New Exact Solutions for Stokes First Problem of a Generalized Jeffreys Fluid in a Porous Half Space

2013 ◽  
Vol 477-478 ◽  
pp. 246-253
Author(s):  
Xiaoyi Guo
Keyword(s):  
Exact Solutions ◽  
Half Space ◽  
Fluid Model ◽  
Maxwell Fluid ◽  
Constitutive Relationship ◽  
New Exact Solutions ◽  
Fourier Sine Transform ◽  
The Laplace Transform ◽  
Porous Half Space ◽  
Relationship Of

The fractional calculus approach has been taken into account in the Darcys law and the constitutive relationship of fluid model. Based on a modified Darcys law for a viscoelastic fluid, Stokes first problem is considered for a generalized Jeffreys fluid in a porous half space. By using the Fourier sine transform and the Laplace transform, two forms of exact solutions of Stokes first problem for a generalized Jeffreys fluid in the porous half space are obtained in term of generalized Mittag-Leffler function, and one of them is presented as the sum of the similar Newtonian solution and the corresponding non-Newtonian contributions. As the limiting cases, solutions of the Stokes first problem for the generalized second fluid, the fractional Maxwell fluid and the Newtonian fluid in the porous half space are also obtained.

scholarly journals Exact Solutions of Rayleigh-Stokes Problem for Heated Generalized Maxwell Fluid in a Porous Half-Space

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Changfeng Xue ◽  
Junxiang Nie
Keyword(s):  
Exact Solutions ◽  
Half Space ◽  
Stokes Problem ◽  
Maxwell Fluid ◽  
Constitutive Relationship ◽  
Classical Solutions ◽  
Maxwell Fluids ◽  
Fourier Sine Transform ◽  
Porous Half Space ◽  
Generalized Maxwell Fluid

The Rayleigh-Stokes problem for a generalized Maxwell fluid in a porous half-space with a heated flat plate is investigated. For the description of such a viscoelastic fluid, a fractional calculus approach in the constitutive relationship model is used. By using the Fourier sine transform and the fractional Laplace transform, exact solutions of the velocity and the temperature are obtained. Some classical results can be regarded as particular cases of our results, such as the classical solutions of the first problem of Stokes for Newtonian viscous fluids, Maxwell fluids, and Maxwell fluids in a porous half-space.

Exact Solutions for Unsteady Magnetohydrodynamic Oscillatory Flow of a Maxwell Fluid in a Porous Medium

2013 ◽  
Vol 68 (10-11) ◽  
pp. 635-645 ◽  
Author(s):  
Ilyas Khan ◽  
Farhad Ali ◽  
Sharidan Shafie ◽  
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Transform Method ◽  
Transient Solutions ◽  
The Laplace Transform ◽  
Porous Half Space ◽  
The Given ◽  
Steady State Solutions

In this paper, exact solutions of velocity and stresses are obtained for the magnetohydrodynamic (MHD) flow of a Maxwell fluid in a porous half space by the Laplace transform method. The flows are caused by the cosine and sine oscillations of a plate. The derived steady and transient solutions satisfy the involved differential equations and the given conditions. Graphs for steady-state and transient velocities are plotted and discussed. It is found that for a large value of the time t, the transient solutions disappear, and the motion is described by the corresponding steady-state solutions.

A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

2020 ◽  
Vol 98 (1) ◽  
pp. 89-101 ◽  
Author(s):  
Nauman Raza ◽  
Muhammad Asad Ullah
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Maxwell Fluid ◽  
Heat Transfer Analysis ◽  
Flow Parameters ◽  
Fluid Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

New Exact Solutions of Steady Plane Flows of an In Compressible Fluid of Variable Viscosity

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Sobia Younus
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Compressible Fluid ◽  
Variable Viscosity ◽  
Plane Motion ◽  
Transformation Technique ◽  
Vorticity Distribution ◽  
New Exact Solutions ◽  
Steady Plane ◽  
Uniform Stream

<span>Some new exact solutions to the equations governing the steady plane motion of an in compressible<span> fluid of variable viscosity for the chosen form of the vorticity distribution are determined by using<span> transformation technique. In this case the vorticity distribution is proportional to the stream function<span> perturbed by the product of a uniform stream and an exponential stream<br /><br class="Apple-interchange-newline" /></span></span></span></span>

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