scholarly journals On Steady MHD Thermally Radiating and Reacting Thermosolutal Viscous Flow through a Channel with Porous Medium

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Promise Mebine ◽  
Rhoda H. Gumus
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Boundary Value Problem ◽  
Viscous Flow ◽  
Nonlinear Boundary ◽  
Approximate Solutions ◽  
Nonlinear Boundary Value Problem ◽  
Arrhenius Kinetics ◽  
Flow Through ◽  
Steady State Solutions

This paper investigates steady-state solutions to MHD thermally radiating and reacting thermosolutal viscous flow through a channel with porous medium. The reaction is assumed to be strongly exothermic under generalized Arrhenius kinetics, neglecting the consumption of the material. Approximate solutions are constructed for the governing nonlinear boundary value problem using WKBJ approximations. The results, which are discussed with the aid of the dimensionless parameters entering the problem, are seen to depend sensitively on the parameters.

Thermal Ignition in a Reactive Viscous Flow Through a Channel Filled With a Porous Medium

2006 ◽  
Vol 128 (6) ◽  
pp. 601-604 ◽  
Author(s):  
O. D. Makinde
Keyword(s):  
Porous Medium ◽  
Nonlinear Boundary ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Exothermic Reaction ◽  
Thermal Ignition ◽  
Arrhenius Kinetics ◽  
Thermal Criticality ◽  
Flow Through ◽  
Steady State Solutions

This paper examines the steady-state solutions of a strongly exothermic reaction of a viscous combustible material in a channel filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption. The Brinkman model is employed and analytical solutions are constructed for the governing nonlinear boundary-value problem using a perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.

scholarly journals On the solution of a nonlinear problem in cell membrane theory

1994 ◽  
Vol 36 (1) ◽  
pp. 26-37 ◽  
Author(s):  
A. M. Arthurs ◽  
J. Clegg
Keyword(s):  
Steady State ◽  
Cell Membrane ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Nonlinear Problem ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Value Problem ◽  
Cable Model ◽  
Membrane Theory ◽  
Better Than

AbstractMethods for integral equations are used to derive upper and lower pointwise bounds for the solution of a nonlinear boundary value problem arising in the steady-state finite cable model of cell membranes. Test calculations are performed to illustrate the results and the accuracy achieved is significantly better than that obtained previously by other methods.

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