D. Senthil kumar Research Scholar K. Murugesan 1 Assistant Professor e-mail: krimufme@iitr.ernet.in Akhilesh Gupta Professor Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, India Numerical Analysis of Interaction Between Inertial and Thermosolutal Buoyancy Forces on Convective Heat Transfer in a Lid-Driven Cavity In this paper, results on double diffusive mixed convection in a lid-driven cavity are discussed in detail with a focus on the effect of interaction between fluid inertial force and thermosolutal buoyancy forces on convective heat and mass transfer. The governing equations for the mathematical model of the problem consist of vorticity transport equa- tion, velocity Poisson equations, energy equation and solutal concentration equation. Numerical solution for the field variables are obtained by solving the governing equa- tions using Galerkin’s weighted residual finite element method. The interaction effects on convective heat and mass transfer are analyzed by simultaneously varying the charac- teristic parameters, 0.1  Ri  5, 100  Re  1000, and buoyancy ratio (N), -10  N  10. In the presence of strong thermosolutal buoyancy forces, the increase in fluid inertial force does not make significant change in convective heat and mass transfer when the thermal buoyancy force is smaller than the fluid inertial force. The fluid inertial force enhances the heat and mass transfer only when the thermal buoyancy force is either of the same magnitude or greater than that of the fluid inertial force. The presence of aiding solutal buoyancy force enhances convective heat transfer only when Ri becomes greater than unity but at higher buoyancy ratios, the rate of increase in heat transfer decreases for Re = 400 and increases for Re = 800. No significant change in heat transfer is ob- served due to aiding solutal buoyancy force for Ri  1 irrespective of the Reynolds number. DOI: 10.1115/1.4002029 Keywords: thermosolutal buoyancy forces, lid-driven cavity, velocity-vorticity equations, mixed convection 1 Introduction The study of mixed convective heat and solute transport phe- nomena find importance in wide engineering applications such as atmospheric fluid convection, oceanography, nuclear waste dis- posal, drying chamber, chemical vapor deposition, crystal growth, plasma spray coating, etc. In applications such as nuclear waste disposal facilities, the primary interest will be the study of thermal energy transport in the presence of solute transport whereas the study of solute transport in the presence of heat transfer becomes important in the analysis of crystal growth, plasma spray coating problems. In all the above applied problems apart from the fluid inertial forces, the fluid momentum balance is also shared by the significant contribution of thermosolutal buoyancy forces gener- ated as a result of temperature and species concentration gradi- ents. When the fluid momentum balance consists of fluid inertial force derived from an external source and thermosolutal buoyancy forces then the resulting convective phenomenon is called double diffusive mixed convection. If the fluid momentum balance is achieved purely by thermosolutal buoyancy forces without exter- nally derived fluid inertial force, then the phenomenon is called double diffusive natural convection. The mechanism behind fluid flow, heat and mass transfer in double diffusive natural convection has been well understood for enclosure problems 1–3 because in such problems only the solutal buoyancy force is superimposed on the well established natural convection heat transfer problems. In contrast, thermosolutal buoyancy driven mixed convection prob- lems give rise to complex flow situations, which in turn signifi- cantly affect the convective heat and mass transfer phenomena. When both thermal and solutal concentration gradients exist in a system, then the resulting density gradients may act in the same direction or in the opposite directions because the volumetric ther- mal expansion coefficient is always negative whereas the volu- metric solutal expansion coefficient may be positive or negative depending upon the relation between density and species concen- tration. In the absence of solutal buoyancy force, the mixed convective heat transfer with only thermal buoyancy force is characterized by Richardson number, defined as Gr T / Re 2 and the Reynolds number for a given Prandtl number fluid. In this case, the fluid momentum conservation is tightly coupled with the fluid energy conservation. For a fixed value of Gr T with increase in Reynolds number, the contribution from thermal buoyancy force to the fluid momentum balance becomes insignificant and the vice versa is expected at high value of Gr T for a fixed Reynolds number. Although the physical mechanism behind mixed convection heat transfer phe- nomena is well understood 4,5, the situation is not straight for- ward in the presence of solutal buoyancy force. The solutal buoy- ancy force can be represented by defining solutal Grashof number Gr S similar to thermal Grashof number Gr T . In order to take into account the relative importance of solutal buoyancy force along with thermal buoyancy force, a buoyancy ratio is defined as the 1 Corresponding author. Contributed by Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 19, 2009; final manuscript received May 3, 2010; published online August 13, 2010. Assoc. Editor: Jayathi Murthy. 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