Three－Dimensional Numerical Simulation of Natural Convection Heat Transfer in an Inclined Cylindrical Annulus

Ｔｈｒｅｅ－ＤｉｍｅｎｓｉｏｎａｌＮｕｍｅｒｉｃａｌＳｉｍｕｌａｔｉｏｎｏｆＮａｔｕｒａｌＣｏｎｖｅｃｔｉｏｎＨｅａｔＴｒａｎｓｆｅｒｉｎａｎＩｎｃｌｉｎｅｄＣｙｌｉｎｄｒｉｃａｌＡｎｎｕｌｕｓＪ．Ｇ．ｗｅｉ；Ｗ．Ｑ．Ｔａｏ（ＳｃｈｏｏｌｏｆＥｎｅｒ...     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

Experimental study of natural convection heat transfer of air layers in vertical annuli under high rayleigh number conditions

In this paper experimental investigations of natural convection heat transfer of air layers in vertical annuli are presented. In these experiments, the surface of the inner cylinder is maintained at a constant heat flux condition and the outer cylinder is cooled in the atmosphere. In order to obtain the convective contribution, the overall heat transfer data are corrected for thermal radiation and axial conduction losses from the end plates in the annuli. Special emphasis, in these investigations, was placed on the high Rayleigh number region where no experimental data are available in the literature. Data were obtained for Rayleigh numbers greater than 10⁹. The radius ratios studied were 2.03 and 3.92, and the aspect ratios studied were 23.94 and 66.67. Heat transfer correlations for average Nusselt numbers were developed for different Rayleigh number regions. For the low Rayleigh number region the results of this paper agree with the correlations reported in the literature. Much needed data and correlations for the high Rayleigh number region are obtained for the first time. These results improve the predictive ability for the heat transfer characteristics in the high Rayleigh number region. ©1999 Scripta Technica, Heat Trans Asian Res, 28(1): 50–57, 1999     

Influences of a confined elliptic cylinder at different aspect ratios and inclinations on the laminar natural and mixed convection flows

Numerical investigations were carried out for natural and mixed convection within domains with stationary and rotating complex geometry by using an immersed-boundary method. The method was first validated with flows induced by natural convection in the annulus between concentric circular cylinder and square enclosure, and the grid-function convergence tests were also examined. Natural convection induced by isothermally elliptic cylinder was further investigated for different Rayleigh numbers within the range of 10⁴–10⁶ and the influence of the outer enclosure was also considered. The parameters investigated in the study included Rayleigh number, axis ratio and inclination angle of the elliptic cross-section. Local and average heat transfer characteristics were fully studied around the surfaces of both inner cylinder and outer enclosure. Finally, mixed convection in a square enclosure with an active rotating elliptic cylinder was considered and the heat transfer quantities of the system were obtained for different rotating speeds.     

Effect of surface radiation on conjugate natural convection in a horizontal annulus driven by inner heat generating solid cylinder

This paper reports a numerical study of the laminar conjugate natural convection heat transfer with and without the interaction of the surface radiation in a horizontal cylindrical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal circular boundary. Numerical solutions are obtained by solving the governing equations with a pressure correction method on a collocated (non-staggered) mesh. Steady-state results are presented for the flow and temperature distributions and Nusselt numbers for the heat generation based Grashof number ranging from , solid-to-fluid thermal conductivity ratios of 1, 5, 10, 50 and 100, radius ratios of 0.226 and 0.452 and surface emissivities of 0–0.8 with air as the working medium. It is observed that surface radiation reduces the convective heat transfer in the annulus compared to the pure natural convection case and enhances the overall Nusselt number.     

NATURAL CONVECTION OVER A ROTATING CYLINDRICAL HEAT SOURCE IN A RECTANGULAR ENCLOSURE

A numerical study of laminar two-dimensional natural convection heat transfer from a uniformly heated horizontal cylinder rotating about its center, and placed in an isothermal rectangular enclosure, is performed using a spectral element method. The physical aspects of the flow and its thermal behavior are studied for a wide range of pure natural convection to mixed convection at low and high rotational speeds of the cylinder. The computer program has been validated against experimental correlations available on pure natural convection of heated bodies in enclosures. The rotation of the cylinder has been found to enhance the heat transfer. At low ratios of Rayleigh number to the square of the rotational Reynolds number, Ra / Re_ω ², the maximum temperature on the cylinder surface is decreased by as much as 25–35% from similar cases with fixed cylinders. At moderate values of Ra/ Re_ω ², the thermal plume rising above the cylinder is shifted in the rotation direction and the angular shift decreases as Ra / Re_ω increases. The rotation produces more uniform temperature and shear stress distributions around the cylinder surface. At high Rayleigh numbers the increase in rotation reduces the cylinder mean Nusselt number by 2–10% as compared with the fixed cylinder.     

Numerical Analysis of Natural Convection in a Cylindrical Envelope with an Internal Concentric Cylinder with Slots

Detailed numerical analysis is presented for natural convection heat transfer in a cylindrical envelope with an internal concentric cylinder with slots. Governing equations are discretized using the finite volume method, and solved using SIMPLE algorithm with QUICK scheme. The results show that the system can reach steady state and be symmetric when the Rayleigh number is below 4 × 10⁵. When the Rayleigh number is greater than 6 × 10⁵, an asymmetric periodical solution is obtained although the initial field and boundary conditions were symmetric. As the Rayleigh numbers increase further, a quasi-periodic solution of the system is achieved at Ra = 2 × 10⁶, and the periodicity is lost at Ra = 6 × 10⁶. It is ascertained that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow.     

Natural convection heat transfer of molten salts around a vertically aligned horizontal cylinder set

The heat transfer from the vertical arrays of a set of equally spaced cylinders in molten salts is studied numerically to obtain the laminar natural convection heat transfer mechanism of molten salts around a vertically aligned horizontal cylinder set. Simulations are performed for arrays of 2–10 horizontal cylinders at a Rayleigh number based on a cylinder diameter between 2 × 10³ and 5 × 10⁵. Results show that the natural convective heat transfer of molten salts from the bottom cylinder of the array remains the same as that from a single cylinder. By contrast, the downstream cylinders may either be enhanced or reduced mainly depending on their location in the array and on the tube spacing. Heat transfer dimensionless correlating equations are proposed for any individual cylinder in the two vertically aligned horizontal cylinders. The heat transfer mechanism from the horizontal cylinders set in a vertical array is also simulated, and the results show that cylinder spacing can influence the average heat transfer rate around the whole tube array. Thus, in real applications, adjusting the cylinder spacing better enhances the average heat transfer from the whole tube array.     

Natural convection heat transfer from a horizontal cylinder using holographic interferometry

The natural convection heat transfer from a horizontal cylinder with a uniform wall temperature in an infinite space was experimentally investigated. Infinite fringe interferograms of the cylinder heated from 295.15 to 355.15 K were recorded using the holographic interferometry technique. The temperature field around the cylinder was reconstructed based on phase difference recovery using a MATLAB code. The distributions of the local and average Nusselt numbers over the cylinder were then obtained. A correlation of the average Nusselt number was proposed for a Rayleigh number range of 2.7–6.0 × 10⁴. The experimental results are in good agreement with previous correlations, with a deviation of ±10%. The holographic interferometry technique was found to be satisfactory and reliable for heat transfer analyses.     

Experimental Study of Free Convection Heat Transfer from Horizontal Isothermal Cylinders Arranged in Vertical and Inclined Arrays

Laminar free convection heat transfer from vertical and inclined arrays of horizontal isothermal cylinders in air were investigated experimentally. Experiments were carried out using a Mach-Zehnder interferometer. For the vertical array, the cylinder spacing (center to center) varied from 2 to 5 cylinder diameter. The same range of vertical spacing also was used for the inclined array. The horizontal spacing varied from 0 to 2 cylinder diameter in the inclined array. The Rayleigh number based on the cylinder diameter varied between 10³ and 3× 10³. The effect of vertical and horizontal cylinder spacing and Rayleigh number on the heat transfer from each individual cylinder and the whole array were investigated. It is found that the free convection heat transfer from any individual cylinder in the array depends on its position relative to the others. Heat transfer correlations have been developed for any individual cylinder in the vertical and inclined arrays and for the arrays. Also the experiment was carried out on a single cylinder for a comparison with the results from other research.     

Free Convection Heat Transfer from a Confined Horizontal Elliptic Cylinder

The laminar free convection heat transfer from an isothermal horizontal cylinder of elliptical cross-section confined between two adiabatic walls is investigated by the Mach-Zehnder interferometry technique. The ellipse major axis is vertical, and the minor to major axis ratio is kept constant to 0.53. This paper focuses on the effect of wall spacing and Rayleigh number variation on the local and average free convection heat transfer coefficient from the cylinder surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 9 × 10 ² to 3.2 × 10 ³ and wall spacing to cylinder minor axis ratios of 1.9, 2.3, 2.67, 3.17, 3.8, 4.6, 6.12, 8, 13, ∞. Results are indicated with a single correlation that gives the average Nusselt number as a function of the ratio of the wall spacing to cylinder minor axis and the Rayleigh number. There is an optimum distance between the walls in which the Nusselt number is maximum. The experiment was also carried out on a cylinder of circular cross-section with the same periphery and length of the elliptic cylinder to allow a comparison with the results of other research.     

Natural cooling of horizontal cylinder using Artificial Neural Network (ANN)

Artificial Neural Network (ANN) is used to determine natural convection heat transfer and fluid flow around a cooled horizontal circular cylinder having constant surface temperature. Governing equations of natural convection were solved using finite volume technique by writing a FORTRAN code to generate the database for ANN scheme and Rayleigh number is changed from Ra = 10⁶ to 10⁸. Results obtained from numerical solutions were used for training and testing the ANN approach. A comparison was performed among the soft programming (ANN), experimental observation and Computational Fluid Dynamic (CFD) code. It is observed that ANN soft programming code can be used more efficiently to determine cold plume and thermal field generated around a cold cylinder. Based on the results a new correlation is developed for natural convection of cooled horizontal cylinders.     

A numerical investigation of the effect of sinusoidal temperature on mixed convection flow in a cavity filled with a nanofluid with moving vertical walls

The aim of this study is to investigate numerically the effect of sinusoidal temperature on mixed convection flow in a cavity filled with nanofluid and moving vertical walls by using a new temperature function, where thermal heating takes the form of the sinusoidal temperature; and could be found in various natural processes and industries such as solar energy, and cooling of electronic components. The heating is concentrated in the center and then distributed to both ends at different values of Rayleigh numbers, Reynolds numbers, and volumetric fractions of nanoparticles ranging from 1.47 × 10³ to 1.47 × 10⁶, 1 to 100, and 0 to 0.1, respectively. The impact of nanoparticle size on thermal characteristics and hydrodynamics was considered and evaluated. From the results, the volume fraction concentration of nanoparticles affects the flow shape and thermal performance in the case of a constant Reynolds number. Moreover, the effect of nanoparticles decreases with the increase of the Reynolds number. Besides this, with increasing the volume percentage of nanoparticles, the rate of heat transmission increases. It is worth noting that the presence of nanoparticles results in height convective heat transfer coefficient. On the other hand, the thickness of thermal boundary layers decreases with increasing Rayleigh number. The current investigation found that the (sinusoidal) temperature change significantly affects heat transfer.     

A model and heat transfer correlation for rooftop integrated photovoltaics with a passive air cooling channel

Photovoltaic (PV) panels can experience undesirably high temperatures due to the heat input by that part of the absorbed solar radiation which is not converted into electricity. Regulation of the temperature rise is necessary to maintain maximum solar to electric conversion. One approach for temperature regulation, suitable for rooftop integrated PV, involves fitting an open channel beneath the PV module. The panels are cooled by radiation and free convection as ambient air rises through the channel. A scale analysis and numerical study of PV modules with a back mounted air channel provides heat transfer rates over a practical range of operating conditions and channel geometries. A generalized correlation for the average channel Nusselt number for the combined convective-radiative cooling is developed for modified channel Rayleigh numbers from 10² to 10⁸, channel aspect ratios between 15 and 50 and inclination angles between 30° and 90°. The usefulness of a passive cooling channel to improve PV efficiency is illustrated by system analyses of typical PV modules.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

NATURAL CONVECTION-RADIATION INTERACTIONS IN A CUBE FILLED WITH A NONGRAY GAS

A three-dimensional numerical study was performed on interactions of natural convection and radiation in a cubical enclosure filled with carbon dioxide gas. The enclosure was heated differentially by two opposing vertical walls. Gas radiation was analyzed by the P₁ differential approximation method and the weighted sum of gray gas model. Computations were carried out over a range of the Rayleigh number, Ra, between 10⁵ and 10⁹. The Prandtl number and the overheat ratio were held fixed at 0·68 and 1·0, respectively. Unsteady transitional flows were computed by a direct simulation method, without using any explicit turbulence models. From the predictions, a mean heat transfer correlation has been proposed as Nu = 0·323 Ra^0·342 in the surface/gas radiation mode, where Nu is the time and spatially averaged Nusselt number at the isothermal walls.     

Free convection in ZnO-Water nanofluid-filled and tilted hemispherical enclosures containing a cubic electronic device

The present work deals with free convection within nanofluid-filled hemispherical enclosure whose base (disc) can be inclined with respect to the horizontal plane by an angle ranging from 0° to 180° (horizontal disc with dome facing upwards and downwards respectively). A cubic active electronic component positioned at the center of the disc generates important heat fluxes leading to high Rayleigh number values ranging from 5.21 × 10⁷ to 7.29 × 10¹⁰. The used nanofluid is a mixture Water-ZnO with a volume fraction varying between 0 (pure water) and 10%. The 3D numerical approach is done by means of the volume control method based on the SIMPLE algorithm, and using a one-phase model. The dynamic and thermal fields are presented for several geometric and thermal configurations. The natural convective heat transfer is quantified by means of the average Nusselt Number whose evolution versus the inclination angle, the Rayleigh Number and the volume fraction is presented and commented on for all considered cases. Correlations of the Nusselt-Rayleigh-Prandtl-inclination angle type are proposed to determine the natural convective heat transfer in this assembly corresponding to applications in electronics.     

A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations

Numerical calculations are carried out for natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on the finite volume method for different Rayleigh numbers varying over the range of 10³–10⁶. The study goes further to investigate the effect of the inner cylinder location on the heat transfer and fluid flow. The location of the inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of the cell strongly depend on the Rayleigh number and the position of the inner circular cylinder. The changes in heat transfer quantities have also been presented.     

A numerical study of laminar free convection heat transfer between inner sphere and outer vertical cylinder

The effects of height and radius ratio with a Newtonian fluid have been investigated numerically to determine heat transfer by natural convection between the sphere and vertical cylinder with isothermal boundary conditions. The inner sphere and outer vertical cylinder were heated and cooled in a steady change of temperature. Calculations were carried out systematically for a range of the Rayleigh numbers to determine the average Nusslet numbers which are affected by the geometric ratio parameters (HR and RR) on the flow and temperature fields. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the Rayleigh number and height and radius ratio, for a Prandtl number of 0.7, with the Rayleigh number ranging from 10³ to 10⁶, and the height and radius ratio varying from 1.2 to 5.0. Above all, the specification of different convective configurations has a significant effect on the average heat transfer rate across the composite annulus gap.