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.     

Enhancement of Free Convection Heat Transfer from a Vertical Array of Isothermal Cylinders by Flow Diverters

Free convection heat transfer from a vertical array of five horizontal isothermal cylinders separated by flow diverters is investigated experimentally through a Mach-Zehnder interferometer. Flow diverters with widths of 1, 2, and 3 cylinder-diameter are placed midway between the cylinders with a 45-degree inclination angle. The cylinders vertical center to center spacing is kept constant to three-cylinder diameter. The experiments are carried out for various Rayleigh numbers based on the cylinder diameter in the range of 10³ to 2.5× 10³ and for different flow diverter width. It is observed that the flow diverters enhance the heat transfer of the array from 10% to 27%, depending on their width. By increasing the width of the diverters and the Rayleigh number, enhancement of the heat transfer from the array increases.     

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.     

Correlating equations for free convection heat transfer from horizontal isothermal cylinders set in a vertical array

Steady laminar free convection from flat vertical arrays of equally-spaced, horizontal isothermal cylinders set in free air, is studied numerically. A specifically developed computer-code based on the SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for arrays of 2-6 circular cylinders, for center-to-center separation distances from 2 up to more than 50 cylinder-diameters, and for values of the Rayleigh number based on the cylinder-diameter in the range between 5 × 10² and 5 × 10⁵. It is found that the heat transfer rate at the bottom cylinder remains the same as a single cylinder. In contrast, the downstream cylinders may exhibit either enhanced or reduced Nusselt numbers depending on their location in the array and on the geometry of the array. Heat transfer dimensionless correlating equations are proposed both for any individual cylinder in the array and for the whole tube-array. New correlation-equations for the calculation of the heat transfer rate from a single cylinder to the surrounding air are also proposed and compared to those available in the open literature.     

Natural convection heat transfer from two horizontal cylinders using a large lateral shearing interferometer

Natural convection heat transfer from two horizontal cylinders in the air was investigated experimentally and numerically. Two cylinders were spaced at 1.3, 1.8, and 2.7 cylinder diameters horizontally. The experiments were carried out by large lateral shear interferometry (LSI) for various Rayleigh numbers in the range of 10³ to 10⁴. Large LSI is common path interferometry with the advantages of simple structure, strong antivibration, and fewer required optical components. It is not necessary for LSI to perform a complex algorithm to restore wavefront with a large shear amount. Simple and infinite fringe interferograms of the cylinders heated from ambient temperature 282.15 to 723.15 K were obtained. A numerical simulation was carried out with ANSYS-Fluent 18.0. The influence of two factors, the distance between the cylinders, and the Rayleigh number, on the heat transfer of two horizontal cylinders was examined. The average Nusselt number and local Nusselt number were determined from the experimental results and numerical results, respectively, and the two results were in good agreement. The rising direction for the plume flow pattern of each horizontal cylinder was no longer simply vertically upward but was inclined toward the central symmetry axis of the two cylinders. In addition, the heat transfer from a cylinder increased with the cylinder spacing at any Rayleigh number.     

Interactive free convection from a pair of vertical tube-arrays at moderate Rayleigh numbers

Steady laminar free convection from a pair of vertical arrays of equally-spaced, horizontal isothermal cylinders set in free air, is studied numerically. A specifically developed computer-code based on the SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for pairs of tube-arrays consisting of 1–4 circular cylinders, for center-to-center horizontal and vertical spacings from 1.4 to 24 cylinder-diameters, and from 2 to 12 cylinder-diameters, respectively, and for values of the Rayleigh number based on the cylinder-diameter in the range between 10² and 10⁴. It is found that any cylinder may exhibit either enhanced or reduced Nusselt numbers with respect to the case of single tube-array, depending on its location in the array, on the geometry of the array, as well as on the Rayleigh number. Heat transfer dimensionless correlating equations are also proposed.     

Experimental study of free convection from a pair of vertical arrays of horizontal cylinders at very low Rayleigh numbers

Steady laminar free convection from a pair of vertical arrays of equally-spaced uniformly heated horizontal cylinders set in free air is studied experimentally. A specifically developed experimental facility is used to perform heat flux and temperature measurements and thermal field visualization by means of Schlieren technique. Experiments are performed for pairs of tube-arrays consisting of five circular cylinders, for center-to-center horizontal and vertical spacing ranging from 2 to 145 cylinder-diameters and from 4 to 12 cylinder-diameters respectively, and for values of the Rayleigh number based on the cylinder-diameter in the range between 2.4 and 11.9. It is found that any cylinder may exhibit either enhanced or reduced Nusselt numbers with respect to the case of single array, depending on its location in the array, on the geometry of the array, as well as on the Rayleigh number. The visualization has allowed to relate a number of observed effects to the fact that side-by-side placement of the arrays produces a lateral air suction into the space between them.     

Laminar free convection underneath a downward facing inclined hot fin array

A combined theoretical, experimental and numerical study was conducted to investigate the problem of laminar free convection underneath a hot isothermal and inclined fin array. The influence of inclination on the location where the flow stagnates, and splits, was examined. Heat transfer rates were calculated for different fin array geometries and temperatures. The results show that for small inclination angles the cooling rate is essentially constant. Beyond a certain angle, the tilting of the fin array enhances substantially the heat transfer rate. Sensitivity analyses indicate that the heat transfer coefficient increases at higher fin temperatures and larger fin spacing, but is of a lesser sensitivity to fin height changes. Additionally, it was discovered that the array optimal fin spacing do not depend on the inclination angle. In the theoretical part, a semi empirical model was developed for the heat transfer coefficient of horizontal and slightly inclined arrays that have large fin spacing. In effect it constitutes the necessary modeling addition to the previously developed model for moderately and tightly spaced fins of slightly tilted arrays. Together, they provide analytical expressions for the heat transfer coefficient of slightly inclined arrays, for any fin spacing.     

Experimental and Numerical Investigation on Free Convection From a Horizontal Cylinder Located Above an Adiabatic Surface

Steady two-dimensional free convection heat transfer from an isothermal horizontal cylinder located above an adiabatic horizontal surface is studied experimentally and numerically. Experiments are carried out using a Mach–Zehnder interferometer for the ratios of cylinder spacing from the adiabatic surface to its diameter L/D = 0, 0.1, 0.2, 0.3, 0.5, 0.7, and 0.9 and the Rayleigh number range of 500 to 15,000. Also, a specifically developed computer code based on the finite-volume method, the SIMPLE algorithm, and nonorthogonal discretization grid system is used for the solution of the mass-, momentum-, and energy-governing equations for the Rayleigh numbers ranging from 100 to 100,000 and L/D ranging from 0.1 to 1.7. The effects of the Rayleigh number and spacing from the adiabatic surface on both local and average Nusselt numbers around the cylinder are investigated. A correlation based on the numerical data for the average Nusselt number of the cylinder as a function of Rayleigh number and L/D is presented in the aforementioned ranges.     

An experimental investigation on the effect of a perforated fin on free convection heat transfer from a confined horizontal cylinder

Natural convection heat transfer from an isothermal horizontal fin attached to a cylinder, confined between two adiabatic walls of constant height is investigated by the Mach–Zehnder interferometry technique. This study is focused on the effect of a perforated fin attached to the bottom of a cylinder while the vertical position of the cylinder (Y ) changes between two walls with a constant distance of W measuring 1.5 times the cylinder diameter. The cylinder's average Nusselt numbers are determined for three ratios of vertical position to its diameter, Y /D = 0.5, 1.5, 2, and 3. The Rayleigh number ranges from 4.5 × 10³ to 1.2 × 10⁴. The distance between the walls is chosen to be 1.5 D, that is, an optimum distance at which the Nusselt number is maximum. The effect of the perforated fin on free convection heat transfer is investigated and compared with other works. Results show outstanding enhancement in heat transfer, with a minimum result of 40% and maximum of 90%. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21041     

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.     

The Effect of Square Tube Location in a Vertical Array of Square Tubes on Natural Convection Heat Transfer

Experimental investigation is reported on natural convection heat transfer from the outer surface of a vertical array of horizontal square tubes in air. Five tubes equally spaced are used with cross section 0.02 × 0.02 m². The tubes are subject to constant heat flux boundary condition using internal constant heat flux heating elements in the range 46–510 W/m². Experiment is done for arrays of 2–5 square tubes and for four center-to-center separation distance to hydraulic diameter ratios. Study is concentrated on the effect of tube location in the array and on the geometry of the array. Results show that the downstream tubes exhibit reduced Nusselt numbers than that of a single tube for small center-to-center separation ratio of 2.5. This reduction depends on the location of the tube in the array and the number of tubes in each array. Results also show that as the ratio increases, enhancement in heat transfer over that of a single tube is observed and critical ratio is obtained at a specified value of the modified Rayleigh number for the upper (downward) tubes in each array. Local circumference averaged correlations are proposed for the upper tubes in each array and for any other individual tube in each array geometry. An overall general averaged correlation is also reported for each tube in the array.     

Effect of orientation on natural convection of a cylinder array in water

Experimental results of free convection from a constant temperature cylinder array of the order of Rayleigh number 10⁷ in water are given in this paper. The effect of a separation distance between cylinders and the effect of the inclination angle of an array on heat transfer are shown.     

Natural convection from a confined horizontal cylinder: the optimum distance between the confining walls

The laminar natural convection from an isothermal horizontal cylinder confined between vertical walls, at low Rayleigh numbers, is investigated by theoretical, experimental and numerical methods. The height of the walls is kept constant, however, their distance is changed to study its effect on the rate of the heat transfer. Results are incorporated into a single equation which gives the Nusselt number as a function of the ratio of the wall distance to cylinder diameter, t/D, and the Rayleigh number. There is an optimum distance between the walls for which heat transfer is maximum.     

Magnetohydrodynamic Natural Convection in a Square Enclosure with Four Circular Cylinders Positioned at Different Rectangular Locations

We deploy a finite volume numerical computation to investigate the two-dimensional hydromagnetic natural convection in a cooled square enclosure in the presence of four inner heated circular cylinders with identical shape. The inner circular cylinders are placed in a rectangular array with equal distance away from each other within the enclosure and moving along the diagonals of the enclosure. All the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed for a range of the controlling parameters such as the Rayleigh number 10³ to 10⁶, Hartmann number 0 to 50, and the dimensionless horizontal and vertical distance from the center of a cylinder to center of another cylinder 0.3 to 0.7. The study specifically aims to understand the effects of the location of the cylinders in the enclosure on the magnetoconvective transport, when they moved along the diagonals of the enclosure. It is observed that the unsteady behavior of the flow and thermal fields at relatively larger Rayleigh numbers and for some cylinder position are suppressed by imposition of the magnetic field. The heat transfer strongly depends on the position of the cylinders and the strength of the magnetic field. Hence, by controlling the position of the objects and the magnetic field strength, a significant control on the hydrodynamic and thermal transport can be achieved.     

Natural convection in cavities with a thin fin on the hot wall

A numerical study has been carried out in differentially heated square cavities, which are formed by horizontal adiabatic walls and vertical isothermal walls. A thin fin is attached on the active wall. Heat transfer by natural convection is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁴ to 10⁹, dimensionless thin fin length from 0.10 to 0.90, dimensionless thin fin position from 0 to 0.90, dimensionless conductivity ratio of thin fin from 0 (perfectly insulating) to 60. It is found that Nusselt number is an increasing function of Rayleigh number, and a decreasing function of fin length and relative conductivity ratio. There is always an optimum fin position, which is often at the center or near center of the cavity, which makes heat transfer by natural convection minimized. The heat transfer may be suppressed up to 38% by choosing appropriate thermal and geometrical fin parameters.     

A Numerical Study on Natural Convention Heat Transfer From a Horizontal Isothermal Cylinder Located Underneath an Adiabatic Ceiling

A numerical analysis is performed for steady-state and two-dimensional natural convection heat transfer from a horizontal isothermal cylinder located underneath a horizontal adiabatic ceiling. The finite-volume method based on the SIMPLE algorithm and a nonorthogonal grid discretization scheme are used to solve the continuity, momentum, and energy equations for the Rayleigh numbers in the range from 10^?1 to 10⁴. The Poisson equations are solved to find the grid points, which are distributed in a nonuniform manner with higher concentration close to the solid regions. In addition, the HYBRID differencing scheme is used for the approximation of the convective terms in the curvilinear coordinate. The effects of the Rayleigh numbers and cylinder spacing from the adiabatic ceiling on both the local and average Nusselt numbers around the cylinder are investigated. Numerical results are performed for the plate-to-cylinder spacing ranging from 0.1 to 1.4.     

An experimental and three-dimensional numerical study of natural convection heat transfer between two horizontal parallel plates

In this study, experimental and three-dimensional numerical studies were performed to investigate the effects of plate spacing and temperature difference on natural convection between isothermally heated upward-facing lower horizontal plate and externally insulated horizontal upper plate. Air is used as the heat transfer medium. Rayleigh number varied in the 1108–2.339 × 10⁵ range. Several numerical simulations for three-dimensional steady laminar and turbulent flows heat transfer were carried out using a commercial CFD code Fluent 6.2. Results have shown that there is a good agreement between the numerical and present experimental results as well as with available data in literature.     

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.     

Natural convection heat transfer of molten salt nanofluids around vertical array of heated horizontal cylinders

Abstract

To analyze the natural convection heat transfer of molten salt nanofluids around vertical array of horizontal cylinders, a numerical simulation is performed with cylinder numbers in the range of N?=?2–8 and pitches in the range of S/D?=?5–10. The results show that the heat transfer of nanofluids around each cylinder is affected by the position in the tube row and its distance from the adjacent cylinder. The average Nusselt number (Nu_a) of the natural convection heat transfer over the whole array of cylinders is determined by cylinder spacing S/D, cylinder number N, and Ra. When S/D?=?5, Nu_a decreases as the cylinder number increases. When S/D?=?10, Nua increases as the cylinder number increases. Compared with the molten salts, the natural convection heat transfer of nanofluids is enhanced. This study provides a theoretical basis for the design of a single-tank energy storage system.