Analytical Investigation into Effects of Capillary Force on Condensate Film Flowing over Horizontal Semicircular Tube in Porous Medium

Abstract

A theoretical investigation is performed into the problem of laminar filmwise condensation flow over a horizontal semicircular tube embedded in a porous medium and subject to capillary forces. The effects of the capillary force and gravity force on the condensation heat transfer performance are analyzed using an energy balance approach method. For analytical convenience, several dimensionless parameters are introduced, including the Jakob number Ja, Rayleigh number Ra, and capillary force parameter Boc. The resulting dimensionless governing equation is solved using the numerical shooting method to determine the effect of capillary forces on the condensate thickness. A capillary suction velocity can be obtained mathematically in the calculation process and indicates whether the gravity force is greater than the capillary force. It is shown that if the capillary force is greater than the condensate gravity force, the liquid condensate will be sucked into the two-phase zone. Under this condition, the condensate film thickness reduces and the heat transfer performance is correspondingly improved. Without considering the capillary force effects, the mean Nusselt number is also obtained in the present study as ${\overline{Nu}|}_{V_2^{\ast }=0}={\left(2RaDa/Ja\right)}^{1/2}{\displaystyle {\int }_0^{\pi }{\left(1+\cos \theta \right)}^{1/2}\text{d}\theta }$ .