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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 0.7

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.v2.i5.30
pages 421-437


Manosh C. Paul
Systems, Power & Energy Research Division, School of Engineering, University of Glasgow, Glasgow, G12 8QQ, UK
D. Andrew S. Rees
Department of Mechanical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom
Michael Wilson
Department of Mechanical Engineering University of Bath Bath BA2 7AY United Kingdom


In a previous paper (Int. J. Thermal. Sci., vol. 47, pp. 1382-1392, 2008), the authors performed a detailed numerical investigation of the linear instability of the thermal boundary layer flow over a vertical surface by introducing unsteady thermal disturbances near the leading edge and by solving numerically the fully elliptic linearized stability equations. The main aim of the present paper is to extend those results into the nonlinear regime by seeding the boundary layer with similar disturbances of finite amplitude. The ensuing nonlinear waves are found to exhibit a variety of behaviours, depending on the precise amplitude and period of the forcing. When the amplitude is sufficiently small, the linearized theory of the previous work is reproduced, but for larger amplitudes, cell splitting or cell merging may occur as waves travel downstream. Cell splitting takes place when disturbance frequencies are somewhat smaller than the most strongly amplified nondimensional disturbance frequency of 0.4 for which the boundary layer response, is at its greatest in terms of the surface rate of heat transfer (see Fig. 8 in previous paper). Cell merging takes place at frequencies what are approximately double that of the most strongly amplified disturbance frequency. Attention is focussed on fluids with a unit Prandtl number.