Advances in Applied Mathematics and Mechanics Adv. Appl. Math. Mech., Vol. 3, No. 1, pp. 121-130 DOI: 10.4208/aamm.10-m1036 February 2011 Natural Convection of Temperature-Sensitive Magnetic Fluids in Porous Media Valentin Roussellet 1,2 , Xiaodong Niu 2, ∗ , Hiroshi Yamaguchi 2 , and Fr´ ed´ eric Magoul´ es 1 1 Applied Mathematics and Systems Laboratory, ´ Ecole Centrale Paris, 92295 Chˆ atenay-Malabry, France 2 Department of Mechanical Engineering, Doshisha University, Kyoto 610-0321, Japan Received 29 June 2010; Accepted (in revised version) 31 August 2010 Available online 15 October 2010 Abstract. In this article, natural convection of a temperature-sensitive magnetic fluid in a porous media is studied numerically by using lattice Boltzmann method. Results show that the heat transfer decreases when the ball numbers increase. When the magnetic field is increased, the heat transfer is enhanced; however the average wall Nusselt number increases at small ball numbers but decreases at large ball numbers due to the induced flow being more likely confined near the bottom walls with a high number of obstacles. PACS (2006): 44.30.+v, 47.65.Cb, 44.25.+f Key words: Temperature sensitive magnetic fluid, natural convection, porous media, lattice Boltzmann method. 1 Introduction Ferrofluids are a mixture of ferromagnetic nanoparticles in suspension in a carrier fluid [1] which makes them reactive to the presence of a magnetic field. The ferrous particles are usually coated with a surfactant, which allows the suspension to remain in a stable state. Among these fluids, temperature-sensitive magnetic fluids (TSMF) have their magnetization strongly dependent of the temperature [2]. Thus, with prop- erties such as energy transfers and flow which can be controlled with a magnetic field, TSMF have various promising applications, ranging from heat transfer tech- nologies [3, 4] to spatial engineering [5], and have been the subject of many researches ∗ Corresponding author. URL: http://kenkyudb.doshisha.ac.jp/rd/search/researcher/108197/index-j.html Email: louen@via.ecp.fr (V. Roussellet), xniu@mail.doshisha.ac.jp (X. D. Niu), hyamaguc@mail.doshisha. ac.jp (H. Yamaguchi), frederic.magoules@hotmail.com (F. Magoul´ es) http://www.global-sci.org/aamm 121 c ⃝2011 Global Science Press