Effect of pressure gradient in forced convection film condensation on a horizontal tube

Abstract

In earlier theoretical studies of film condensation from a vapour flowing over a horizontal tube, the pressure gradient, arising from the flow of vapour over the curved surface, has been omitted in the momentum balance for the condensate film. This has been included in the present work and shown to lead to higher heat-transfer coefficients over the forward half of the tube. It is shown further that, under certain circumstances, a solution (calculation of the condensate film thickness around the tube) is not possible for the lower part of the tube where the surface shear stress and pressure gradient act in opposite directions. Specifically, for the problem considered [vertical vapour downflow, ‘potential’ flow assumed outside the vapour boundary layer, asymptotic (infinite suction) approximation used for surface shear stress] an infinite rate of increase of film thickness with angle is encountered at some location on the downstream half of the tube when ρ gU ∞ 2/ρgd > 1 8 . This may lead to instability of the laminar condensate film followed by some degree of waviness, turbulence, or conceivably, removal of condensate from the tube into the vapour stream. All of these possibilities would lead to enhanced heat transfer over the rear part of the tube. When ρ gU ∞ 2/ρgd < 1 8 it is found that the increase in heat transfer for the forward half of the tube is almost balanced by a decrease for the rear half, so that the mean Nusselt number for the tube is very close to that found when the pressure gradient is neglected. Numerical solutions have been obtained for wide ranges of the relevant dimensionless parameters and used to obtain accurate expressions for : (a) the mean heat-transfer coefficient for the whole tube when the pressure gradient term is unimportant, (b) the angle,φ c at which dδ dgf becomes infinite when ρ gU ∞ 2/ρgd > 1 8 and (c) the mean heat-transfer coefficient up to φ. A conservative equation for estimatingthe mean heat-transfer coefficient for the whole tube is also given and compared with available experimental data.