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 N u ¯ | V 2 ∗ = 0 = 2 R a D a / J a 1 / 2 ∫ 0 π 1 + cos θ 1 / 2 d θ .
Highlights
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. e effects of the capillary force and gravity force on the condensation heat transfer performance are analyzed using an energy balance approach method
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
E problem of laminar film condensation was first investigated by Nusselt [1], who considered a condensate film flowing down a vertical plate
Summary
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. Introduction e problem of laminar film condensation in porous media has received considerable attention in the literature due to its importance in many engineering applications, including packed-bed heat exchangers, chemical reactors, petroleum recovery, heat pipes, casting solidification, geothermal reservoirs, and oil recovery in reservoir engineering In such applications, the capillary force has a significant effect on the heat transfer performance and must be taken into account when designing and evaluating the system. Since the capillary forces have a significant effect on the heat transfer performance in porous media and must be taken into consideration, the present study investigates the influence of capillary forces on the laminar film condensation flow on a finite-size horizontal semicircular tube embedded in a porous medium and maintained at a constant temperature.
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