caa a22 4500 463163451 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s11242-006-9028-9 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9028-9 The effect of thermal dispersion on free convection film condensation on a vertical plate with a thin porous layer [Elektronische Daten] [M. Asbik, B. Zeghmati, H. Louahlia-Gualous, W. Yan] An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless thickness film and the local Nusselt number. In the porous region, the Darcy-Brinkman-Forchheimer (DBF) model describes the flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing of heat transfer is significant. The comparison of the DBF model and the Darcy-Brinkman (DB) one is carried out. Springer Science+Business Media B.V., 2006 Condensation nationallicence Natural convection nationallicence Porous layer nationallicence Thermal dispersion nationallicence Darcy-Brinkman-Forchheimer model nationallicence Analytical method nationallicence A : Dimensionless flow inertia term ( $$A=\lambda \varepsilon Re_K H^{\ast 2}\sqrt{Da} )$$ nationallicence C p : Specific heat of fluid at constant pressure (Jkg−1K−1) nationallicence Da : Darcy number ( $$Da=K \mathord{\left/ {\vphantom {K {L^2}}} \right. \kern-\nulldelimiterspace} {L^2}$$ ) nationallicence F : Flow inertia term nationallicence g : Gravitational acceleration (ms−2) nationallicence h fg : latent heat of vaporization (Jkg−1) nationallicence H : Thickness of porous coating (m) nationallicence Ja : Jakob number nationallicence k : Thermal conductivity (Wm−1K−1) nationallicence K : Permeability (m2) nationallicence L : Length of plate (m) nationallicence Nu x : Local Nusselt number nationallicence Pe : Peclet number nationallicence Pr : Prandtl number nationallicence Re K : Reynolds number based on $$\sqrt{K}$$ nationallicence T : Temperature (K) nationallicence u : x-component velocity (ms−1) nationallicence u r : Reference velocity (ms−1) nationallicence x : Vertical coordinate (m) nationallicence y : Horizontal coordinate (m) nationallicence Greek Symbols nationallicence γ : Dimensionless dispersion parameter nationallicence δ : Film condensation thickness (m) nationallicence ɛ : Porosity nationallicence λ : Dimensionless inertia parameter nationallicence μ : Dynamic viscosity (kgm−1s−1) nationallicence ν : Kinematic viscosity (m2s−1) nationallicence θ : Dimensionless temperature nationallicence ρ : Density (kgm−3) nationallicence Subscripts—Superscripts nationallicence ar : Arbitrary nationallicence d : Dispersion nationallicence eff : Effective nationallicence $$\ell$$ : Liquid nationallicence i : Porous layer-pure condensate interface nationallicence p : Porous layer nationallicence s : Saturation nationallicence v : Vapor nationallicence w : Wall nationallicence * : Dimensionless quantity nationallicence Asbik M. Faculté des Sciences et Techniques, Groupe de Thermodynamique Energétique (G.T.E), B.P 509, Boutalamine Errachidia, Morocco aut Zeghmati B. Laboratoire de Mathématiques et Physique des Systèmes,—Groupe de Mécanique Energétique, (MEPS—GME), Université de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860, Perpignan Cedex, France aut Louahlia-Gualous H. Département CREST, FEMTO ST, UTBM-UFC, UMR CNRS 6174, 2 Avenue Jean Moulin, 90000, Belfort, France aut Yan W. Department of Mechatronic Engineering, Huafan University, Shih Ting, 22305, Taipei, Taiwan, Republic of China aut Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 335-352 0169-3913 67:3<335 2007 67 11242 https://doi.org/10.1007/s11242-006-9028-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9028-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Asbik M. Faculté des Sciences et Techniques, Groupe de Thermodynamique Energétique (G.T.E), B.P 509, Boutalamine Errachidia, Morocco aut NATIONALLICENCE 700 1- Zeghmati B. Laboratoire de Mathématiques et Physique des Systèmes,—Groupe de Mécanique Energétique, (MEPS—GME), Université de Perpignan Via Domitia, 52 avenue Paul Alduy, 66860, Perpignan Cedex, France aut NATIONALLICENCE 700 1- Louahlia-Gualous H. Département CREST, FEMTO ST, UTBM-UFC, UMR CNRS 6174, 2 Avenue Jean Moulin, 90000, Belfort, France aut NATIONALLICENCE 700 1- Yan W. Department of Mechatronic Engineering, Huafan University, Shih Ting, 22305, Taipei, Taiwan, Republic of China aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 335-352 0169-3913 67:3<335 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer