Refrigeration efficiency analysis for fully wet semi-spherical porous fins M. Hatami a , GH.R. Mehdizadeh Ahangar b , D.D. Ganji c,⇑ , K. Boubaker d a Esfarayen University, Mechanical Engineering Department, Esfarayen, North Khorasan, Iran b Department of Mechanical Engineering, Yazd University, Yazd, Iran c Babol University of Technology, Mechanical Engineering Faculty, Babol, Mazandaran, Iran d Equipe de Physique des Dispositifs à Semiconducteurs, Faculté des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisia article info Article history: Received 28 February 2014 Accepted 1 May 2014 Keywords: Semi-spherical porous fin Least Square Method (LSM) Darcy number Rayleigh number Lewis number Humidity abstract In this study, temperature distribution equation for a fully wet semi-spherical porous fin is presented by a new modified fin parameter introduced by Sharqawy and Zubair which can be calculated without needing to fin tip conditions. The driving forces for the heat and mass transfer are considered tempera- ture and humidity ratio differences, respectively. It is assumed that heat and mass convective coefficients are temperature-dependent and heat transfer through the porous media is simulated by using the passage velocity from the Darcy’s model. After introducing the governing equation, Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied to predict the temperature distribution in a Si 3 N 4 porous fin. Also, the effects of porosity, Darcy number, Rayleigh number, Lewis number, etc. on the fin efficiency are investigated. As a main outcome, results confirm that Lewis number should be significantly more than unit to make high refrigeration efficiency. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction In cooling, refrigeration and dehumidification processes, heat and mass transfer occur simultaneously when the coil surface tem- perature is below the dew point temperature of the cooled air. If the fin surface temperature is higher than the dew point, sensible heat transfers from air to the fin and fin is in fully dry condition. If whole the fin surface temperature is below the dew point while both sensible and latent heat generate, fin would be fully wet. Also, fin is partially wet when the fin base temperature is below the air dew point and the fin tip temperature is higher than the air dew point [1]. Many researches carried out on straight solid fins such as Sharqawy and Zubair’s study [2] and in limited cases, semi- spherical solid fins have been investigated such as Sabbaghi et al. [1] under the fully wet condition, but efficiency investigation for semi spherical porous fins under fully wet conditions is carried out for the first time in this paper. Finned semi-spherical heat exchangers are widely used in many industrial applications such as aerospace, electronic kits and chemical processing systems. Also, porous media has an extensive application such as catalytic and inert packed bed reactors, enhancing drying efficiency, filtering, insulation, lubrication, reactor cooling, heat exchangers and solar collectors [3]. The concept of using fins made of porous materials by introducing the Darcy model [4,5] is firstly proposed by Kiwan and Al-Nimr [6]. Following some researches about extended surfaces analysis and porous fins are presented. Saedodin and Sadeghi [7] studied heat transfer of a cylindrical porous fin through fourth order Runge–Kutta method and found that the heat transfer rate of the porous fin could exceed from that of a solid fin. Turkyilmazoglu [8] found an exact solution for ther- mal diffusion in a straight fin with different exponential shape when the thermal conductivity and heat transfer coefficients are temperature-dependent by power laws. Aziz and Beers-Green [9] investigated the performance and optimum design of a longitudi- nal rectangular fin attached to a convectively heated wall by a numerical method, Adomian’s Decomposition Method (ADM) and the Differential Quadrature Method (DQM). Also, Khani and Aziz [10] applied Homotopy Analysis Method (HAM) for predicting the thermal performance of a straight fin with trapezoidal profile when both the thermal conductivity and heat transfer coefficient are temperature-dependent. Least Square Method (LSM) is applied to obtain thermal performance of some longitudinal porous fins with different section shapes and materials by Hatami and Ganji [11]. Recently, Hatami et al. [12] investigated the effect of Darcy and Rayleigh numbers on a rectangular porous fin by three efficient analytical methods; also they showed that LSM has the most accurate results among the applied methods. Fin efficiencies for http://dx.doi.org/10.1016/j.enconman.2014.05.007 0196-8904/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel./fax: +98 111 3234205. E-mail addresses: m.hatami2010@gmail.com (M. Hatami), ddg_davood@yahoo. com (D.D. Ganji). Energy Conversion and Management 84 (2014) 533–540 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman