• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.613-620
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• 1985

An analysis on the thermal instability of horizontal Blasius flow in the form of longitudinal vortices has been carried out by introducing the 3-dimensional spatial dependence of the disturbance quantities. The stability problem has been simplified significantly by considering the limiting case of infinite Prandtl number and by skilfully replacing the boundary conditions at infinity with the interface conditions at the edge of the thermal boundary layer (or by simply confining the thermal disturbances in the thermal boundary layer). The advantage of this approach is that the critical values marking the onset of thermal instability can be readily obtained as solutions of the eigenvalues problems formulated by a 6*6(or a 5*5) determinant. Present analysis provides reasonable explanations on the existing experimental and theoretical data. Especially, the heat transfer correlation based on the present analysis agrees well with the existing experimental data.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.4
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• pp.390-396
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• 1982

The onset of longitudinal vortices in horizontal Blasius flow isothermally heated from below is studied analytically. The assumption that at the onset of thermal instability the thermal disturbances are confined within the thermal boundary layer is employed for the limiting case of large Prandtl number. Polynomial representations for the basic quantities obtained by the integral method of the boundary layer analysis have been used. Then the system of differential equations and boundary conditions for disturbance quantities is reformulated in a convenient form so that the solutions may be constructed as rapidly convergent power series. The critical buoyancy parameter G $r_{x}$ $^{*}$ /R $e^{*1.5}$ falls between 2 and 6, which is about one order of magnitude lower than the existing experimental values. It is also shown that the positions of the onset of instability can be closely predicted by the present theory.y.y.