The paper discusses free convective flows above a horizontal plate, both theoretically and on the basis of experiments which yield quantitative data. The theory is applicable to the semi-infinite plate and is extended to cover the complete range of Prandtl number values including Pr → 0 and Pr → ∞. Experiments were carried out to demonstrate the existence of a laminar boundary layer above a horizontal plate at intermediate Grashof (respectively Rayleigh) numbers, and its extent along the plate. This layer breaks down into large-eddy instability some distance from the leading edge. The value of the critical Rayleigh number for this to occur, obtained experimentally using semi-focusing colour-Schlieren photography is in reasonable qualitative agreement with previously known data (Tritton 1963a,b).
The investigation of laminar free convective plumes in an otherwise stationary environment has formed the basis of numerous investigations, initiated by Zeldovich (1937). For the non-rotating environment alone the authors have been able to locate twenty-nine papers: many of these repeat work previously undertaken. There are, however, two cases of some technological significance which have so far not been considered: (i) the plume in an otherwise quiescent environment for a fluid of very large Prandtl number, of importance in the heating of reservoirs of viscous fluid such as fuel oil; and (ii) the case of vanishingly small Prandtl number, of application to liquid metal-cooled nuclear reactors. Both of these cases have some theoretical interest, as will be shown. Their analysis leads to singular asymptotic perturbations and hence to matched-expansions techniques.
Equations for the calculation of velocity profiles and flow rate for the steady, isothermal and laminar flow of an incompressible, inelastic, non-Newtonian fluid in annuli are presented. A solution for the Rabinowitsch equation type of pseudoplastic behavior is obtained as a special case. Solutions presented should prove of interest in viscosity pump and screw extruder design.
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