Natural Convection Heat Transfer in Horizontal Rod-Bundle Enclosures

1996 ◽  
Vol 118 (3) ◽  
pp. 598-605 ◽  
Author(s):  
M. Keyhani ◽  
T. Dalton
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Heat Transfer ◽  
Diameter Ratio ◽  
Array Size ◽  
Maximum Temperature ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Natural convection heat transfer in enclosed horizontal N × N arrays (N = 3, 5, and 7) of electrically heated rods with a pitch-to-diameter ratio (P/d) of 1.35 has been experimentally investigated. Each array was positioned in an isothermal square enclosure with a width-to-diameter ratio (W/d) of 20.6. Pressurized air or helium was used as the working fluid. It was observed that the bottom-tow rods were relatively insensitive to increases in the array size, as they exhibit only slight temperature variations, but the top-row rods demonstrated substantial temperature increases. Natural convection correlations in the form of Nusselt number (Nud) as a function of modified Rayleigh number (Rad*) were obtained for each rod in each array. The correlations cover three flow regimes of conduction, transition, and convection in the range of 6.45 < Rad* < 3.08 × 105. A generalized enclosure Nusselt number was correlated as a function of enclosure modified Rayleigh number and the array size (N). Comparison of the data with previous numerical prediction showed that this correlation may be readily used to obtain a conservative estimate of the maximum temperature in the arrays with N = 3, 5, 7, and 9.

scholarly journals Prediction of Natural Convection Heat Transfer Phenomena of Nanofluids in Corrugated Annulus

2020 ◽  
Author(s):  
Sattar Aljobair ◽  
Akeel Abdullah Mohammed ◽  
Israa Alesbe
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Outer Cylinder ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Abstract The natural convection heat transfer and fluid flow characteristic of water based Al2O3 nano-fluids in a symmetrical and unsymmetrical corrugated annulus enclosure has been studied numerically using CFD. The inner cylinder is heated isothermally while the outer cylinder is kept constant cold temperature. The study includes eight models of corrugated annulus enclosure with constant aspect ratio of 1.5. The governing equations of fluid motion and heat transfer are solved using stream-vorticity formulation in curvilinear coordinates. The range of solid volume fractions of nanoparticles extends from PHI=0 to 0.25, and Rayleigh number varies from 104 to 107. Streamlines, isotherms, local and average Nusselt number of inner and outer cylinder has been investigated in this study. Sixty-four correlations have been deduced for the average Nusselt number for the inner and outer cylinders as a function of Rayleigh number have been deduced for eight models and five values of volume fraction of nano particles with an accuracy range 6-12 %. The results show that, the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. Also, increase the number of undulations in unsymmetrical annuli reduces the heat transfer rates which remain higher than that in symmetrical annuli. There is no remarkable change in isotherms contour with increase of volume fraction of nanofluid.

scholarly journals Enhancement of natural convection heat transfer in a U-shaped cavity filled with Al2O3-water nanofluid

2012 ◽  
Vol 16 (5) ◽  
pp. 1317-1323 ◽  
Author(s):  
Ching-Chang Cho ◽  
Her-Terng Yau ◽  
Cha’o-Kuang Chen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Heated Wall ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
The Mean

This paper investigates the natural convection heat transfer enhancement of Al2O3-water nanofluid in a U-shaped cavity. In performing the analysis, the governing equations are modeled using the Boussinesq approximation and are solved numerically using the finite-volume numerical method. The study examines the effects of the nanoparticle volume fraction, the Rayleigh number and the geometry parameters on the mean Nusselt number. The results show that for all values of the Rayleigh number, the mean Nusselt number increases as the volume fraction of nanoparticles increases. In addition, it is shown that for a given length of the heated wall, extending the length of the cooled wall can improve the heat transfer performance.

Natural Convection Heat Transfer in a Rectangular Water Pool with Internal Heating and Top and Bottom Cooling

2006 ◽  
Author(s):  
Jong K. Lee ◽  
Seung D. Lee ◽  
Kune Y. Suh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Exchanger ◽  
Rayleigh Number ◽  
Test Section ◽  
Convection Heat Transfer ◽  
The Other ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

During a severe accident, the reactor core may melt and be relocated to the lower plenum to form a hemispherical pool. If there is no effective cooling mechanism, the core debris may heat up and the molten pool run into natural convection. Natural convection heat transfer was examined in SIGMA RP (Simulant Internal Gravitated Material Apparatus Rectangular Pool). The SIGMA RP apparatus comprises a rectangular test section, heat exchanger, cartridge heaters, cooling jackets, thermocouples and a data acquisition system. The internal heater heating method was used to simulate uniform heat source which is related to the modified Rayleigh number Ra′. The test procedure started with water, the working fluid, filling in the test section. There were two boundary conditions: one dealt with both walls being cooled isothermally, while the other had to with only the upper wall being cooled isothermally. The heat exchanger was utilized to maintain the isothermal boundary condition. Four side walls were surrounded by the insulating material to minimize heat loss. Tests were carried out at 1011 &lt; Ra′ &lt; 1013. The SIGMA RP tests with an appropriate cartridge heater arrangement showed excellent uniform heat generation in the pool. The steady state was defined such that the temperature fluctuation stayed within ±0.2 K over a time period of 5,000 s. The conductive heat transfer was dominant below the critical Rayleigh number Ra′c, whereas the convective heat transfer picked up above Ra′c. In the top and bottom boundary cooling condition, the upward Nusselt number Nuup was greater than the downward Nusselt number Nudn. In particular, the discrepancy between Nuup and Nudn widened with Ra′. The Nuup to Nudn ratio was varied from 7.75 to 16.77 given 1.45×1012 &lt; Ra′ &lt; 9.59×1013. On the other hand, Nuup was increased in absence of downward heat transfer for the case of top cooling. The current rectangular pool testing will be extended to include circular and spherical pools.

Natural Convection Heat Transfer Coefficients for a Short Horizontal Cylinder Attached to a Vertical Plate

1981 ◽  
Vol 103 (4) ◽  
pp. 630-637 ◽  
Author(s):  
E. M. Sparrow ◽  
G. M. Chrysler
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Plate ◽  
Convection Heat Transfer ◽  
Horizontal Cylinder ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
End Effects

Experiments were performed to investigate the natural convection heat transfer characteristics of a short isothermal horizontal cylinder attached to an equi-temperature vertical plate. The apparatus was designed so that the cylinder could be attached to the plate at any one of three positions along the height of the plate. Two cylinders were employed (one at a time) during the course of the experiments, one of which had a length equal to its diameter while the other had a length that was half the diameter. At each attachment position and for each cylinder, the Rayleigh number (based on the cylinder diameter) ranged from 1.4 × 104 to 1.4 × 105. It was found that the interaction of the flat plate boundary layer with the cylinder brought about a reduction of the cylinder Nusselt number relative to that for the classical case of the long isolated horizontal cylinder without end effects. The respective deviations of the Nusselt numbers for the shorter and longer of the participating cylinders from the literature correlation for the isolated cylinder were twenty percent and ten percent. At a given Rayleigh number, the cylinder Nusselt number was quite insensitive to the position of the cylinder along the plate, with the typical data spread due to height being in the 5–7 percent range. The Nusselt number was also rather insensitive to cylinder length, showing a ten percent increase as the length-diameter ratio was increased from one-half to one.

Numerical Investigation of Natural Convection Heat Transfer From a Stack of Horizontal Cylinders

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Subhasisa Rath ◽  
Sukanta Kumar Dash
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Investigation ◽  
Turbulent Flows ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Horizontal Cylinders

Natural convection heat transfer from horizontal solid cylinders has been studied numerically by varying the Rayleigh number in the range of (104≤Ra≤108) and (1010≤Ra≤1013) for both laminar and turbulent flows, respectively. The computations were carried out for three different geometries of three, six, and ten cylinders in a stack arranged in a triangular manner having same characteristic length scale. The present numerical investigation on natural convention is able to capture a very interesting flow pattern and temperature field over the stack of horizontal cylinders which has never been reported in the literature so far. Visualization of plume structure over the horizontal cylinders has also been obtained pictorially in the present work. From the numerical results, it has been observed that the total heat transfer is marginally higher for three-cylinder stack in the laminar range. In contrast, for turbulent flow, starting from Ra = 1010, heat transfer for six-cylinder case is higher but when Ra exceeds 5 × 1011, heat transfer for ten cylinders stack is marginally higher. The average surface Nusselt number is higher for the stack of three cylinders compared to six- and ten-cylinder cases for all range of Ra in both laminar and turbulent regimes. A correlation for the average Nusselt number has also been developed as a function of Rayleigh number which may be useful for researchers and industrial purposes.

Numerical Analysis of Natural Convection Heat Transfer From a Vertical Hollow Cylinder Suspended in Air

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Swastik Acharya ◽  
Sumit Agrawal ◽  
Sukanta K. Dash
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Hollow Cylinder ◽  
Outer Surface ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Natural convection heat transfer from a vertical hollow cylinder suspended in air has been analyzed numerically by varying the Rayleigh number (Ra) in the laminar (104 ≤ Ra ≤ 108) regime. The simulations have been carried out by changing the ratio of length to pipe diameter (L/D) in the range of 0.05 ≤ L/D≤20. Full conservation equations have been solved numerically for a vertical hollow cylinder suspended in air using algebraic multigrid solver of fluent 13.0. The flow and the temperature field around the vertical hollow cylinder have been observed through velocity vectors and temperature contours for small and large L/D. It has been found that the average Nusselt number (Nu) for vertical hollow cylinder suspended in air increases with the increase in Rayleigh number (Ra) and the Nu for both the inner and the outer surface also increases with Ra. However, with the increase in L/D, average Nu for the outer surface increases almost linearly, whereas the average Nu for the inner surface decreases and attains asymptotic value at higher L/D for low Ra. In this study, the effect of parameters like L/D and Ra on Nu is analyzed, and a correlation for average Nusselt number has been developed for the laminar regime. These correlations are accurate to the level of ±6%.

Natural Convection Heat Transfer and Entropy Generation From a Horizontal Cylinder With Baffles

2000 ◽  
Vol 122 (4) ◽  
pp. 679-692 ◽  
Author(s):  
B. A/K Abu-Hijleh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Entropy Generation ◽  
Convection Heat Transfer ◽  
Horizontal Cylinder ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Wide Range

The problem of laminar natural convection heat transfer from a horizontal cylinder with multiple, equally spaced, low conductivity baffles on its outer surface was investigated numerically. The effect of several combinations of number of baffles and baffle height on the average Nusselt number was studied over a wide range of Rayleigh numbers. The computed velocity and temperature fields were also used to calculate the local and global entropy generation for different cylinder diameters. The results showed that there was an optimal combination of a number of baffles and baffle height for minimum Nusselt number for a given value of the Rayleigh number. Short baffles slightly increased the Nusselt number at small values of the Rayleigh number. The global entropy generation increased monotonically with increasing Rayleigh number and decreased with increasing cylinder diameter, baffle height, and number of baffles. [S0022-1481(00)01203-2]

Natural Convection Heat Transfer of Concentric/Eccentric Annulus Subjected to Inner Tube of Constant Heat Flux

2011 ◽  
Author(s):  
R. Hosseini ◽  
M. Alipour ◽  
A. Gholaminejad
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Surface Temperature ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Eccentric Annulus

This paper describes the experimental results of natural convection heat transfer from vertical, electrically heated cylinder in a concentric/eccentric annulus and develops correlations for the dependence of the average annulus Nusselt number upon the Rayleigh number. Wall surface temperature have been recorded for diameter ratio of d/D = 0.4, with the apparatus immersed in stagnant air with uniform temperature. Measurements have been carried out for eccentric ratios of E = 0, 0.19, 0.34, 0.62 and 0.89 in the range of heat flux of 45 to 430 W/m2. The surface temperature of the heater was found to increase upwards and reach a maximum at some position, beyond which it decreases again. It is observed, that this maximum temperature occurs near h/l = 0.8 for 0 ≤ E ≤ 0.62 at almost all power levels, but shifts downwards for E = 0.89. Moreover, empirical correlations between the average Nusselt number and the Rayleigh number are derived for concentric and eccentric annuli.

Influence of Cu-Water and CNT-Water Nanofluid on Natural Convection Heat Transfer in a Triangular Solar Collector

2020 ◽  
Author(s):  
Didarul Ahasan Redwan ◽  
Md. Habibur Rahman ◽  
Hasib Ahmed Prince ◽  
Emdadul Haque Chowdhury ◽  
M. Ruhul Amin
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Solar Collector ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

Abstract A numerical study on natural convection heat transfer in a right triangular solar collector filled with CNT-water and Cuwater nanofluids has been conducted. The inclined wall and the bottom wall of the cavity are maintained at a relatively lower temperature (Tc), and higher temperature (Th), respectively, whereas the vertical wall, is kept adiabatic. The governing non-dimensional partial differential equations are solved by using the Galerkin weighted residual finite element method. The Rayleigh number (Ra) and the solid volume-fraction of nanoparticles (ϕ) are varied in the range of 103 ≤ Ra ≤ 106, and 0 ≤ ϕ ≤ 0.1, respectively, to carry out the parametric simulations within the laminar region. Corresponding thermal and flow fields are presented via isotherms and streamlines. Variations of average Nusselt number as a function of Rayleigh number have been examined for different solid volume-fraction of nanoparticles. It has been found that the natural convection heat transfer becomes stronger with the increment of solid volume fraction and Rayleigh number, but the strength of circulation reduces with increasing nanoparticles’ concentration at low Ra. Conduction mode dominates for lower Ra up to a certain limit of 104. It is also observed that when the solid volume fraction is increased from 0 to 0.1 for a particular Rayleigh number, the average Nusselt number is increased to a great extent, but surprisingly, the rate of increment is more pronounced at lower Ra. Moreover, it is seen that Cu-water nanofluid offers slightly better performance compared to CNT-water but the difference is very little, especially at lower Ra.

Experimental and Numerical Investigation of Natural Convection Heat Transfer From Horizontal Rectangular Plate Fin Pin Fin Arrays

2020 ◽  
Author(s):  
Sunil V. Dingare ◽  
Narayan K. Sane ◽  
Ratnakar R. Kulkarni
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Model ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Pin Fin ◽  
Pin Fins ◽  
Fin Spacing

Abstract Fins are commonly employed for cooling of electronic equipment, compressors, Internal Combustion engines and for heat exchange in various heat exchangers. In short fin (length to height ratio, L/H = 5) arrays used for natural convection cooling, a stagnation zone forms at the central portion and that portion is not effective for carrying away heat. An attempt is made to modify plate fin heat sink geometry (PFHS) by inserting pin fins in the channels formed between plate fins and a plate fin pin fin heat sink (PFPFHS) is constructed to address this issue. An experimental setup is developed to validate numerical model of PFPFHS. The three-dimensional elliptic governing equations were solved using a finite volume based computational fluid dynamics (CFD) code. Fluent 6.3.26, a finite volume flow solver is used for solving the set of governing equations for the present geometry. Cell count based on grid independence and extended domain is used to obtain numerical results. Initially, the numerical model is validated for PFHS cases reported in the literature. After obtaining a good agreement with results from the literature, the numerical model for PFHS is modified for PFPFHS and used to carry out systematic parametric study of PFPFHS to analyze the effects of parameters like fin spacing, fin height, pin fin diameter, number of pin fins and temperature difference between fin array and surroundings on natural convection heat transfer from PFPFHS. It is observed that it is impossible to obtain optimum performance in terms of overall heat transfer by only concentrating on one or two parameters. The interactions among all the design parameters must be considered. This thesis presents Experimental and Numerical study of natural convection heat transfer from horizontal rectangular plate fin and plate fin pin fin arrays. The parameters of study are fin spacing, temperature difference between the fin surface and ambient air, fin height, pin fin diameter, number of pin fins and method of positioning pin fins in the fin channel. Experimental set up is validated with horizontal plate standard correlations. Results are generated in the form of variation in average heat transfer coefficient (ha), base heat transfer coefficient (hb), average Nusselt number (Nua) and base Nusselt number (Nub). Total 512 cases are studied numerically and finally an attempt is made to correlate the Nusselt Number (Nu), Rayleigh Number (Ra), increase in percentage by inserting pin fins (% Area), ratios like spacing to height (S/H) and L/H obtained in the present study.

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