SynopsisDual similarity solutions in the context of mixed convection are presented. In contrast to the Falkner–Skan solutions the bifurcation point is found to be distinct from the point of vanishing skin friction. The eigenvalue problem arising out of a stability analysis of these solutions is examined numerically. The numerical evidence would seem to indicate that the margin of stability is associated with the onset of reverse flow as opposed to the bifurcation point, as conjectured by Banks and Drazin in 1973.
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which exploits the hydrodynamic similarity solution for thin film flow. The approximate solution may provide a valuable basis for assessing flow and heat transfer in more complex settings.
A comprehensive study of the problem of laminar film condensation with both a gravitational type body force and a moving vapour concurrent and parallel to the surface has been presented here. It demonstrates where both the body force and vapour velocity are significant through a comprehensive numerical solution obtained by a modified Keller box method. Important parameters governing condensation and heat transfer of pure vapour are determined. A perturbation analysis is applied in the leading edge and downstream regimes. The thin film approximations for the both regimes are obtained and compared with exact numerical solutions.
INTRODUCTIONThe problem of laminar film condensation on a vertical plate with both a gravitational type body force and a moving vapour concurrent and parallel to the surface is not only of theoretical interest but also of great practical importance in a number of technological processes. There have been sporadic publications in the area of the laminar body-force-only film condensation problem and in the area of the laminar forced convection film condensation problem.In the area of the laminar body-force-only film condensation, the pioneer work was reported by Nusselt (1916), who formulated this problem in terms of simple force and heat balances within the condensate film. The effects of inertia forces, energy convection and vapour drag were not taken into account. In the area of the laminar forced convection film condensation, Jacobs (1966) assumed that the inertia terms of the liquid film have negligible effect and that the temperature distribution across the film is linear. Beckett and Poots (1972) using boundary-layer similarity techniques presented a comprehensive solution to this problem without a body force.In the present investigation, a comprehensive theoretical model for the problem of combined body force and forced convection laminar film condensation has been built up. Accordingly the heat transfer and condensation rates in this problem have accurately been predicted by employing perturbation techniques and exact numerical results which have been computed by using the continuous transformation computation (Hunt and Wilks 1981) and the modified Box scheme (Shu and Wilks 1995).
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method, it solves the problem of systems of differential equations involving integral operators not previously considered by the Keller Box method. Two main preparatory stages are required: (i) a merging procedure for differential equations and conditions without integral operators and; (ii) a reduction procedure for differential equations and conditions with integral operators. The differencing processes are effectively simplified by means of the unit-step function. The nonlinear difference equations are solved by Newton's method using an efficient block arrow-like matrix factorization technique. As an example of the application of this method, the systems of equations for combined gravity body force and forced convection in laminar film condensation can be solved for prescribed values of physical constants.
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