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.

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.

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.

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