Numerical Investigation of Variable Property Effects on Laminar Natural Convection of Gases Between Two Horizontal Isothermal Concentric Cylinders

1986 ◽  
Vol 108 (4) ◽  
pp. 783-789 ◽  
Author(s):  
D. N. Mahony ◽  
R. Kumar ◽  
E. H. Bishop
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boussinesq Approximation ◽  
Variable Properties ◽  
Transfer Rates ◽  
Concentric Cylinders ◽  
Weighted Mean Temperature ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Gap Width

A numerical finite difference investigation has been conducted to determine the effects of variable properties on the laminar natural convection of gases between horizontal isothermal concentric cylinders. Velocity profiles, temperature profiles, and heat transfer rates have been computed for diameter ratios of 1.5, 2.28, 2.6, and 5.0 and Rayleigh numbers based on gap width up to 1.8 × 105. The temperature difference ratio θo was varied from 0.2 to 3.0, and the range of validity of the Boussinesq approximation was determined to be θo = 0.2. A volume-weighted mean temperature was shown to be the most effective reference temperature to reduce the heat transfer data for each diameter ratio to a single curve of the form keq = C RaLn, for 0.2 ≤ θo ≤ 3.0 and RaL = 2.0 × 105.

Laminar Natural Convection Heat Transfer From a Horizontal Circular Cylinder to Liquid Metals

1991 ◽  
Vol 113 (1) ◽  
pp. 91-96 ◽  
Author(s):  
K. Sugiyama ◽  
Y. Ma ◽  
R. Ishiguro
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Circular Cylinder ◽  
Liquid Metals ◽  
Convection Heat Transfer ◽  
Boussinesq Approximation ◽  
Large Temperature ◽  
Transfer Rates ◽  
Laminar Natural Convection ◽  
Horizontal Circular Cylinder

The objective of the present study is to clarify the heat transfer characteristics of natural convection around a horizontal circular cylinder immersed in liquid metals. Experimental work concerning liquid metals sometimes involves such a degree of error that it is impossible to understand the observed characteristics in a measurement. Numerical analysis is a powerful means to overcome this experimental disadvantage. In the present paper we first show that the Boussinesq approximation is more applicable to liquid metals than to ordinary fluids and that the present analysis gives accurate heat transfer rates, even for a cylinder with a relatively large temperature difference (>100 K) between the heat transfer surface and fluid. It is found from a comparison of the present results with previous work that the correlation equations that have already been proposed predict values lower than the present ones.

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.

A Pseudospectral Analysis of Laminar Natural Convection Flow and Heat Transfer Between Two Inclined Parallel Plates

2006 ◽  
Author(s):  
Serkan Kasapoglu ◽  
Ilker Tari
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Boussinesq Approximation ◽  
Temperature Fields ◽  
Convection Flow ◽  
Parallel Plates ◽  
Natural Convection Flow ◽  
Constant Wall Temperature ◽  
Laminar Natural Convection

Three dimensional laminar natural convection flow of and heat transfer in incompressible air between two inclined parallel plates are analyzed with the Boussinesq approximation by using spectral methods. The plates are assumed to be infinitely long in streamwise (x) and spanwise (z) directions. For these directions, periodic boundary conditions are used and for the normal direction (y), constant wall temperature and no slip boundary conditions are used. Unsteady Navier-Stokes and energy equations are solved using a pseudospectral approach in order to obtain velocity and temperature fields inside the channel. Fourier series are used to expand the variables in × and z directions, while Chebyshev polynomials are used to expand the variables in y direction. By using the temperature distribution between the plates, local and average Nusselt numbers (Nu) are calculated. Nu values are correlated with φ, which is the inclination angle, and with Ra·cosφ to compare the results with the literature.

Heat Transfer by Natural Convection of Helium Between Horizontal Isothermal Concentric Cylinders at Cryogenic Temperature

1988 ◽  
Vol 110 (1) ◽  
pp. 109-115 ◽  
Author(s):  
E. H. Bishop
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Transfer Rate ◽  
Correlation Equation ◽  
Diameter Ratio ◽  
Temperature Profiles ◽  
Cryogenic Temperatures ◽  
Transfer Rates ◽  
Concentric Cylinders

An experimental study was performed of the heat transfer by natural convection of helium between horizontal isothermal concentric cylinders at cryogenic temperatures. Time-averaged temperature profiles at various locations in the annulus and overall heat transfer rates were measured as the Rayleigh number was varied from 6 × 106 to 2 × 109 and the expansion number from 0.20 to 1.0 for a constant Prandtl number of 0.688 and diameter ratio of 3.36. It was found that the heat transfer rate depends on the magnitude of the expansion number as well as on the magnitude of the Rayleigh number. With gas properties evaluated at a volume-weighted reference temperature, a correlation equation is presented that correlates the heat transfer data with maximum deviations of −8.2 and +8.5 percent. The results of this study are compared with previously published studies of other investigators.

The Influences of Property Variations on Natural Convection from Vertical Surfaces

1981 ◽  
Vol 103 (4) ◽  
pp. 609-612 ◽  
Author(s):  
A. M. Clausing ◽  
S. N. Kempka
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Ambient Temperature ◽  
Radiative Heat ◽  
Heated Surface ◽  
Convection Heat Transfer ◽  
Absolute Temperature ◽  
Turbulent Regime ◽  
Transfer Rates ◽  
Rayleigh Numbers

The objective of this paper is to show the influences of property variations in natural convection. Heat transfer from a vertical isothermal, heated surface to gaseous nitrogen is experimentally investigated. The ambient temperature, T∞, is varied in order to cover a large range of the Rayleigh number and also to enable the generation of large values of this parameter. The range 80 K < T∞ < 320 K results in Rayleigh numbers between 107 and 2 × 1010 for the 0.28 m model. By using a cryogenic environment, large ratios of the absolute temperature of the wall to the ambient temperature, Tw/T∞, are generated without the results being masked by radiative heat transfer. The range 1 < Tw/T∞ < 2.6 is investigated. Variable properties cause dramatic increases in heat transfer rates in the turbulent regime, and virtually no influence is seen in the laminar regime. The results obtained correlate extremely well with the addition of a single parameter Tw/T∞.

Experimental Study of Laminar Natural Convection in Cells With Various Convex and Concave Bottoms

1992 ◽  
Vol 114 (1) ◽  
pp. 94-98 ◽  
Author(s):  
W. M. Lewandowski ◽  
M. J. Khubeiz
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Natural Convection ◽  
Dead Space ◽  
Convective Motion ◽  
Flat Bottom ◽  
Local Overheating ◽  
Laminar Natural Convection ◽  
Shape Influence ◽  
Rayleigh Numbers

Heat transfer and free convective motion in limited space from the bottoms of different hemispherical convex or concave shapes have been studied experimentally. The ratio of the diameter of the hemisphere (d) to the diameter of the bottom (D) (0 < d/D < 1) has been tested for a range of Rayleigh numbers (105 < Ra <107). In comparison with a flat bottom (d/D = 0), about 40 percent inhibition or about 50 percent intensification depending on the bottom configuration (d/D) have been observed. The mechanism of the phenomenon based on dead space, local overheating, and shape influence effects has been proposed.

Numerical analysis of laminar natural convection in isosceles triangular enclosures

2009 ◽  
Vol 223 (5) ◽  
pp. 1157-1169 ◽  
Author(s):  
E F Kent
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Rayleigh Number ◽  
Flow Field ◽  
Water Heaters ◽  
Thermal Boundary Conditions ◽  
Laminar Natural Convection ◽  
Solar Water Heaters ◽  
Rayleigh Numbers

In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 103 to 105. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.

Effect of an Insulated Baffle on Pseudosteady-State Natural Convection Inside Spherical Containers

2007 ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Bulk Temperature ◽  
Transfer Path ◽  
Extended Surface ◽  
Parametric Studies ◽  
Energy Equations ◽  
Rayleigh Numbers

The effect of an insulated thin baffle on pseudosteady-state natural convection within spherical containers is studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables, whereby the time-dependent, two-dimensional axisymmetric form of the governing continuity, momentum and energy equations are solved. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106 and 107, baffles with 3 lengths positioned at 5 different locations were investigated. In effect, a parametric study involving 60 cases were performed. The computational results were benchmarked against previous data available in the literature by comparing the heat transfer correlations, temperature distribution and streamline patterns for cases with no baffle. In general, regardless of the presence of an insulated baffle, fluid that is heated adjacent to the surface of the sphere rises replacing the colder fluid which sinks downward. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid. This behavior can lead to onset of oscillations in the temperature and flow fields. Due to blockage effect of an insulated thin baffle, multi-cell recirculating vortex structures are observed. The number and strength of these vortices depend on the position and length of the baffle. In the absence of heat transfer path through the insulated baffle, flow obstruction is the major feature of this problem. For the majority of the length and location combinations investigated, less heat is brought into the fluid thus lowering the time rate of rise of the bulk temperature. The extent of heat transfer modification depends on the Rayleigh number, length and location of the extended surface.

Effect of an Isothermal Baffle on Pseudosteady-State Natural Convection Inside Spherical Containers

2007 ◽  
Author(s):  
S. F. Hosseinizadeh ◽  
Yuping Duan ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Bulk Temperature ◽  
Dependent Variables ◽  
Parametric Studies ◽  
Energy Equations ◽  
Rayleigh Numbers ◽  
Temperature And Flow Fields

The influence of an isothermal thin baffle on pseudosteady-state natural convection within spherical containers is studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables, whereby the time-dependent, two-dimensional axisymmetric form of the governing continuity, momentum and energy equations are solved. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106 and 107, baffles with 3 lengths positioned at 5 different locations were investigated. In effect, a parametric study involving 60 cases were performed. The computational results were benchmarked against previous data available in the literature by comparing the heat transfer correlations, temperature distribution and streamline patterns for cases with no baffle. In general, regardless of the presence of an isothermal baffle, fluid that is heated adjacent to the surface of the sphere rises replacing the colder fluid which sinks downward. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid. This behavior can lead to onset of oscillations in the temperature and flow fields. Partly due to the blockage effect of an isothermal thin baffle and also the extra heating afforded by the baffle, multi-cell recirculating vortex structures are observed. The number and strength of these vortices depend on the position and length of the baffle. The additional heat that is brought into the baffle through the isothermal baffle is directly linked to creation of a counter clockwise rotating vortex next to the baffle. This baffle, in turn, directs hot fluid into the center of the sphere and disrupts thermal stratified layers. For the majority of the length and location combinations investigated, the Nusselt number is lower than the case with no baffle, however the time rate of rise of the bulk temperature can be greater for some combinations. The extent of heat transfer modifications depends on the Rayleigh number, length and location of the baffle.

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