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

Arthur S O Sanya,Emile A Sanya,Gerard Degan,Christian Akowanou

doi:10.1186/2193-1801-3-659

Abstract

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.

Highlights

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)
The same result is found by Sanya et al (2014) in their work on film condensation on a vertical surface embedded in a thick porous medium with anisotropic permeability
When K* > 1, the dimensionless thickness of the liquid film is maximum at θ = 90° and minimum at θ = 0 while the opposite result is observed for K* < 1. It follows from these results that the orientation of the principal axis with higher anisotropic permeability of the thin porous medium perpendicular to the gravity vector implies a maximum liquid film thickness on the vertical surface

Summary

Introduction

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). Where the following dimensionless parameters of the porous liquid film are defined as: The Jacob number : Ja 1⁄4 CpLðT S−T W Þ hLv ð42aÞ

Results

Conclusion