Abstract

The effect of a small uniform applied horizontal magnetic field on separation of a binary mixture for the case of the fully developed natural convection of a fluid between two heated vertical walls in presence of heat generation has been studied analytically. Neglecting the induced electric field the equations governing the motion, temperature and concentration are solved by series expansion in terms of dimensionless parameter measuring buoyancy force. The solution obtained for concentration distribution is plotted against the width of the channel. It is found that the dimensionless number measuring the buoyancy force, the Hartmann number measuring the magnetic force, the thermal diffusion number and the heat generation parameter affects the species separation of rarer and lighter component significantly.

References

• Vajravelu K, Hadjinicolaou A (1993) Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation. Int. Comm. Heat Mass Transfer 20: 417-430
• Mendez F, Trevino C(2000) The conjugate conduction-natural convection heat transfer along a thin vertical plate with non-uniform internal heat generation. Int. J. Heat Mass Transfer 43: 2739-2748
• Sharma BR, Singh RN, Gogoi RK(2011) Effect of a strong transverse magnetic field on separation of species of a binary fluid mixture in generalisedCouette flow. Int. J. Applied Engineering Research 6(19): 2223-2235
• Sharma BR, Singh RN (2007) Soret effect in natural convection between heated vertical plates in a horizontal magnetic field. J ultra SciPhySci 19 (1)M:97-106
• Osterle JF, Young FJ (1961) Natural convection between heated vertical plates in a horizontal magnetic field. J. Fluid Mech. 11(4):512-518
• Srivastava AC ( 1992) Mass Diffusion in a Binary Mixture of Viscous Fluids. ProclNatlAcadSci 69 (A2):103-117
• Sharma BR, HazarikaGC(2002) Baro- diffusion and Thermal – diffusion in a Binary Mixture. Nepali Math Sci Report 20(1-2):65-73
• Sharma BR (2003) Baro – diffusion and Thermal diffusion in a Binary Mixture of Electrically Conducting Incompressible Fluids due to Rotation of a Circular Cylinder. Bull Pure ApplSci 22( E1):79-87
• Sharma BR(2004) Pressure- diffusion and Soret Effect in a Binary Fluid mixture. Bull Pure ApplSci 23(E1):165-173
• Sharma BR, Shah NA (1996) Baro- diffusion and Thermal – diffusion in a Binary Mixture. J Math PhySci 30(4):169-179
• Sharma BR,Gogoi RK (2000) The Effect Curvature of a Curved Annulus on Seperation of a Binary Mixture. In: Proceeding of the 46th annual technical session, Assam science Society, pp 81-89
• Sharma BR, Singh RN (2004) Soret Effect in Generalized MHD Couette Flow of a Binary Mixture. Bull Cal Math Soc 96(5):367-374
• Sharma BR, Singh RN (2003) The Effect of Inclination of a Channel on Seperation of a Binary Mixture of Viscous Incompressible Thermally and Electrically conducting fluids. Proc ISTAM 48:36-43
• Sharma BR, Shah NA(2002) the effect of pressure gradient and teperature gradient on seperation of a binary mixture of incompressible viscous fluids filling the space outside a uniformly rotating cylinder. In: Proceeding of the 47th annual technical session,vol. 3. Assam Science Society,pp 72-81
• Srivastava AC (1985) Barodiffusion in a binary mixture near a stagnation point. Nepali Math Sci Report 10(2):53-62
• SrivastavaAC(1999)Separation of a binary mixture of viscous fluids by thermal diffusion near a stagnation point. Ganit 50(2):129-134
• Srivastava AC (1999) Historical development of fluid dynamicsand mass diffusion in a binary mixture of viscous fluids. Math Stud 68( 1-4):73-85
• Srivastava AC ( 1991) seperation of binary mixture in a viscous fluid due to rotating heated sphere . Bull GUMA 6:63-72
• SrivastavaPK(2003) A study of flow of two component fluids , its heat transfer. Ph. D. Thesis, University of Lucknow, Lucknow, India
• Srivastava AC (1979) Barodiffusion in a binary mixture confined between two disk. Math Forum 2 (2): 16-21
• Sharma BR, Hazarika GC, Singh RN (2006) Influence of magnetic field on seperation of a binary mixture in free convection flow considering Soret effect. J natlAcad Math 20:1-20
• Sharma BR, Singh RN (2007) Soret effect in natural convection between heated vertical plates in a horizontal magnetic field. J ultra SciPhySci 19 (1)M:97-106
• Sharma BR, Singh RN ( 2008) Baro – diffussion and thermal – diffusionin a binary fluid mixture confined between two parallel discs in presence of an small axial magnetic field. Latin Am Appl Res 38:313 – 320
• Sharma BR, Singh RN ( 2009) Thermal diffusion in a binary fluid mixture confined between two concentric circular cylinders in presence of radial magnetic field. J Energy Heat Mass Transfer 31:27 – 38
• Sharma BR, Singh RN ( 2009) Baro – diffussion and Thermal – diffusionin a Binary Fluid Mixture Confined in an Inclined Channel in Presence of a Weak Magnetic Field. ProcNatlAcadSci India 79 ( AIII): 273-278
• Sharma B R, Singh R N (2010) Separation of species of a binary fluid mixture confined between two concentric rotating circular cylinders in presence of a strong radial magnetic field. Heat Mass Transfer 46:769-777