A Boundary-Layer Treatment of Laminar-Film Condensation

Abstract

The problem of laminar-film condensation on a vertical plate is attacked using the mathematical techniques of boundary-layer theory. Starting with the boundary-layer (partial differential) equations, a similarity transformation is found which reduces them to ordinary differential equations. Energy-convection and fluid-acceleration terms are fully accounted for. Solutions are obtained for values of the parameter cpΔT/hfg between 0 and 2 for Prandtl numbers between 1 and 100. These solutions take their place in the boundary-layer family along with those of Blasius, Pohlhausen, Schmidt and Beckmann, and so on. Heat-transfer results are presented. It is found that the Prandtl-number effect, which arises from retention of the acceleration terms, is very small for Prandtl numbers greater than 1.0. Low Prandtl number (0.003–0.03) heat-transfer results are given in Appendix 2, and a greater effect of the acceleration terms is displayed.

Analysis of laminar film condensation over vertical permeable hollow short fins

“…Chen [9] considered the vapor to be stagnant far from the interface while considering it to be dragged downward by the falling film of the condensate near the interface. He found that the values of Nusselt numbers are smaller than these reported by Sparrow and Gregg [4] and agree better with experimental data.…”

“…Sparrow and Gregg [4] included momentum effects and energy convection in the Nusselt model [1]. They used the boundary layer theory in the mathematical modelling.…”

Film-wise and drop-wise condensation of steam on short inclined plates

“…Following the pioneering analysis performed by Nusselt [3] on laminar free convection film-wise condensation, a number of studies were reported involving refinements to his assumptions concerning the effects of sub-cooling, the temperature profile in the condensate film, the effects of inertia and drag [4][5][6]. And his theory has been extended to condensation with the presence of a non-condensable gas [1,6].…”

Laminar film condensation on the outside of a vertical circular cylinder; including surface-tension effects

“…The case of condensation on the outside of a vertical circular cylinder was first investigated by Sparrow and Gregg [2]. There it was assumed that the thickness of the condensate layer was small compared with the radius of the cylinder and so the conventional boundary-layer approximation may be evoked.…”

“…Two modifications of the Sparrow and Gregg [2] condensate flow are manifest. The first is that far downstream of the thermal leading edge the condensate thickness may be of the same order as the radius of the cylinder and so the above assumption of Sparrow and Gregg is no longer valid.…”