Nonlinear stability theory of channel flow with heat transfer – an asymptotic approach |
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Authors: | X You H Herwig |
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Institution: | (1) Technische Thermodynamik, TU Chemnitz, D-09107, Chemnitz, Germany, DE |
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Abstract: | A fully developed laminar Poiseuille flow subject to constant heat flux across the wall is analysed with respect to its stability
behavior by applying a weakly nonlinear stability theory. It is based on an expansion of the disturbance control equations
with respect to a perturbation parameter ε. This parameter is the small initial amplitude of the fundamental wave. This fundamental
wave which is the solution of the linear (Orr-Sommerfeld) first order equation triggers all higher order effects with respect
to ε. Heat transfer is accounted for asymptotically through an expansion with respect to a small heat transfer parameter ε
T
. Both perturbation parameters, ε and ε
T
, are linked by the assumption ε
T
=O(ε2) by which a certain distinguished limit is assumed. The results for a fluid with temperature dependent viscosity show that
heat transfer effects in the nonlinear range continue to act in the same way as in the initial linear range.
Received on 11 August 1997 |
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Keywords: | |
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