On the flow of MHD generalized maxwell fluid via porous rectangular duct

The purpose of this proposed investigation is to study unsteady magneto hydrodynamic (MHD) mixed initial-boundary value problem for incompressible fractional Maxwell fluid model via oscillatory porous rectangular duct. Considering the modified Darcy’s law, the problem is simplified by using the method of the double finite Fourier sine and Laplace transforms. As a limiting case of the general solutions, the same results can be obtained for the classical Maxwell fluid. Also, the impact of magnetic parameter, porosity of medium, and the impact of various material parameters on the velocity profile and the corresponding tangential tensions are illuminated graphically. At the end, we will give the conclusion of the whole paper.

Influence of Inclined MHD on Unsteady Flow of Generalized Maxwell Fluid with Fractional Derivative between Two Inclined Coaxial Cylinders through a Porous Medium

"This paper presents a study of inclined magnetic field on the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative between two inclined infinite circular cylinders through a porous medium. The analytic solutions for velocity field and shear stress are derived by using the Laplace transform and finite Hankel transform in terms of the generalized G functions. The effect of the physical parameters of the problem on the velocity field is discussed and illustrated graphically.

The First Solution for the Helical Flow of a Generalized Maxwell Fluid within Annulus of Cylinders by New Definition of Transcendental Function BNrrn

Most articles choose the transcendental function B1rrn to define the finite Hankel transform, and very few articles choose B0rrn. The derivations of B0rrn and B1rrn are also considered the same. In this paper, we find that the derivative formulas for the transcend function BNrrn are different and prove the derivative formulas for B0rrn and B1rrn. Based on the exact formulas of B0rrn and B1rrn, we keep on studying the helical flow of a generalized Maxwell fluid between two boundless coaxial cylinders. In this case, the inner and outer cylinders start to rotate around their axis of symmetry at different angular frequencies and slide at different linear velocities at time t=0+. We deduced the velocity field and shear stress via Laplace transform and finite Hankel transform and their inverse transforms. According to generalized G and R functions, the solutions we obtained are given in the form of integrals and series. The solution of ordinary Maxwell fluid has been also obtained by solving the limit of the general solution of fractional Maxwell fluid.

The analytic solutions for the unsteady rotating flows of the generalized Maxwell fluid between coaxial cylinders

In this paper, we consider the unsteady rotating flow of the generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field is determined by means of the combine of the Laplace and finite Hankel transforms. The analytic solutions of the velocity and the shear stress are presented by series form in terms of the generalized G and R functions. The similar solutions can be also obtained for ordinary Maxwell and Newtonian fluids as limiting cases.

Analysis of thin film flow of generalized Maxwell fluid confronting withdrawal and drainage on non-isothermal cylindrical surfaces

This investigation is concerned with the study of thin film flow of a generalized Maxwell fluid along with slip conditions, confronting withdrawal and drainage on non-isothermal cylindrical surfaces. The governing equations have been formulated from the continuity equation, momentum equation, and energy equation. Analytical solutions for the velocity field, volume flow rate, average film velocity, tangential stress, and temperature are obtained in series form through the Binomial expansion technique in both withdrawal and drainage cases. The well-known solutions for a Newtonian fluid are regained as a particular case of our acquired general solutions in all flow cases. In addition, solutions for the power-law fluid model, executing alike motion, can be recovered as a limiting case of our acquired general solutions. The influence of different dimensionless parameters on all physical quantities (i.e. velocity, volume flow rate, average film velocity, tangential stress, and temperature profile) is examined and discussed graphically for both generalized Maxwell and Newtonian fluids.