Non-Darcy transient and steady film condensation in a porous medium

Ebinuma, Carlos Daniel; Nakayama, A.

doi:10.1016/0735-1933(90)90078-x

Cited by 9 publications

(8 citation statements)

References 7 publications

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“…The variation of the dimensionless thickness of the liquid film with the Jacob number is plotted in Figure 4 where it is shown that the liquid film increases as Ja is increased. This result is similar to that obtained analytically by Cheng ( 1981 ) using the Darcy flow model and Ebinuma and Nakayama ( 1990 ) using the Ergun model (Ergun 1952 ). Moreover, it is seen that the porous medium has the effect of increasing the condensate’s film thickness as similar to the result obtaining by Al-Nimr and Alkam ( 1997 ).…”

Section: Resultssupporting

confidence: 90%

“…In what follows, the main results of our study related to the effects of anisotropic permeability parameters based on the Brinkman-Darcy flow model are compared essentially with Cheng’s steady solution (Cheng 1981 ) based on the Darcy flow model and Ebinuma’s steady solution (Ebinuma and Nakayama 1990 ) based on the Ergun model (Ergun 1952 ) and Sanya’s steady solution (Sanya et al 2014 ) for thick porous medium with anisotropic permeability based also on the Brinkman-Darcy flow model.…”

Section: Resultsmentioning

confidence: 99%

“…Many investigations have been directed recently to attack film condensation in a porous medium in both steady (Cheng 1981 ; Chui et al 1983 ; Nakayama and Koyama 1987 ; Vovos and Poulikakos 1987 ; Reeken et al 1994 ) and transient problems (Cheng and Chui 1984 ; Ebinuma and Nakayama 1990 ; Masoud et al 2000 ). Since the basic understanding of the transfer mechanisms of heat, momentum and mass in porous media during phase change have still developed, the two phase change flows have possible applications in geophysics and engineering problems such as geothermal energy, steam stimulation of oil fields, food drying and heat pipes problems (Ebinuma and Nakayama 1990 ). Al-Nimr and Alkam ( 1997 ) have studied steady film condensation on a vertical plate imbedded in a porous medium and have considered the Brinkman-Darcy model by neglecting the macroscopic and microscopic inertial terms to obtain analytical solutions for the three following requests: liquid film thickness, condensate mass flow rate and convective heat transfer coefficient.…”

Section: Introductionmentioning

confidence: 99%

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Liquid film condensation along a vertical surface in a thin porous medium with large anisotropic permeability

et al. 2014

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The problems of steady film condensation on a vertical surface embedded in a thin porous medium with anisotropic permeability filled with pure saturated vapour are studied analytically by using the Brinkman-Darcy flow model. The principal axes of anisotropic permeability are oriented in a direction that non-coincident with the gravity force. On the basis of the flow permeability tensor due to the anisotropic properties and the Brinkman-Darcy flow model adopted by considering negligible macroscopic and microscopic inertial terms, boundary-layer approximations in the porous liquid film momentum equation is solved analytically. Scale analysis is applied to predict the order-of-magnitudes involved in the boundary layer regime. The first novel contribution in the mathematics consists in the use of the anisotropic permeability tensor inside the expression of the mathematical formulation of the film condensation problem along a vertical surface embedded in a porous medium. The present analytical study reveals that the anisotropic permeability properties have a strong influence on the liquid film thickness, condensate mass flow rate and surface heat transfer rate. The comparison between thin and thick porous media is also presented.

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Section: Resultssupporting

confidence: 90%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Liquid film condensation along a vertical surface in a thin porous medium with large anisotropic permeability

et al. 2014

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“…they found that the presence of the coating enhanced the heat transfer rates substantially. Ebinuma and Nakayama 12 studied the non‐Darcy problem and the transient problem with lateral mass flux over a vertical surface in a porous medium. They showed the effect of quadratic drag on the time required to reach the steady state and the surface heat transfer rate.…”

Section: Introductionmentioning

confidence: 99%

“…They showed the effect of quadratic drag on the time required to reach the steady state and the surface heat transfer rate. Moreover, Ebinuma and Nakayama 12 used the Forchheimer model in their analytical treatment of film condensation in the presence of gravity and externally forced flow. A similarity transformation involving a modified Peclet number was introduced based on the resultant velocity of the condensate.…”

Section: Introductionmentioning

confidence: 99%

Theoretical study of superheated vapor effect on liquid film condensation in a saturated porous medium using Forchheimer's model

Yaseen

Alrbai

2022

Heat Trans

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In this work, the superheated vapor effect on liquid film condensation in a saturated porous medium using Forchheimer's model has been investigated analytically and numerically. The applied governing equations, the continuity equation, the Forchheimer equation, and the energy equation were transformed using the similarity transformation technique into a dimensionless form using a set of suitable variables and then solved numerically using the Runge–Kutta method. Results obtained were graphically drawn to illustrate the effects of superheated vapor and subcooled liquid on the liquid film condensation, temperature, and heat transfer rate through the porous medium. It was found that the film thickness is a function of dimensionless parameters related to the degree of subcooling and Grashof number without a superheating effect. Consequently, the Nusselt number depends on the square root of the Rayleigh number, the Grashof number, and the dimensionless film thickness. It was also found that if superheating exists, the liquid film thickness then depends on four dimensionless parameters related to the Grashof number, the degree of subcooling of the liquid, the extent of the superheating of the surrounding vapor, and a property ratio of the liquid and the vapor phase.

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Convection with Change of Phase

Nield

Bejan

2012

Convection in Porous Media

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Non-Darcy transient and steady film condensation in a porous medium

Cited by 9 publications

References 7 publications

Liquid film condensation along a vertical surface in a thin porous medium with large anisotropic permeability

Liquid film condensation along a vertical surface in a thin porous medium with large anisotropic permeability

Theoretical study of superheated vapor effect on liquid film condensation in a saturated porous medium using Forchheimer's model

Convection with Change of Phase

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