The role of variable viscosity in the stability of channel flow

The stability of plane Poiseuille flow is studied for liquids exhibiting exponential viscosity-temperature dependence. In contrast to previously published studies, viscosity and temperature fluctuations are included in the formulation. Equations describing the evolution of small, two-dimensional dis...

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Vydáno v:International communications in heat and mass transfer Ročník 22; číslo 6; s. 837 - 847
Hlavní autoři: Pinarbasi, A., Liakopoulos, A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Elsevier Ltd 1995
Elsevier
Témata:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Instability of shear flows
Physics
Viscous instability
Variable viscosity
Temperature distribution
Pipe flow
Poiseuille flow
Hydrodynamic instability
Numerical simulation
Velocity distribution
Incompressible fluid
Pressure gradients
Parallel plate
ISSN:0735-1933, 1879-0178
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Shrnutí:The stability of plane Poiseuille flow is studied for liquids exhibiting exponential viscosity-temperature dependence. In contrast to previously published studies, viscosity and temperature fluctuations are included in the formulation. Equations describing the evolution of small, two-dimensional disturbances are derived and the stability problem is formulated as an eigenvalue problem for a set of two ordinary differential equations. A Chebyshev collocation discretization method leads to a generalized matrix eigenvalue problem which is solved by the QZ algorithm. It is found that an imposed wall temperature difference, Δ T − , is always destabilizing. The instability region in the wavenumber-Reynolds number plane grows considerably as Δ T − increases. The influence of Prandtl number, temperature fluctuations and viscosity fluctuations on the flow stability/instability is small. However, their influence on the margin of stability for small wavenumbers is appreciable.
ISSN:0735-1933
1879-0178
DOI:10.1016/0735-1933(95)00072-0