Exact solutions to nonlinear diffusion-convection problems on finite domains

1992 ◽  
Vol 33 (3) ◽  
pp. 384-401 ◽  
Author(s):  
G. C. Sander
Keyword(s):  
Exact Solutions ◽  
Nonlinear Diffusion ◽  
Lower Boundary ◽  
Finite Domain ◽  
Initial Condition ◽  
New Exact Solutions ◽  
Special Cases ◽  
Diffusion And Convection ◽  
Diffusion Convection ◽  
Finite Domains

AbstractNew exact solutions are presented for nonlinear diffusion and convection on a finite domain 0 ≤ z ≤ 1. These solutions are developed for the conditions of constant fluxes at both boundaries z = 0 and z = 1. In particular, solutions for the flux QL at the lower boundary z = 1, being a multiple of the flux Qs at the surface z = 0, (that is QL = aQs, where a = constant), are presented. Solutions for any constant, a, are given for an initial condition which is independent of space z. For the special cases (i) a = 1, and (ii) Qs = 0 and hence QL = 0, solutions are given for an initial condition which has an arbitrary dependence on z.

scholarly journals Fractional magnetohydrodynamics Oldroyd-B fluid over an oscillating plate

2013 ◽  
Vol 17 (4) ◽  
pp. 997-1011 ◽  
Author(s):  
Muhammad Jamil ◽  
Alam Khan ◽  
Nazish Shahid
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Infinite Plate ◽  
Second Grade ◽  
Oscillating Flows ◽  
New Exact Solutions ◽  
Special Cases ◽  
In Series ◽  
Similar Solutions ◽  
Oscillating Plate

This paper presents some new exact solutions corresponding to the oscillating flows of a MHD Oldroyd-B fluid with fractional derivatives. The fractional calculus approach in the governing equations is used. The exact solutions for the oscillating motions of a fractional MHD Oldroyd-B fluid due to sine and cosine oscillations of an infinite plate are established with the help of discrete Laplace transform. The expressions for velocity field and the associated shear stress that have been obtained, presented in series form in terms of Fox H functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary MHD Oldroyd-B, fractional and ordinary MHD Maxwell, fractional and ordinary MHD Second grade and MHD Newtonian fluid as well as those for hydrodynamic fluids are obtained as special cases of general solutions. Finally, the obtained solutions are graphically analyzed through various parameters of interest.

scholarly journals A modified generalized projective Riccati equation method

2016 ◽  
Vol 12 (6) ◽  
pp. 6318-6334
Author(s):  
Luwai Wazzan ◽  
Shafeek A Ghaleb
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
New Exact Solutions ◽  
Special Cases ◽  
Projective Riccati Equation Method

A modification of the generalized projective Riccati equation method is proposed to treat some nonlinear evolution equations and obtain their exact solutions. Some known methods are obtained as special cases of the proposed method. In addition, the method is implemented to find new exact solutions for the well-known Dreinfelds-Sokolov-Wilson system of nonlinear partial differential equations.

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