The analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here. Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical illustrations
This paper presents a study for the influence of magnetohydrodynamic (MHD) on the oscillating flows of fractional Burgers’ fluid. The fractional calculus approach in the constitutive relationship model is introduced and a fractional Burgers’ model is built. The exact solution of the oscillating motions of a fractional Burgers’ fluid due to cosine and sine oscillations of an infinite flat plate are established with the help of integral transforms (Fourier sine and Laplace transforms). The expressions for the velocity field and the resulting shear stress that have been obtained, presented under integral and series form in terms of the generalized Mittag-Leffler function, satisfy all imposed initial and boundary conditions. Finall
... Show MoreThis paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the figures are plotted to show the effects of different parameters on the velocity profile.
This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for
... Show MoreIn this paper we present a study on Peristaltic of fractional generalized Maxwell viscoelastic fluid through a porous medium. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a porous medium in an inclined channel with slip effect. The governing equation is simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, permeability parameter, Froude number, Reynolds number and inclination of channel on
... Show MoreNumerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate th
... Show MoreIn this article, an efficient reliable method, which is the residual power series method (RPSM), is used in order to investigate the approximate solutions of conformable time fractional nonlinear evolution equations with conformable derivatives under initial conditions. In particular, two types of equations are considered, which are time coupled diffusion-reaction equations (CD-REs) and MKdv equations coupled with conformable fractional time derivative of order α. The attitude of RPSM and the influence of different values of α are shown graphically.
The aim of this paper is to study the combined effects of the concentration and the thermo-diffusion on the unsteady oscillation flow of an incompressible Carreau fluid through an inclined porous channel. The temperature is assumed to affect exponentially the fluid's viscosity. We studied fluid flow in an inclined channel under the non-slip condition at the wall. We used the perturbation series method to solve the nonlinear partial differential equations. Numerical results were obtained for velocity distribution, and through the graphs, it was found that the velocity of fluid has a direct relation with Soret number, Peclet number, and Grashof number, while it has a reverse variation with chemical reaction, Schmidt number, frequency of os
... Show MoreThis paper aims to study a mathematical model showing the effects of mass transfer on MHD oscillatory flow for Carreau fluid through an inclined porous channel under the influence of temperature and concentration at a slant angle on the centre of the flow with the effect of gravity. We discussed the effects of several parameters that are effective on fluid movement by analyzing the graphs obtained after we reached the momentum equation solution using the perturbation series method and the MATHEMATICA program to find the numerical results and illustrations. We observed an increased fluid movement by increasing radiation and heat generation while fluid movement decreased by increasing the chemical reaction parameter and Froude number. 
... Show MoreThe purpose of this study is to investigate the effect of an elastic wall on the peristaltic flow of Williamson fluid between two concentric cylinders, where the inner tube is cylindrical with an inelastic wall and the outer wall is a regular elastic sine wave. For this problem, cylindrical coordinates are used with a short wavelength relative to channel width for its length, as well as the governing equations of Williamson fluid in the Navier-Stokes equations. The results evaluated using the Mathematica software program. The Mathematica program used by entering the various data for the parameters, where the program shows the graphs, then the effect of these parameters became clear and the results mentioned in the conclusion. Williamso
... Show MoreThe purpose of this study is to calculate the effect of the elastic wall of a hollow channel of Jeffrey's fluid by peristaltic flow through two concentric cylinders. The inside tube is cylindrical and the outside is a regular elastic wall in the shape of a sine wave. Using the cylindrical coordinates and assuming a very short wavelength relative to the width of the channel to its length and using governing equations for Jeffrey’s fluid in Navier-Stokes equations, the results of the problem are obtained. Through the Mathematica program these results are analysed.