Effects of magnetic field on 3D double diffusive convection in a cubic cavity filled with a binary mixture (original) (raw)
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Numerical study of double-diffusive natural convection in a square cavity
International Journal of Heat and Mass Transfer, 1992
Steady-state thermosolutal convection in a square cavity filled with air, submitted to horizontal temperature and concentration gradients, is studied numerically. In the first series of numerical simulations, the influence of solutal buoyancy force on heat or mass transfer rate is investigated : Lewis and thermal Rayleigh numbers are kept constant (Le = 1. Ra, = lo'), solutal Rayleigh number is varied (Ra, = lo'-5 x 10'). The second series deals with the influence of Lewis number on fluid motion for heat transfer driven flow (RaT = lo', Ra, = 0) and mass transfer driven flow (Ra, = 0, Ra, = 10') configurations. Lewis number is varied from 0.3 to 5. Correlations are obtained between heat and mass transfer rates and the non-dimensional numbers characterizing both phenomena.
Heat Transfer Engineering, 2018
This paper deals with natural convection flows evolving inside an ended and differentially heated cavity, which is filled either with an air or an air-CO 2 mixture. The investigation was conducted through the laminar regime to analyze buoyancy ratio changes' effect on heat and mass transfers both in aiding and opposing flows. The thermal Rayleigh number was varied from 10 3 to 10 7. Streamlines, isotherms, isoconcentrations, and local and average Nusselt and Sherwood numbers are provided to demonstrate the convective flow induced. The governing equations are solved by finite volume method using SIMPLEC algorithm to handle the pressure-velocity coupling. The buoyancy ratio effect on dynamic, thermal and mass fields is noteworthy, exhibiting both the competition between thermosolutal forces and fields' stratification. From the results, it turned out that, in general, when the buoyancy ratio is (1) positive, thermosolutal buoyancy forces are cooperative, (2) nil, solutal buoyancy forces are weak and the flow is merely thermoconvective, (3) negative and greater than-1, buoyancy effects are competing and thermal convection dominates, (4)-1, buoyancy effects are canceled and heat and mass transfers are driven only by diffusion, and (5) less than-1, buoyancy forces compete with a dominant solutal convection.
Numerical Heat Transfer, Part A: Applications, 2017
In this paper double diffusive natural convection in a square cavity in the presence of external magnetic field has been studied numerically by Galerkin's weighted residual finite element method using velocity-vorticity formulation. Simulation results are reported for 0 < Ha < 200, buoyancy ratio, 2 < N < 2, 104 < Ra < 106 and field inclination angle varying from 00 to 3600 for different fluid systems, namely gas, water, and liquid Gallium. Results indicate that the streamline pattern is greatly influenced by the direction and intensity of magnetic field and at Ra = 1.0e5, the increase in Ha from 0 to 30 has resulted in a decrease in Nusselt number and Sherwood number by about 72% and 78% respectively. The inclination angle has played an important role in the suppression of heat and mass transfer, maximum suppression is experienced at Θ = 45 and 270 while minimum is recorded at Θ = 135 and 315. Liquid Gallium showed the least response to change in magnetic field intensity compared to other two fluids.
Double Diffusive Convection in an Inclined Rectangular Cavity
IJMTT, January, 2018
The natural convection which is caused by combined effect of temperature buoyancy and concentration buoyancy is studied analytically in an inclined tall rectangular cavity with uniform heat flux and mass flux along the vertical sides. The analytical part is true to the boundary layer regime where the heat transfer and mass transfer rates are governed by convection. An Oseen-linearized solution is for tall rectangular cavity filled with the combination characterized by Lewis number Le which is equal to one and arbitrary buoyancy ratios. The influence of the angle of inclination for different Rayleigh number Ra, on velocity and temperature distributions is determined. It is found that Nusselt number Nu and Sherwood number Sh increases the angle of inclination, passes through an apex and then begins to fall down. The effect of inclination on Nu and Sh is more identified as the Ra is increased. The apex of the Nu and Sh occurs at a lesser inclination angle when Ra is raised. The effect of Le is recorded by a similarity solution valid for Le beyond one in heat transfer driven flow, and for Le less than one in mass transfer driven flow.
International Journal of Heat and Mass Transfer, 2014
A numerical investigation of laminar natural double diffusive convection in an open ended vertical cylindrical annulus with unheated entry and unheated exit is performed. Both boundary conditions of uniform wall temperature/uniform wall concentration (UWT/UWC) and uniform heat flux/uniform mass flux (UHF/UMF) are considered. Results of dimensionless induced volume rate Q, average Nusselt number Nu and Sherwood number Sh are obtained for air flow under various buoyancy ratio N, Grashof numbers due to heat and mass transfer Gr T and Gr M , Schmidt number Sc and combinations of unheated entry, heated section and unheated exit length. Since the flow under consideration is a boundary layer type, the governing partial differential equations was discretized to a linear system of equations by the use of an implicit finite difference method. The nonlinear convective terms are approximated by second upwind difference method for the numerical stability. The numerical results reveal that the presence of unheated entry and unheated exit severely affects the heat and mass transfer rates. The numerical solutions are found to approach asymptotically the closed form solutions for fully developed flow. Further, the present numerical results are validated with the existing solutions for pure thermal convection and are found to be in good agreement.
Double diffusive convection in a vertical rectangular cavity
Physics of Fluids, 1997
In the present work, we study the onset of double diffusive convection in vertical enclosures with equal and opposing buoyancy forces due to horizontal thermal and concentration gradients ͑in the case Gr S /Gr T ϭϪ1, where Gr S and Gr T are, respectively, the solutal and thermal Grashof numbers͒. We demonstrate that the equilibrium solution is linearly stable until the parameter Ra T ͉LeϪ1͉ reaches a critical value, which depends on the aspect ratio of the cell, A. For the square cavity we find a critical value of Ra c ͉LeϪ1͉ϭ17 174 while previous numerical results give a value close to 6000. When A increases, the stability parameter decreases regularly to reach the value 6509, and the wave number reaches a value k c ϭ2.53, for A→ϱ. These theoretical results are in good agreement with our direct simulation. We numerically verify that the onset of double diffusive convection corresponds to a transcritical bifurcation point. The subcritical solutions are strong attractors, which explains that authors who have worked previously on this problem were not able to preserve the equilibrium solution beyond a particular value of the thermal Rayleigh number, Ra o1. This value has been confused with the critical Rayleigh number, while it corresponds in fact to the location of the turning point.
The present study has been conducted to numerically investigate the heat and mass transport mechanism of laminar mixed convection in a shear- and buoyancy-driven cavity subjected to differential heating and differential species concentration. The focus is on the interaction of the forced convection induced by the moving sidewalls with the natural convection induced by the buoyancy. Two orientations of the direction of the moving walls at the cavity are considered in order to simulate the aiding and opposing buoyancy mechanisms. The two-dimensional transport equations for continuity, momentum, energy and species transfer are solved using the finite element formulation based on the Galerkin method of weighted residuals. Parametric studies of the effect of the mixed convection parameter, Richardson number on the fluid flow and heat and mass transfer have been performed. It is found that both Richardson number and the direction of moving walls affect the fluid flow and heat and mass transfer in the cavity. In addition, the predicted results for the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions.
Journal of Advanced Chemical Engineering
In this paper, entropy generation of double-diffusive natural convection in a 2D dimensional enclosure with magnetic and Dufour effects has been numerically performed. Dirichlet boundary conditions for temperature and solute concentration are applied to the two vertical walls of the enclosure; wheras the two horizontal walls are adiabatic and insulated. The governing equations of continuity, momentum, energy and concentration are numerically solved by using a Control Volume Fined Elements Method, CVFEM of Patankar. The governing parameters of the problem are the thermal Grashof number (Gr T), the buoyancy ratio (N), the Hartmann number (Ha), the Dufour parameter (Du) and the Prandtl number (Pr). The obtained results were presented graphically via the velocity field components, temperature and concentration distributions, entropy genertion rate behaviour and by isotherms, streamlines and isentropic lines maps. The average Nusselt and Sherwood numbers are also derived and discussed numerically. The investigated results showed that the flow field and then entropy generation are notably influenced by the considering parameters.
Onset of double-diffusive convection in a rectangular cavity with stress-free upper boundary
Physics of Fluids, 2010
Double-diffusive buoyancy convection in an open-top rectangular cavity with horizontal temperature and concentration gradients is considered. Attention is restricted to the case where the opposing thermal and solutal buoyancy effects are of equal magnitude ͑buoyancy ratio R =−1͒. In this case, a quiescent equilibrium solution exists and can remain stable up to a critical thermal Grashof number Gr c. Linear stability analysis and direct numerical simulation show that depending on the cavity aspect ratio A, the first primary instability can be oscillatory, while that in a closed cavity is always steady. Near a codimension-two point, the two leading real eigenvalues merge into a complex coalescence that later produces a supercritical Hopf bifurcation. As Gr further increases, this complex coalescence splits into two real eigenvalues again. The oscillatory flow consists of counter-rotating vortices traveling from right to left and there exists a critical aspect ratio below which the onset of convection is always oscillatory. Neutral stability curves showing the influences of A, Lewis number Le, and Prandtl number Pr are obtained. While the number of vortices increases as A decreases, the flow structure of the eigenfunction does not change qualitatively when Le or Pr is varied. The supercritical oscillatory flow later undergoes a period-doubling bifurcation and the new oscillatory flow soon becomes unstable at larger Gr. Random initial fields are used to start simulations and many different subcritical steady states are found. These steady states correspond to much stronger flows when compared to the oscillatory regime. The influence of Le on the onset of steady flows and the corresponding heat and mass transfer properties are also investigated.