Features of Laminar-Turbulent Transition for the Coolant Flow in a Plane Heat-Exchanger Channel

The presented work is devoted to one problem of hydrodynamic stability of a thermoviscous fluid. The stability of the flow of a 45 aqueous solution of propylene glycol in a plane channel with a linear temperature distribution was considered. The solution of the obtained generalized Orr-Sommerfeld eq...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-09, Vol.42 (9), p.2211-2215
Main Authors: Nizamova, A. D., Murtazina, R. D., Kireev, V. N., Urmancheev, S. F.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Aqueous solutions
Chebyshev approximation
Eigenvalues
Eigenvectors
Flow stability
Fluid flow
Geometry
Heat exchangers
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Orr-Sommerfeld equations
Polynomials
Probability Theory and Stochastic Processes
Propylene
Reynolds number
Spectral methods
Temperature distribution
Viscosity
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Summary:The presented work is devoted to one problem of hydrodynamic stability of a thermoviscous fluid. The stability of the flow of a 45 aqueous solution of propylene glycol in a plane channel with a linear temperature distribution was considered. The solution of the obtained generalized Orr-Sommerfeld equation was carried out using the spectral method of expanding the sought functions in terms of the first kind Chebyshev polynomials. As a result of calculations, the distributions of eigenvalues were constructed for different parts of the curve of the dependence of viscosity on the temperature of the liquid under consideration, in each case the critical Reynolds numbers and eigenfunctions were determined. It was found that taking into account the dependence of the viscosity on the temperature of the liquid leads to an increase in the region of unstable flow regimes in the channels of heat exchangers.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080221090249