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Stability of convective flow between vertical planes

Al-Ali, A. A. (1993). Stability of convective flow between vertical planes. (Unpublished Doctoral thesis, City, University of London)

Abstract

This thesis considers instability of the convective flow between differentially heated vertical planes at infinite and large Prandtl numbers.

For infinite Prandtl number, asymptotic methods are used to describe the solution of the linear stability problem in the limit A-»oo, where A is the Rayleigh number. The solution is expanded in the neighbourhood of y0, where y0 is the critical value of a convective parameter y associated with the base flow. The base flow vanishes mid-way between the planes where a thermal critical layer forms. Matching across the critical layer leads to two sets of bridging conditions which allow the critical wavelength of the stationary disturbance to be found.

The effect of large (but not infinite) Prandtl number on the neutral stability equation is considered in Chapter 5, and in Chapter 6 the lower branch of the neutral stability curve for finite and large Prandtl numbers is studied. This leads to a complete picture of the neutrally stable stationary disturbances in the limit A-»oo for both large and infinite Prandtl numbers.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
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