Exact solution of the transport equation in finite media with a plane and uniform point source and flux normally incident at the faces from outside

1991 ◽  
Vol 176 (2) ◽  
pp. 217-262 ◽  
Author(s):  
S. Bishnu ◽  
S. R. Das Gupta
Keyword(s):  
Exact Solution ◽  
Point Source ◽  
Transport Equation

A simple exact solution for a point source above a reacting surface

1991 ◽  
Vol 89 (4B) ◽  
pp. 1991-1991
Author(s):  
Xiao Di ◽  
Kenneth E. Gilbert
Keyword(s):  
Exact Solution ◽  
Point Source

An exact solution for a normal point source problem

2004 ◽  
Vol 49 (7) ◽  
pp. 653-657
Author(s):  
Kaixin Liu ◽  
Guangyu Liu
Keyword(s):  
Exact Solution ◽  
Point Source

scholarly journals ACCURATE MODELLING OP TWO-DIMENSIONAL MASS TRANSPORT

1984 ◽  
Vol 1 (19) ◽  
pp. 163
Author(s):  
Lance Bode ◽  
Rodney J. Sobey
Keyword(s):  
Exact Solution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Transport Equation ◽  
Spatial Dimension ◽  
Convective Transport ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Numerical Errors ◽  
Moving Coordinate

Any numerical solution of the convective transport equation in an Eulerian framework will exhibit inherent numerical dispersion and solution oscillations. The magnitude of such numerical errors is often so severe as to destroy the value of many computed solutions. A successful and economical algorithm for the convective transport equation in one spatial dimension has been published recently by one of the authors (RJS), in which an exact solution is achieved by means of a moving coordinate system. The present study describes the extension of this work to the more important and challenging two-dimensional case.

Submerged Jet of a Conducting Fluid in the Presence of the Magnetic Field

2012 ◽  
Vol 7 (2) ◽  
pp. 25-38
Author(s):  
Rustam Mullyadzhanov ◽  
Nikolay Yavorsky
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Point Source ◽  
Electric Current ◽  
Stokes Equations ◽  
Conducting Fluid ◽  
Mhd Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Submerged Jet

We consider a steady flow of a viscous incompressible conducting fluid. New exact solution of the magnetohydrodynamic (MHD) equations is obtained, when the flow is induced by the point source of hydrodynamic momentum located at the end of a semi-infinite linear conductor with a set value of the electric current. The effects of the confinement of the current density and the loss of existence of the solution with the finite values of electric current and various values of the Reynolds number and the Batchelor number (magnetic Prandtl number) are found. The non-self-similar problem is considered, when the flow is induced by the point source of momentum, angular momentum, flow rate and electric current that are set at the origin. In this case, the first term of the asymptotic expansion of the velocity at the infinity is described by the exact solution of the Navier – Stokes equations of the submerged jet (Slezkin – Landau – Squire solution). We analyze the conservation laws. It is shown that the induced magnetic field reduces the intensity of the jet flow

Generating Functions for the Exact Solution of the Transport Equation. I

1968 ◽  
Vol 9 (10) ◽  
pp. 1722-1731 ◽  
Author(s):  
I. K. Abu‐Shumays ◽  
E. H. Bareiss
Keyword(s):  
Exact Solution ◽  
Transport Equation ◽  
Generating Functions
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