examined. It is also shown that in case of third-grade fluid, a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. Several limiting situations with their implications are given and discussed.

Unsteady flow of a third-grade fluid in the case of suction

The flow of an incompressible third-grade fluid along an infinite permeable wall is discussed. The nonlinear partial differential equation resulting from the momentum equation is solved analytically. Effects of suction and material parameter of third-grade fluid on the flow phenomena are analyzed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.

On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.

HYDROMAGNETIC UNSTEADY RIVLIN-ERICKSEN THIRD-GRADE FLOW FOR STOKES' SECOND PROBLEM

In this article, the flow of an unsteady third-grade Rivlin-Ericksen fluid on an oscillating plate is discussed. The magnetic lines of force act perpendicular to the flow field. Several interesting features of the flow are obtained. The physical interpretation of the second-grade parameters, third-grade parameters, oscillating frequency, and magnetohydrodynamic parameters are examined graphically and then are deduced to already known results in the literature.

Inverse solutions for a second-grade fluid for porous medium channel and Hall current effects

Assuming certain forms of the stream function inverse solutions of an incompressible viscoelastic fluid for a porous medium channel in the presence of Hall currents are obtained. Expressions for streamlines, velocity components and pressure fields are described in each case and are compared with the known viscous and second-grade cases.

On semi-inverse solutions for the time-dependent flows of a second-grade fluid

This paper deals with analytical solutions for the time-dependent equations arising in a second-grade fluid. The solutions have been developed by assuming certain forms of the stream function. Expressions for velocity components are obtained for flows in plane polar, axisymmetric cylindrical, and axisymmetric spherical polar coordinates. The obtained solutions are compared with existing results.

Few exact solution of the stokes’ problem with slip at the wall in case of suction/blowing

We provide an analytic solution for the problem of the unsteady, incompressible viscous fluid flow in the case of variable suction/blowing by applying similarity transform; the ‘slip’ condition at the boundary is considered. Several special cases with their solutions are given and are discussed graphically. It is observed that with an increase in suction the velocity increases and hence the boundary layer thickness decreases and with increase in blowing the velocity decreases and boundary layer thickness increases. It is also found that with an increase in slip parameter the velocity decreases.