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Continuous dependence on the heat source and non‐linear stability for convection with internal heat generation
Author(s) -
Straughan Brian
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670130502
Subject(s) - internal heating , mathematics , heat flux , convection , constant (computer programming) , mechanics , boundary value problem , film temperature , thermodynamics , boundary layer , stability (learning theory) , heat transfer , mathematical analysis , physics , nusselt number , machine learning , reynolds number , computer science , turbulence , programming language
It is shown that the solution to the boundary‐initial value problem for a heat‐conducting viscous fluid depends continuously on changes in the heat supply function, for the improperly posed backward in time problem. A non‐linear convection threshold is also determined for the problem of a layer of fluid heated internally (non‐uniformly), with zero neat flux on the lower boundary and constant‐temperature upper surface.