Numerical study of double-diffusive natural convection in a square cavity (original) (raw)
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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, 2011
A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra e = 10 3-10 5 , while the influence of the heat source was evaluated through the relation R = Ra i /Ra e , investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra e whereas these features are absent at higher Ra e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.
Double-diffusive natural convection in an open top square cavity, partially heated and salted from the side, is studied numerically via the heatline approach. Constant temperatures and concentrations are imposed along the right and left walls, while the heat balance at the surface is assumed to obey Newton's law of cooling. The finite difference method is used to solve the dimensionless governing equations. The governing parameters involved in this investigation are the thermal Marangoni number (0 Ma T 1000), the solutal Marangoni number (0 Ma c 1000), the Lewis number (10 Le 100), the heater size, (0.2 s 0.8), Grashof number, Gr ¼ 10 4 , Prandtl number, Pr ¼ 10, Biot number, Bi ¼ 0.1 and aspect ratio 1. The numerical results are reported for the effect of the Marangoni number, Lewis number and heater size on the contours of streamlines, isotherms, isoconcentrations, masslines and heatlines. The predicted results for the average Nusselt number and Sherwood number are presented for various parametric conditions. It is shown that the heat and mass transfer mechanisms are affected by the heater segment length. A direct relation between both opposing (N ¼ À2) and aiding flow (N ¼ 2), and heat and mass transfer process is found for various values of the Marangoni and Lewis numbers.
Double diffusive natural convection in a square enclosure with heat and mass diffusive walls
International Journal of Heat and Mass Transfer, 1997
Double-diffusive convective flow in a square enclosure with segmental heat sources is solved numerically .Constant temperatures and concentration are imposed along the right wall of the enclosure at low temperature and concentration which assumed as a heat and mass sink .The heaters are at constant temperature and concentration assumed as source of heat and mass at the left wall while the rest of this wall is adiabatic. The other two sides from the cavity are assumed adiabatic walls .The flow laminar and under steady state condition are considered .The transport equations for continuity, momentum, energy and mass transfer are solved. The numerical procedure adopted in this analysis yields consistent performance over a wide range of parameters, Rayleigh number (10 3 ≤ Ra ≤ 10 6) dimensionless heater lengths (0.2≤ L 1 /H≤1) ,buoyancy ratio (-10 ≤ N ≤10) and Prandtl number, (0.01 <Pr <100) .This study was done for constant Lewis number Le = 2.The results show the average Nusselt number and average sherwood number are increased with the increasing of the Rayleigh number, the dimensionless heater length and Prandtl number. On the other hand, the Prandtl number has significant effect on the Nusselt number and average Sherwood number to the value of Pr = 0.7 .The results for the average Nusselt number are correlated as a function of dimensionless heater length, buoyancy ratio, Rayleigh number and Prandtl number .The results were compared with previous results and good agreement was found.
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 Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top
Journal of The Institution of Engineers (India): Series C, 2020
The prime objective of the present numerical study is to analyse buoyancy-driven thermal flow behaviour inside an enclosure with the application of nonlinear heating from top surface which is commonly essential in glass industries. A fluid-filled square cavity with sinusoidal heating from top surface, adiabatic bottom wall and constant temperature side walls is considered here. The thermal flow behaviour has been numerically observed with the help of relevant parameters like stream functions, isotherms and Nusselt number. For the present investigation, Rayleigh number (Ra), Prandtl number (Pr) and heating frequency of the wall (x) are varied from 10 3 to 10 6 , 0.7 to 7 and 0.5 to 2, respectively. It has been noticed from the investigation that flow dynamics drastically alter with Ra, x and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by x and Pr. Keywords Free convection Á Buoyancy Á Rayleigh number Á Pr number Á Sinusoidal heating Greek letters a Thermal diffusivity (m 2 s-1) b Volumetric expansion coefficient (K-1) q Kinetic viscosity (m 2 s-1) t Density of fluid (kg m-3) h Dimensionless temperature x Heating frequency of the top wall
Double Diffusive Convection in an Inclined Rectangular Cavity Bounded by Porous Lining
2020
The natural convection that is caused by the joined effect of temperature buoyancy and concentration buoyancy is analytically studied in an inclined rectangular cavity with uniform heat flow and mass flow along the vertical sides bounded by the porous lining. And the BJ condition is employed on the porous fluid interface. The analytical part is exact to the boundary layer regime where heat transfer and mass transfer rates are directed by convection. A linearized Oseen solution is for a tall rectangular cavity filled with the combination characterized by the Lewis number Le which is equal to one and arbitrary buoyancy ratios. The effect of Le is recorded by a valid similarity solution for Le over one in the heat transfer-driven flow, and for Le less than one in the mass-transfer-driven flow. The solutions are estimated for different values of the slip parameter N and the angle of inclination . The results are equated with those of the limiting cases of the slip parameter which tends ...
Simulation of Natural Convection in a Square Cavity with Partially Heated and Cooled Vertical Walls
Proceeding of 5th Thermal and Fluids Engineering Conference (TFEC)
Natural convection driven by temperature differences between partially heated and cooled vertical walls in a square cavity is studied numerically. Steady or unsteady cellular flow structures and temperature patterns are illustrated along with the evolution of heat transfer rates in terms of Nusselt number. The cavity is filled with fluids of various Prandtl number, including .024 (liquid metal), .71 (air), 6 (water), and 450 (silicon oil). The effect of Prandtl and Rayleigh numbers on the flow regime and heat transfer is established along with two different thermal boundary conditions.