Double‐diffusive flow in enclosures

Numerical calculations are conducted for two‐dimensional steady‐state double‐diffusive flow in enclosures, where both the temperature and solute gradients are imposed horizontally, and the two buoyancy effects can either augment or counteract each other. Important controlling parameters including the thermal and solutal Grashof numbers, Schmidt number, and Prandtl number, are varied and new insights into the solutions of both the augmenting and counteracting modes gained. Even though the relative directions of the two buoyancy mechanisms reverse between the augmenting and counteracting modes, qualitative similarities in convection characteristics emerge. For both modes, with fixed thermal and solutal Grashof numbers, convection strength increases as the ratio between the Schmidt and Prandtl numbers, i.e., the Lewis number, becomes higher. With appropriate combinations of the Grashof number and buoyancy ratio, multiple‐cell flow patterns also appear in both modes, where the length scale disparity due to a ...

[1]  Frank P. Incropera,et al.  Solidification of an aqueous ammonium chloride solution in a rectangular cavity—II. Comparison of predicted and measured results , 1989 .

[2]  Wei Shyy,et al.  a Study of Recirculating Flow Computation Using Body-Fitted Coordinates: Consistency Aspects and Mesh Skewness , 1986 .

[3]  P. Le Quéré,et al.  Computation of natural convection in two-dimensional cavities with Chebyshev polynomials , 1985 .

[4]  R. Soulsby,et al.  The effect of horizontal gradients on thermohaline convection , 1969, Journal of Fluid Mechanics.

[5]  Christoph Beckermann,et al.  Double-diffusive convection due to melting , 1988 .

[6]  Wei Shyy,et al.  Numerical Recirculating Flow Calculation Using a Body-Fitted Coordinate System , 1985 .

[7]  Martin E. Glicksman,et al.  Interaction of Flows with the Crystal-Melt Interface , 1986 .

[8]  Marcel Vinokur,et al.  Conservation equations of gasdynamics in curvilinear coordinate systems , 1974 .

[9]  S. Ostrach.  Fluid Mechanics in Crystal Growth—The 1982 Freeman Scholar Lecture , 1983 .

[10]  S. Ostrach,et al.  Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients , 1985 .

[11]  Hwataik Han,et al.  Double diffusive natural convection in a vertical rectangular enclosure-!. Experimental study , 1991 .

[12]  A. E. Gill,et al.  Instabilities of a buoyancy-driven system , 1969, Journal of Fluid Mechanics.

[13]  Wei Shyy,et al.  A study of three-dimensional natural convection in high-pressure mercury lamps—II. Wall temperature profiles and inclination angles , 1990 .

[14]  Robert A. Brown,et al.  Convection and segregation in directional solidification of dilute and non-dilute binary alloys: Effects of ampoule and furnace design , 1987 .

[15]  Sergio D. Felicelli,et al.  Thermosolutal convection during dendritic solidification of alloys: Part II. Nonlinear convection , 1989 .

[16]  Julian Szekely,et al.  Mathematical and physical modelling of doublediffusive convection of aqueous solutions crystallizing at a vertical wall , 1988, Journal of Fluid Mechanics.

[17]  G. de Vahl Davis,et al.  Natural convection in a square cavity: A comparison exercise , 1983 .

[18]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[19]  S. Thangam,et al.  Double-diffusive convection in an inclined fluid layer , 1982, Journal of Fluid Mechanics.

[20]  G. Golub,et al.  Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. , 1972 .

[21]  Wei Shyy,et al.  On the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates , 1990 .

[22]  Wei Shyy,et al.  A study of finite difference approximations to steady-state, convection-dominated flow problems , 1985 .

[23]  Bahgat Sammakia,et al.  Buoyancy-Induced Flows and Transport , 1988 .