A NEW APPROXIMATE ANALYTIC METHOD FOR SOME HEAT-CONDUCTION PROBLEMS

1998 ◽  
Author(s):  
ChunLu Zhang ◽  
Hao Li ◽  
GuoLiang Ding ◽  
ZhiJiu Chen
Keyword(s):  
Heat Conduction ◽  
Analytic Method ◽  
Approximate Analytic Method

Bidimensional Fluid-Film Flows of Stokesian Fluids

1982 ◽  
Vol 104 (2) ◽  
pp. 227-233
Author(s):  
Patrick Bourgin ◽  
Bernard Gay
Keyword(s):  
Laminar Flow ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Differential System ◽  
Analytic Method ◽  
Shearing Stress ◽  
Flow Equations ◽  
Approximate Analytic Method ◽  
Film Flows

The bidimensional flow equations of a Stokesian fluid are solved for the case of steady, incompressible, and laminar flow between two arbitrary moving surfaces separated by a small gap. The stress T22 and the shearing stress at one of the walls are coupled through nonlinear integro-differential equations, depending on the viscous function only. The form of this differential system is specified for the equations derived from the theory of phenomenological macrorheology, as developed by Reiner and Rivlin. The solution is proved to be unique under certain conditions and for adequate boundary conditions. An example is worked out in the particular case of one single non-Newtonian parameter. The problem is solved in two different ways, using an approximate analytic method and a numerical method. The conception of the latter allows to generalize it by introducing only slight modifications into the program.

A catastrophe-theory study of a two-chamber model for a tokamak scrape-off and divertor

1989 ◽  
Vol 42 (1) ◽  
pp. 59-74
Author(s):  
Alkesh Punjabi
Keyword(s):  
Heat Conduction ◽  
Catastrophe Theory ◽  
Geometric Mean ◽  
Plasma Transport ◽  
Analytic Method ◽  
Mode Transition ◽  
Threshold Values ◽  
Electron Heat ◽  
Chamber Model ◽  
Field Lines

The two-chamber model (TCM) of Singer and Langer is employed to study the plasma transport in the scrape-off and divertor regions of a tokamak. Collisiondominated transport along the field lines is considered, with a. geometric-mean flux-limited expression for parallel electron heat conduction. An analytic method for the catastrophe-theory study of the TCM is developed. Maxwell convention for the catastrophes is adopted. Catastrophes occur when the energy flux entering the divertor chamber from the main plasma scrape-off, the recycling coefficient and the ratio of electron temperatures in the scape-off to that in the divertor exceed some threshold values. It is seen that the behaviour of the plasma during these catastrophes is in qualitative agreement with the experimentally observed features of the plasma during the H-mode transition.

Application of an Approximate Analytic Method of Computing Solute Profiles with Dispersion in Soils

1982 ◽  
Vol 11 (1) ◽  
pp. 151-155 ◽  
Author(s):  
C. W. Rose ◽  
F. W. Chichester ◽  
J. R. Williams ◽  
J. T. Ritchie
Keyword(s):  
Analytic Method ◽  
Approximate Analytic Method
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