Effect of optical properties on oscillatory hydromagnetic double-diffusive convection within semitransparent fluid Mohamed Naceur Borjini a , Habib Ben Aissia b , Kamel Halouani c , Belkacem Zeghmati d, * a De ´partement de Physique, Faculte ´ des Sciences 5019 Monastir, Tunisia b Ecole Nationale d’Inge ´nieurs, 5012 Monastir, Tunisia c METS – ENIS – IPEIS – Route Menzel Chaker B.P: 805, 3000 Sfax, Tunisia d MEPS-GME, Universite ´ de Perpignan Via Domitia, 52 Avenue Paul Alduy, 68660 Perpignan Cedex, France Received 2 June 2005; received in revised form 24 February 2006 Available online 19 June 2006 Abstract The effect of radiative heat transfer on the hydromagnetic double-diffusive convection in two-dimensional rectangular enclosure is studied numerically for fixed Prandtl, Rayleigh, and Lewis numbers, Pr = 13.6, Ra = 10 5 , Le = 2. Uniform temperatures and concentra- tions are imposed along the vertical walls while the horizontal walls are assumed to be adiabatic and impermeable to mass transfer. The influences of the optical thickness and scattering albedo of the semitransparent fluid on heat and mass transfer with and without mag- netic damping are depicted. When progressively varying the optical thickness, multiple solutions are obtained which are steady or oscil- latory accordingly to the initial conditions. the mechanisms of the transitions between steady compositionally dominated flow and unsteady thermally dominated flow are analyzed. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Hydromagnetic double-diffusive convection; Internal radiation; Radiative properties; Thermosolutal instability 1. Introduction The double-diffusive convection, which takes place when compositionally driven buoyant convection and thermally driven buoyant convection occur simultaneously, arises in a very wide range of fields such as oceanography, astro- physics, chemical vapour transport process, drying process, crystal growth process, etc. This convection was widely experimentally and numerically studied for varied several non-dimensional parameters namely the Lewis and Prandtl numbers, the buoyancy ratio and for either aiding or opposing heat and mass gradients. Reviews on this subject can be found in the publications of Nishumira et al. [1], Ostrach [2], Viskanta et al. [3], Be ´ghein et al. [4], Zhou and Zebib [5], Chamkha and Al-Naser [6], Costa [7,8] and Papanicalaou and Belessiotis [9]. It has been found that, for a buoyancy ratio close to the unity, an oscillatory flow caused by the interaction between thermal and com- positional recirculations occurs. Nishumira et al. [1] carried out a careful depiction of the mechanism of this oscillatory flow. For the crystal growth process, the double-diffusive convection is induced because of the non-uniform distribu- tion of impurities [10] and the quality of the growing crys- tal is severely affected by the melt convection and any oscillations are disadvantageous. The request of an external magnetic field to control fluid flow and heat transfer in electrically conducting fluids has long been recognized in many applications such as crystal growth. Numerous studies on magnetoconvection were presented in the last few years especially for lower values of Prandtl number. Detailed bibliography can be found in Grandet et al. [11], Mo ¨ßner and Mu ¨ller [12] and Cham- kha and Al-Naser [6]. Lately Aleksandrova and Molokov 0017-9310/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2006.03.041 * Corresponding author. E-mail addresses: naceur.borjini@fsm.rnu.tn (M.N. Borjini), Habib. benaissia@enim.rnu.tn (H.B. Aissia), Kamel.Halouani@ipeis.rnu.tn (K. Halouani), Zeghmati@univ-perp.fr (B. Zeghmati). www.elsevier.com/locate/ijhmt International Journal of Heat and Mass Transfer 49 (2006) 3984–3996