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.     

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.     

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 a Square Enclosure with Two Horizontal Cylinders

This study investigates natural convection in a cooled square enclosure with two inner heated circular cylinders with the same diameter. The centers of two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively. The immersed boundary method (IBM) to model the inner circular cylinders based on the finite volume method is used to study a two-dimensional natural convection for different Rayleigh numbers varying in the range of 10³ ≤ Ra ≤ 10⁵. The effect of the radius of inner circular cylinders in an enclosure on heat transfer and fluid flow at different Rayleigh numbers has been examined. As the Rayleigh number increases, the horizontal symmetry is broken and the asymmetry occurred from the smaller radius. As the radius decreases, the dependence of the convection on the Rayleigh number is considerable. The dependence of the Nusselt number on the radius and the Rayleigh number is presented.     

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.     

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.     

Numerical investigation of unsteady natural convection heat transfer and entropy generation from a pair of cylinders in a porous enclosure

Abstract

The present study analyses numerically the unsteady heat transfer and entropy generation characteristics in a two-dimensional porous enclosure embedded with two heated circular cylinders at different positions at the vertical mid-plane. The heat transfer is primarily due to conduction for lower values of Darcy number (10^?4), while heat transfer by convection becomes significant for higher values of Darcy number (10^?3, 10^?2). Contrasting features are observed in the variation of time-average Nusselt number with interspacing distance. The major contributor of irreversibility is the entropy generation due to heat transfer for lower values of Darcy number, while for larger values of Darcy number, it varies with Rayleigh number.     

Fluid flow and heat transfer of natural convection around large horizontal cylinders: Experiments with air

Natural convective flows of air around large horizontal cylinders were investigated experimentally. The main concerns were the turbulent transition mechanisms and the heat transfer characteristics of turbulent flows. The cylinders were heated with uniform heat flux and their diameters were varied from 200 to 1200 mm to enable experiments over a wide range of modified Rayleigh numbers, Ra_D^* = 1.0 × 10⁸ to 5.5 × 10¹¹. The flow fields around the cylinders were visualized with smoke to investigate the turbulent transition mechanisms. The results show that three‐dimensional flow separations occur first at the trailing edge of the cylinder when Ra_D^* exceeds 3.5 × 10⁹, and the separation points shift upstream with increasing Rayleigh numbers. These separations become a trigger to the turbulent transition and transitional and turbulent flows appear downstream of the separations at higher Rayleigh numbers. However, they occupy a relatively small portion of the cylinder surfaces even at the maximum Rayleigh numbers of the present experiments. The local heat transfer coefficients were also measured. The results show that the coefficients are increased significantly in the transitional and turbulent regions compared with the laminar coefficients. Moreover, the present results for air were compared with previous results for water and the effects of Prandtl number on the flow and heat transfer were discussed. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 293–305, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10080     

Experimental study of the natural convection flow around an array of heated horizontal cylinders

Natural convection heat transfer from an array of heated cylinders has recently attracted much attention. However, in almost all of the investigations, attention has been restricted to the influence of geometrical parameters on the overall heat transfer. The present work deals with an experimental study of natural convection flow from a vertical array of two heated horizontal cylinders. A detailed analysis of the local temperature and velocity fields is performed. The modifications of the average Nusselt number evolution compared with the single cylinder are explained in terms of velocity and temperature fields of the flow around the cylinders. Results that are obtained for a variety of combinations of spacings and Rayleigh numbers are compared with known numerical results. The comparison shows a satisfactory agreement.     

Natural Convection of Al2O3 Nanofluid Between Two Horizontal Cylinders Inside a Circular Enclosure

Natural convection heat transfer within horizontal annuli has many engineering applications such as heat exchangers like fire tube heaters. In this paper numerical methods were used for the computational analysis of heat transfer from the fire tube/hot tube to the gas tube/cold tube inside the water medium using alumina nanoparticles. Because of eccentricities of both hot and cold cylinders and different diameters, the geometry is asymmetric. The mathematical model is based on two-dimensional continuity, momentum, energy, and volume fraction equations, which are solved numerically. The simulation was done for different values of particle loading, 1%, 2%, and 5%, at Rayleigh numbers 10³, 10⁴, and 10⁵. The results show that nanoparticles enhance the heat transfer by increasing the volume concentrations of particles. It was observed that the maximum and minimum augmentation of the average Nusselt number are about 30% and 14% at the Ra = 10³ and Ra = 10⁵, respectively. Although the average Nusselt number rises by increasing the Rayleigh number, the ratio of heat transfer using nanofluid to that by pure fluid decreases. Using 5% volume fraction of alumina nanoparticles at Rayleigh number of 10³ increases the heat transfer to cold tube by about 23% compared to the pure water. The effect of nanolayer formation around particles was considered in a thermal conductivity model, which shows approximately 5% increase in the Nusselt number. To verify the solution results, comparisons with previously published work on the basis of special cases are performed.     

Free Convection in Confined Power-Law Fluids From Two Side-by-Side Cylinders in a Square Enclosure

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 10⁷; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a positive dependence on both the Grashof number and the Prandtl number irrespective of the values of power-law index and relative positioning of the cylinders. Also, all else being equal, shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. When the two cylinders are situated close to the bottom wall, the rate of heat transfer is augmented with reference to that for the symmetric positioning of the cylinders along the horizontal mid-plane of the enclosure. Conversely, heat transfer deteriorates as the cylinders are located above the centerline of the enclosure. The present numerical results have been consolidated via the use of a modified Rayleigh number, thereby enabling the estimation of the average Nusselt number in a new application.     

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.     

An experimental investigation on the free convection heat transfer in a horizontal cavity consisting of flow diverters

The free convection heat transfer in a horizontal cavity with adiabatic vertical and isothermally horizontal walls and adiabatic diverters has been studied experimentally in this paper. The experiments have been carried out using a Mach–Zehnder interferometer. The effects of the diverter angle ranging from 0 to 90$\circ$ and Rayleigh number based on the cavity side wall length, from 6 × 10³ to 1.2 × 10⁴ on the heat transfer from the heated wall, were studied. The results indicate that, at each Rayleigh number, the maximum and the minimum heat transfer occur at a diverter angle of 30 and 90$\circ$ , respectively. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21014     

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.     

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 10² to 10⁶, Prandtl number, 10 to 100, and Bingham number, 0.01 to 100, for seven locations of inner cylinders as ±0.25, ±0.2, ±0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 10⁵. The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of the local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number, and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.     

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 simulation of natural convection in a horizontal enclosure with a heat-generating conducting body

The physical model considered here is a horizontal layer of fluid heated below and cold above with heat-generating conducting body placed at the center of the layer. The dimensionless thermal conductivities of body considered in the present study are 0.1, 1 and 50. The dimensionless temperature difference ratios considered are 0.0, 0.25, 2.5 and 25. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral methodology for variety of Rayleigh number from 10³ to 10⁶. Multi-domain technique is used to handle square-shaped heat-generating conducting body. The fluid flow, heat transfer and time- and surface-averaged Nusselt number are investigated for various ranges of Rayleigh number, thermal conductivity ratio and dimensionless temperature difference ratio. The results for the case of conducting body with heat generation are also compared to those without heat generation to see the effects of heat generation from the conducting body on the fluid flow and heat transfer in the enclosure.     

Numerical study of the laminar natural convection flow around horizontal isothermal cylinder

Natural convection around a horizontal circular cylinder under constant temperature or constant heat flux conditions in an infinite space has been the subject of numerous investigations in recent years. However, these studies use the inflow-outflow boundary in cylindrical coordinates that gives a sensible error, especially when the Rayleigh number is small. This investigation, that enters within the framework of general study dealing with natural convection from an array of cylinders, states the problem in cartesian coordinates system, involves the use of a control-volume method and resolves various apparent redundancies in boundary conditions. This problem was investigated numerically for laminar case by solving the full vorticity transport equation together with the stream function and energy equations. Results are obtained for 10¹ < Ra < 10⁶ and for Prandtl number equal to 0.7. Further, typical isotherms, local and mean Nusselt number, velocities and temperature distribution are clarified in detail. The numerical approach presented here appears to be sufficiently versatile to permit computation of a vertical array of cylinders.     

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio

The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10³ to 3.1 × 10⁴ by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.