Heat Transfer by Natural Convection From an Array of Short, Wall-Attached Horizontal Cylinders

1982 ◽  
Vol 104 (1) ◽  
pp. 125-131 ◽  
Author(s):  
E. M. Sparrow ◽  
D. S. Cook ◽  
G. M. Chrysler
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Plate ◽  
Diameter Ratio ◽  
Nusselt Numbers ◽  
Cylinder Length ◽  
Horizontal Cylinders ◽  
Length To Diameter Ratio

Per-cylinder natural convection Nusselt numbers were measured for an in-line array of short horizontal cylinders that were affixed to a convectively participating vertical plate. The effect of cylinder length-to-diameter ratio, intercylinder spacing, position at which the cylinder is attached to the vertical plate, and Rayleigh number were investigated. The experiments were performed in air. It was found that the extent to which a given cylinder in the array was affected by cylinders situated below it depended on the Rayleigh number, with enhanced heat transfer coefficients being more likely at higher Rayleigh numbers. Greater enhancement occurred at larger intercylinder spacings. The qualitative characteristics of the Nusselt number results were insensitive to the cylinder length-to-diameter ratio, but the longer cylinders exhibited higher values of the Nusselt number. For the most part, the Nusselt numbers for the wall-attached horizontal cylinders fell below those for the classical horizontal cylinder of infinite length.

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.

ANALYSIS OF NATURAL CONVECTION HEAT TRANSFER BETWEEN TWO HORIZONTAL CYLINDERS AND THEIR ENCLOSURE

1992 ◽  
Vol 16 (1) ◽  
pp. 17-32 ◽  
Author(s):  
M. Lacroix
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Nusselt Numbers ◽  
Horizontal Cylinders ◽  
Rayleigh Numbers

A numerical study has been conducted for natural convection heat transfer for air around two horizontal heated cylinders placed inside a rectangular enclosure cooled from the side. Three cylinder spacings were investigated. The local and overall Nusselt numbers were determined over the range of Rayleigh numbers from 104 to 106. It is found that the thermal performance of the unit is strongly influenced by the Rayleigh number and, to a lesser extent, by the cylinder spacing. A correlation is suggested for the overall Nusselt number.

Effects of uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity

2017 ◽  
Vol 27 (2) ◽  
pp. 334-357 ◽  
Author(s):  
T. Javed ◽  
Z. Mehmood ◽  
M.A. Siddiqui ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Absorption Coefficient ◽  
Uniform Magnetic Field ◽  
Left Wall ◽  
Content Type ◽  
Nusselt Numbers

Purpose The purpose of this paper is to perform a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity. Design/methodology/approach For this flow problem, the left wall of the cavity subjected to uniform/nonuniform heat was considered, while right and bottom walls of the cavity were kept cold. The obtained equations were solved by using the Galerkin weighted residual technique. Results are computed for a wide range of parameters including Rayleigh number (Ra) (10^3 < Ra < 10^7), Hartman number (Ha) (0 < Ha < 60), and heat-generation/-absorption coefficient (q) (−10 < q < 10), while, Prandtl number (Pr) was kept fixed at 6.2. These computed results are presented in terms of stream functions, isotherms, Nusselt numbers and average Nusselt numbers through figures. Findings It is observed that, in case of uniform heating of the side wall, the strength of stream lines’ circulations increases with an increase in Ra and decreases with an increase in Ha. Similarly, by increasing heat-absorption coefficient q, an increase in the circulation strength is noted and the circulation cell moves towards the left wall in the presence of a heat sink (q < 0) and moves to the cold right wall in the presence of a heat source (q > 0). In the case of nonuniformly heated left wall in the presence of a heat source (q > 0), a higher-temperature gradient is observed in the cavity and isotherms are clustered to the left wall in the lower portion and to right wall in the upper portion; these appear to be straight and parallel to the x-axis near the bottom wall. On the other hand, the heat transfer rate along all the walls of the cavity is observed to be higher for smaller values of q. Whereas, Nusselt number along the bottom wall (Nu-B) increases with an increase in the values of x, while, that along the left wall (Nu-L) first increases and then decreases. But Nusselt number along the right wall (Nu-R) is found to be qualitatively opposite to Nu-L with an increase in distance x. Whereas, average Nusselt number increases with an increase in Rayleigh number Ra and heat-generation/-absorption coefficient q. Research limitations/implications The problem is formulated for an incompressible flow; viscous dissipation has been neglected, negligible induced magnetic field has been considered and local thermal equilibrium has been considered. Originality/value Results presented in this paper are original and new for the effects of a uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity. Hence, this study is important for researchers working in the area of heat transfer in cavity flows involving the nanofluid to become familiar with the flow behavior and properties.

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.

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

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 Effect of Fin Length and Location on Natural Convection Heat Transfer in a Wavy Cavity

2020 ◽  
Vol 7 (3) ◽  
Author(s):  
M. Fayz-Al-Asad ◽  
M. J. H. Munshi ◽  
M.M.A. Sarker
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Flow Structure ◽  
Model Parameters ◽  
Flow And Heat Transfer ◽  
Wavy Cavity ◽  
Fin Length

The present study aims to analyze the natural convection flow and heat transfer in a wavy cavity with a single horizontal fin attached to its hot wall. Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear dimensionless equations. The effects of model parameters like Rayleigh number, fin length and location on the fluid flow and heat transfer are investigated. The obtained results are exhibited graphically in terms of flow structure, temperature dispersion, velocity field, fin effectiveness, local Nusselt number, and average Nusselt number. It is observed that the different fin length and location have a substantial effect on flow structure and temperature field. Fin effectiveness is also studied and the highest fin effectiveness was found at fin length (L = 0.75). Besides, it is also found that the mean Nusselt number increases significantly with the increase of Rayleigh number and fin length. Wavy cavity becomes more effective on heat transfer behaviors and fluid flow than that of a square cavity.

scholarly journals Effect of Various Tilted Positions of a Thin Fin on Natural Convection of Laminar Viscous Flow in a Square Cavity

2021 ◽  
Vol 39 (5) ◽  
pp. 1634-1642
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G Sankara Sekhar Raju
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Finite Difference ◽  
Average Nusselt Number ◽  
Vertical Position ◽  
Inclination Angles ◽  
Rayleigh Numbers

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

Numerical computation of natural convection inside a curved-shape nanofluid-filled enclosure with nonuniform heating of the bottom wall

2019 ◽  
Vol 30 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Abdellaziz Yahiaoui ◽  
Mahfoud Djezzar ◽  
Hassane Naji
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Pure Water ◽  
Bottom Wall ◽  
Working Fluid ◽  
Nonuniform Heating ◽  
Square Enclosure ◽  
Nusselt Numbers

This paper performs a numerical analysis of the natural convection within two-dimensional enclosures (square enclosure and enclosures with curved walls) full of a H2O-Cu nanofluid. While their vertical walls are isothermal with a cold temperature [Formula: see text], the horizontal top wall is adiabatic and the bottom wall is kept at a sinusoidal hot temperature. The working fluid is assumed to be Newtonian and incompressible. Three values of the Rayleigh number were considered, viz., 103, 104, 105, the Prandtl number is fixed at 6.2, and the volume fraction [Formula: see text] is taken equal to 0% (pure water), 10% and 20%. The numerical simulation is achieved using a 2D-in-house CFD code based on the governing equations formulated in bipolar coordinates and translated algebraically via the finite volume method. Numerical results are presented in terms of streamlines, isotherms and local and average Nusselt numbers. These show that the heat transfer rate increases with both the volume fraction and the Rayleigh number, and that the average number of Nusselt characterizing the heat transfer raises with the nanoparticles volume fraction.

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