Asymptotics of Transport Equations for Spherical Geometry in L2 with Reflecting Boundary Conditions

2001 ◽  
pp. 183-195
Author(s):  
Degong Song ◽  
William Greenberg
Keyword(s):  
Boundary Conditions ◽  
Spherical Geometry ◽  
Transport Equations

Thermal Transport Equations and Boundary Conditions at the Nanoscale

2019 ◽  
pp. 37-44
Author(s):  
Marc Calvo-Schwarzwälder ◽  
Matthew G. Hennessy ◽  
Pol Torres ◽  
Timothy G. Myers ◽  
F. Xavier Alvarez
Keyword(s):  
Boundary Conditions ◽  
Thermal Transport ◽  
Transport Equations

Stationary-state solutions for coupled reaction–diffusion and temperature-conduction equations II. Spherical geometry with Dirichlet boundary conditions

1990 ◽  
Vol 430 (1880) ◽  
pp. 479-488 ◽  
Keyword(s):  
Boundary Conditions ◽  
Stationary State ◽  
Reaction Zone ◽  
Dirichlet Boundary ◽  
Spherical Geometry ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions ◽  
Temperature Position ◽  
Temperature Excess ◽  
Arrhenius Temperature Dependence

The stationary-state heat and mass transfer equations for an exothermic process following first-order kinetics and an Arrhenius temperature dependence in a spherical reaction zone may show an infinite number of solutions. Precise numerical computations for a particular case realizes this high multiplicity and determines the evolution of the shape of the temperature–position and reaction–rate–position profiles as a bifurcation parameter λ is varied. With Dirichlet boundary conditions, there is an initial concentration of self heating and reaction close to the centre of the reaction zone. This concentration is enhanced as the central temperature excess increases. At high temperature excesses and with large λ , however, the profiles flatten out, giving rise to sharp boundary layers close to the edge of the sphere.

scholarly journals Transport equations and perturbations of boundary conditions

2020 ◽  
Vol 43 (18) ◽  
pp. 10511-10531
Author(s):  
Marta Tyran‐Kamińska
Keyword(s):  
Boundary Conditions ◽  
Transport Equations
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