Premium
Continuous Dependence on the Heat Source in Resonant Porous Penetrative Convection
Author(s) -
Straughan B.
Publication year - 2011
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2011.00521.x
Subject(s) - internal heating , porous medium , convection , mechanics , instability , plane (geometry) , thermodynamics , thermal , resonance (particle physics) , porosity , source function , physics , convective heat transfer , nonlinear system , materials science , mathematics , geometry , particle physics , quantum mechanics , astrophysics , composite material
I study the structural stability for a problem in a porous medium when the density of saturating liquid is a nonlinear function of temperature and an internal heat source is present. It has been shown that for this problem when one considers thermal convection in a plane infinite layer then resonance may occur between internal layers that arise. A key parameter is the internal heat source and its presence may lead to oscillatory instability inducing resonance. Therefore, in this paper, I analyze the general structural stability problem of continuous dependence on the heat source itself for a model of nonisothermal flow in a porous medium of Forchheimer type, in a general three‐dimensional domain.