The Random Steady State Diffusion Problem. I: Random Generalized Solutions to Laplace’s Equation

1976 ◽  
Vol 31 (1) ◽  
pp. 134-147 ◽  
Author(s):  
Georges A. Bécus ◽  
F. A. Cozzarelli
Keyword(s):  
Steady State ◽  
Diffusion Problem ◽  
Generalized Solutions ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
State Diffusion ◽  
Steady State Diffusion

scholarly journals ON THE SOLUTION OF THE STEADY‐STATE DIFFUSION PROBLEM FOR FERROMAGNETIC PARTICLES IN A MAGNETIC FLUID

2008 ◽  
Vol 13 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Viktor Polevikov ◽  
Lutz Tobiska
Keyword(s):  
Steady State ◽  
Magnetic Fluid ◽  
Particle Concentration ◽  
Diffusion Problem ◽  
Gradient Magnetic Field ◽  
Concentration Problem ◽  
State Diffusion ◽  
Steady State Problem ◽  
Steady State Diffusion ◽  
Ferromagnetic Particles

A mathematical model for the diffusion process of ferromagnetic particles in a magnetic fluid is described. The unique solvability of the steady‐state particle concentration problem is investigated and an analytical expression for its solution is found. In case that the fluid is under the action of a high‐gradient magnetic field a Stefan‐type diffusion problem can arise. An algorithm for solving the Stefan‐type steady‐state problem is developed.

Hedge's Ultimate Numerical Technique (HUNT) for Steady State Diffusion Problem

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Ganesh S Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Numerical Technique ◽  
Taylor Series Expansion ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
One Dimensional ◽  
Partial Derivatives ◽  
State Diffusion ◽  
Steady State Diffusion

A more realistic numerical technique hereafter known as Hegde's Ultimate Numerical Technique (HUNT) is developed and demonstrated on a one dimensional and a two dimensional steady state diffusion problem of heat transfer. The available numerical methods developed are based on finite difference technique neglecting the contribution of higher order terms in Taylor series expansion of the function leading to an approximation and the error in the solution. In the present effort of the HUNT, the optimization of the partial derivatives leads to the elimination of the error and justifies the stability and the convergence of the solution. The HUNT procedure based on the interface theory developed by the author, is capable of providing the ultimate optimum solution to all the partial derivatives considered as decision vectors. Even though the HUNT is demonstrated on one dimensional and two dimensional steady state diffusion equations, it does not require rigorous efforts to apply it to three dimensional problems of fluid flow and heat transfer. As pilot exercises the HUNT is demonstrated on a one dimensional circular fin and a two dimensional plate to obtain the temperature distribution. The result is compared with the analytical method and the finite volume method for which the results are available in the literature. To the knowledge of the authors, HUNT is both different and a unique example of its kind.

scholarly journals Bioelectrocatalytic endpoint assays based on steady-state diffusion current at microelectrode array

2010 ◽  
Vol 12 (6) ◽  
pp. 839-842 ◽  
Author(s):  
Tatsuo Noda ◽  
Katsumi Hamamoto ◽  
Maiko Tsutsumi ◽  
Seiya Tsujimura ◽  
Osamu Shirai ◽  
...  
Keyword(s):  
Steady State ◽  
Microelectrode Array ◽  
Diffusion Current ◽  
State Diffusion ◽  
Steady State Diffusion
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