Natural Convection in Inclined Two Dimensional Rectangular Cavities

2009 ◽  
Author(s):  
Lyes Khezzar ◽  
Dennis Siginer
Keyword(s):  
Natural Convection ◽  
Two Dimensional ◽  
Square Cavity ◽  
Transfer Rates ◽  
Aspect Ratios ◽  
Temperature Distributions ◽  
Start Up ◽  
Side Walls ◽  
Boussinesq Fluid ◽  
Rayleigh Numbers

Steady two-dimensional natural convection in fluid filled cavities has been investigated numerically. The conservation equations of mass, momentum and energy governing the motion of a Newtonian Boussinesq fluid have been numerically solved using the finite volume technique. The computations were performed for three cavity height based Rayleigh numbers 104, 105 and 106. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for several aspect ratios. For the case of the square cavity the calculated values are in excellent agreement with previously published benchmark results. The effects of the inclination of the cavity to the horizontal, with the angle varying from 0 to 180° and the initial start up conditions were investigated in turn for each aspect ratio. The inclination and the “initial” assumed conditions have a significant effect on the flow patterns, temperature distributions and the heat transfer rates. In particular it is found that the average Nusselt number exhibits discontinuities for rectangular cavities and that the occurrence of the discontinuity with angle of inclination is strongly influenced by the assumed start up field in the steady calculations in much the same way as the hysteresis effect that was identified by other workers.

Natural Convection With Non-Newtonian Shear-Thinning Power Law Fluids in Inclined Two Dimensional Rectangular Cavities

2009 ◽  
Author(s):  
Lyes Khezzar ◽  
Dennis Siginer
Keyword(s):  
Natural Convection ◽  
Numerical Experiments ◽  
Newtonian Fluids ◽  
Flow Mode ◽  
Mode Transition ◽  
Two Dimensional ◽  
Power Law Fluids ◽  
Side Walls ◽  
Differential Scheme ◽  
Boussinesq Fluid

Steady two-dimensional natural convection in rectangular cavities has been investigated numerically. The conservation equations of mass, momentum and energy under the assumption of a Newtonian Boussinesq fluid have been solved using the finite volume technique embedded in the Fluent code for a Newtonian (water) and three non Newtonian carbopol fluids. The highly accurate Quick differential scheme was used for discretization. The computations were performed for one Rayleigh number, based on cavity height, of 105 and a Prandtl number of 10 and 700, 6,000 and 1.2×104 for the Newtonian and the three non-Newtonian fluids respectively. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for one aspect ratio of 6. Comparison between the Newtonian and the non-Newtonian cases is conducted based on the behaviour of the average Nusselt number with angle of inclination. Both Newtonian and non-Newtonian fluids exhibit similar behavior with a sudden drop around an angle of 50° associated with flow mode transition from multi-cell to single-cell mode.

scholarly journals Transient Natural Convection in Porous Square Cavity Heated and Cooled on Adjacent Walls

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. S. Selamat ◽  
I. Hashim ◽  
M. K. Hasan
Keyword(s):  
Steady State ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Transient State ◽  
Governing Equations ◽  
Square Cavity ◽  
Transient Natural Convection ◽  
Temperature Distributions ◽  
Rayleigh Numbers

Transient natural convection in a square cavity filled with a porous medium is studied numerically. The cavity is assumed heated from one vertical wall and cooled at the top, while the other walls are kept adiabatic. The governing equations are solved numerically by a finite difference method. The effects of Rayleigh number on the initial transient state up to the steady state are investigated for Rayleigh number ranging from 10 to2×102. The evolutions of flow patterns and temperature distributions were presented for Rayleigh numbers,Ra=102and103. It is observed that the time taken to reach the steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

Steady, Two-Dimensional, Natural Convection in Rectangular Enclosures With Differently Heated Walls

1987 ◽  
Vol 109 (2) ◽  
pp. 400-406 ◽  
Author(s):  
K. S. Chen ◽  
J. R. Ho ◽  
J. A. C. Humphrey
Keyword(s):  
Natural Convection ◽  
Moving Boundary ◽  
Side Wall ◽  
Temperature Inversion ◽  
Bottom Wall ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Aspect Ratios ◽  
Temperature Boundary ◽  
Rayleigh Numbers

Numerical results are presented for steady natural convection in two-dimensional rectangular enclosures in which the side walls, top wall, and bottom wall are at uniform temperatures θs, θt, and θb, respectively, and θs > θt > θb. Raylight numbers ranging from 104 to 107 and aspect ratios of 1 and 1.5 were investigated. The top wall was modeled as an impermeable rigid surface or an impermeable free-moving boundary. The calculations reveal two flow regions. In the upper part of the enclosure two large counterrotating cells appear, separated by a descending plume of fluid. Near the bottom wall the flow is almost motionless and stably stratified. The temperature in the central portion of the enclosure is almost uniform due to mixing by the recirculating cells. A temperature inversion occurs near the top wall and is particularly noticeable at high Rayleigh numbers. At high Rayleigh numbers the flow breaks up into smaller cells. The result is that each main recirculation region develops a secondary counterrotating eddy within it. The condition of a free surface as the top wall boundary condition significantly affects the circulation and heat transfer throughout the flow domain. Numerical experiments reveal the extent to which the flow field in the enclosure is affected by an asymmetric specification of side-wall temperature boundary conditions.

scholarly journals Heat transfer and entropy generation for natural convection by adiabatic obstacles inside a cavity heated on the left side

2020 ◽  
Vol 48 (4) ◽  
pp. 825-832
Author(s):  
Jamal Baliti ◽  
Mohamed Hssikou ◽  
Youssef Elguennouni ◽  
Ahmed Moussaoui ◽  
Mohammed Alaoui
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Entropy Generation ◽  
Temperature Gradients ◽  
Large Temperature ◽  
Square Cavity ◽  
Transfer Rates ◽  
Thermal Fields ◽  
Rayleigh Numbers

By using finite difference method, the problem of heat transfer and entropy generation for natural convection of a fluid inside a square cavity with inner adiabatic bodies has been investigated numerically. Calculations have been made for Rayleigh numbers ranging from 102 to 5·104 for two obstacles with different heights. Results are presented as streamlines, isotherm contours and Nusselt number for Prandtl number of 0.71 (assuming the cavity is filled with air). The obtained results demonstrate the effects of pertinent parameters on the fluid flow, thermal fields and heat transfer inside the cavity. The results show that the heat transfer rates generally increase with the shrink of the obstacle size and with the increase of Rayleigh number. The entropy generation is higher at locations with large temperature gradients. Excellent agreement is obtained with previous results in the literature.

Natural Convection in a Horizontal Fluid Layer With Volumetric Energy Sources

1975 ◽  
Vol 97 (2) ◽  
pp. 204-211 ◽  
Author(s):  
F. A. Kulacki ◽  
M. E. Nagle
Keyword(s):  
Natural Convection ◽  
Fluid Layer ◽  
Lower Boundary ◽  
Linear Stability Theory ◽  
Volumetric Heating ◽  
Aspect Ratios ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Steady Heat ◽  
Horizontal Fluid Layer

Natural convection with volumetric heating in a horizontal fluid layer with a rigid, insulated lower boundary and a rigid, isothermal upper boundary is experimentally investigated for Rayleigh numbers from 114 to 1.8 × 106 times the critical value of linear stability theory. Joule heating by alternating current passing horizontally through the layer provides the volumetric energy source. Layer aspect ratios are kept small to minimize the effects of side walls. A correlation for mean Nusselt number is obtained for steady heat transfer, and data are presented on fluctuating temperatures at high Rayleigh numbers and on developing temperature distributions when the layer is subjected to a step change in power.

Natural Convection for Air and Molten Gallium in Square- and Elbow-Shaped Enclosures

2015 ◽  
Vol 789-790 ◽  
pp. 462-470
Author(s):  
Emel Evren-Selamet ◽  
Ahmet Selamet
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Scheme ◽  
Lead Author ◽  
Convection Flow ◽  
Two Dimensional ◽  
Natural Convection Flow ◽  
Transfer Rates ◽  
Chaotic Flow ◽  
Rayleigh Numbers

Natural convection flow of air and molten gallium in square and elbow-shaped enclosures is studied by a two-dimensional numerical scheme developed by the lead author. The dependence of the flow field and Nusselt number (Nu) on the Rayleigh (Ra) and Prandtl (Pr) numbers is examined in both enclosures. Results are obtained with sufficiently large Rayleigh numbers to observe transition from steady to damped or undamped oscillatory, and chaotic flow. Constant and oscillatory heat transfer rates are compared in both enclosures for air (Pr=0.71) and molten gallium (Pr=0.024).

Oscillatory Natural Convection of a Liquid Metal in Circular Cylinders

1994 ◽  
Vol 116 (3) ◽  
pp. 627-632 ◽  
Author(s):  
Y. Kamotani ◽  
F.-B. Weng ◽  
S. Ostrach ◽  
J. Platt
Keyword(s):  
Experimental Study ◽  
Natural Convection ◽  
Liquid Metal ◽  
Oscillatory Flow ◽  
Circular Cylinders ◽  
Flow Structures ◽  
Supercritical Flow ◽  
Aspect Ratios ◽  
Oscillation Frequencies ◽  
Rayleigh Numbers

An experimental study is made of natural convection oscillations in gallium melts enclosed by right circular cylinders with differentially heated end walls. Cases heated from below are examined for angles of inclination (φ) ranging from 0 deg (vertical) to 75 deg with aspect ratios Ar (height/diameter) of 2, 3, and 4. Temperature measurements are made along the circumference of the cylinder to detect the oscillations, from which the oscillatory flow structures are inferred. The critical Rayleigh numbers and oscillation frequencies are determined. For Ar=3 and φ = 0 deg, 30 deg the supercritical flow structures are discussed in detail.

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

2003 ◽  
Vol 125 (4) ◽  
pp. 624-634 ◽  
Author(s):  
Xundan Shi ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Left Wall ◽  
Flow Modification ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Blockage Effect

A finite-volume-based computational study of steady laminar natural convection (using Boussinesq approximation) within a differentially heated square cavity due to the presence of a single thin fin is presented. Attachment of highly conductive thin fins with lengths equal to 20, 35 and 50 percent of the side, positioned at 7 locations on the hot left wall were examined for Ra=104,105,106, and 107 and Pr=0.707 (total of 84 cases). Placing a fin on the hot left wall generally alters the clockwise rotating vortex that is established due to buoyancy-induced convection. Two competing mechanisms that are responsible for flow and thermal modifications are identified. One is due to the blockage effect of the fin, whereas the other is due to extra heating of the fluid that is accommodated by the fin. The degree of flow modification due to blockage is enhanced by increasing the length of the fin. Under certain conditions, smaller vortices are formed between the fin and the top insulated wall. Viewing the minimum value of the stream function field as a measure of the strength of flow modification, it is shown that for high Rayleigh numbers the flow field is enhanced regardless of the fin’s length and position. This suggests that the extra heating mechanism outweighs the blockage effect for high Rayleigh numbers. By introducing a fin, the heat transfer capacity on the anchoring wall is always degraded, however heat transfer on the cold wall without the fin can be promoted for high Rayleigh numbers and with the fins placed closer to the insulated walls. A correlation among the mean Nu, Ra, fin’s length and its position is proposed.

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