Free convective heat transfer and criterion of onset of free convection in a horizontal melt layer of ice heated by upper rigid surface

An experimental and analytical investigation pertaining to the effect of density inversion of water on the free convective heat transfer and the onset of free convection in a horizontal melt layer of ice heated by upper rigid surface is carried out. Temperatures of the upper surface are varied from 1°C to 15°C, with Rayleigh number ranging from 2 × 10² to 1 × 10⁵. From the present study, it can be demonstrated both experimentally and analytically that the density inversion of water plays an influential role in such a melt layer and the onset of free convection and the free convective heat transfer are considerably affected by the temperature of upper rigid surface T₂, in the case of T₂ ≤ 8° C, unlike the results obtained for common fluids without density inversion.     

Effect of vertical separation distance on laminar natural convective heat transfer over two vertically spaced equitemperature horizontal cylinders

A numerical study of laminar natural convective heat transfer in air from a pair of equitemperature horizontal cylinders placed one above the other in a vertical plane was carried out. Prime attention was focused on how heat transfer characteristics of the upper cylinder are affected by center-to-center separation distance between two cylinders (CCD). The study was limited to Rayleigh number ranging from 2×10⁴ to 2×10⁵. The vertical center-to-center separation distance between the cylinders was varied from two to ten cylinder diameters. A finite difference scheme based on the integration of the governing equations over finite cells was used. Temperature profiles around two cylinders, and heat transfer coefficients for each cylinder were obtained. The effect of center-to-center separation distance between the cylinders on heat transfer from the upper cylinder was considered. For assessing the accuracy of the current computational approach the results are compared with the experimental results reported by Sparrow and Niethammer [10].     

Free convection heat transfer from a horizontal fin attached cylinder between confined nearly adiabatic walls

Steady state two-dimensional free convection heat transfer from a horizontal, isothermal fin attached cylinder, located between nearly two adiabatic walls is studied experimentally using a Mach–Zehnder interferometer. Effects of the walls inclination angel (θ) on heat transfer from the cylinder is investigated for Rayleigh number ranging from 1000 to 15,500. Two cylinders with different diameters of D = 10 and 20 mm are used to cover wide Rayleigh range. Results indicate that, heat transfer phenomena differ for different Rayleigh number. For Rayleigh numbers lower than 5500, heat transfer rate from cylinder surface is lower than the heat transfer from a single cylinder. In this range by the use of walls, heat transfer from the cylinder decreases slightly and walls’ inclination does not change heat transfer rate from the cylinder surface. For Rayleigh number ranging from 5500 to 15,500, amount of heat transfer from the cylinder surface is less than that of a single cylinder. However, by adding nearly adiabatic walls to experimental model heat transfer mechanism differs and chimney effect between fin and walls increases the heat transfer rate from the cylinder surface. By increasing the walls inclination angel from 0° to 20°, the chimney effect between walls and fin diminishes and heat transfer rate from the cylinder surface is approaching to the heat transfer rate of fin attached cylinder without adiabatic walls.     

Experimental study of cylinder drag in a rarefied gas

Results are presented of experimental studies of the drag of a cylinder in transverse rarefied gas flow.The flow regimes varied from free-molecular to nearly continuum. The physical pendulum method was used to obtain experimental curves showing the effect of the temperature factor T_w/T₀, Reynolds number R₀ and cylinder fineness ratio L/D on the aerodynamic drag coefficient.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).     

Effect of flow diverters on free convection heat transfer from a pair of vertical arrays of isothermal cylinders

Laminar free convection heat transfer from two vertical arrays of five isothermal cylinders separated by flow diverters is studied experimentally using a Mach-Zehnder interferometer. The width of flow diverters is kept constant to two-cylinder diameters and the cylinders vertical center-to-center spacing is equal to three-cylinder diameter. Effect of the ratio of the horizontal spacing between two cylinder arrays to their diameter (S_h/D) on heat transfer from the cylinders is investigated for various Rayleigh numbers. The experiments are performed for S_h/D = 2-4, and the Rayleigh number based on the cylinder diameter ranging from 10³ to 3 × 10³. It is observed that for small S_h/D ratios, the flow diverters have a negative effect on the total rate of heat transfer from the arrays; while by increasing the horizontal center to center spacing, they tend to enhance the overall cooling rate of the array. Moreover, increasing Ra and S_h/D generally results in a higher average Nusselt number for each cylinder in the array.     

Free convection heat transfer from the outer surface of vertically oriented helical coils in glycerol-water solution

Steady state natural convection heat transfer from vertical helical coiled tubes, in glycerol-water solution 57% (g/w) by mass, is studied experimentally. Average heat transfer coefficients were obtained for laminar and transition to turbulent natural convection. The experiments have been carried out for three coil diameter to tube diameter ratios, D/d_o, and for five and ten coil turns, N. Effects of Rayleigh number, D/d_o ratios, and N on the heat transfer behavior of the coils are investigated. Correlations are presented to calculate the average Nusselt number in terms of Rayleigh number, D/d_o ratios, and N. The results show that the heat transfer coefficient is enhanced either by reducing the diameter ratio or the number of coil turns. The overall correlations covering all the data points using the coil length as a characteristic length are also presented.     

Taguchi design of three dimensional simulations for optimization of turbulent mixed convection in a cavity

This study discusses the application of Taguchi method in assessing maximum heat transfer rate for the turbulent mixed convection in an enclosure embedded with rotating isothermal cylinder. The simulations were planned based on Taguchi’s L16 orthogonal array with each trial performed under different conditions of position of the cylinder, Reynolds number (Re) and Rayleigh number (Ra). The thermal lattice Boltzmann based on D3Q19 methods without any turbulent submodels was purposed to simulate the flow and thermal fields. A relaxation time method with the stability constants is introduced to solve turbulent natural convection problems. Signal-to-noise ratios (S/N) analysis were carried out in order to determine the effects of process parameters and optimal factor settings. Finally, confirmation tests verified that Taguchi method achieved optimization of heat transfer rate with sufficient accuracy.     

Visualization of natural convection heat transfer on horizontal cylinders

Natural convection heat transfer phenomena on horizontal cylinders were investigated experimentally in order to explore the applicability of analogy experimental method using the copper electroplating system and to visualize the local heat transfer depending on the angular position and the diameter of the horizontal cylinder. The diameters of the cylinders are varied from 0.01 to 0.15 m, which correspond to the Rayleigh numbers of 1.73 × 10⁷–5.69 × 10¹¹. The measured mass transfer coefficients show good agreements with the existing heat transfer correlations. The patterns of copper plated on the aluminum cathodes for various Rayleigh numbers reveal and visualize the local heat transfer depending on the angular position and show good agreement with the works of Kitamura et al. The hydrogen bubbles produced at higher applied potential visualize the plumes appeared on top region of the cylinders.     

Experimental study of natural convection heat transfer between an outer horizontal cylindrical envelope and an inner concentric heated square cylinder with two slots

This paper presents the results of an experimental study of natural convection heat transfer between a horizontal cylindrical envelope and an internal concentric heated square cylinder with two slots. The internal cylinder was a hollow one with horizontal slots on its top and bottom surfaces. The ratio of slot widthS to the side heightH was 0.0612 and 0.3878. The ratio of the envelope inner diameterD _o to the side heightH was 2.653. Air was used as the working fluid. The range of Ray-leigh number was 1.77×10²8.72×10⁶ forS/H=0.0612 and 1.32×10²6.25×10⁶ forS/H=0.3878. The results show that there are three different heat transfer regimes in different Ray-leigh number regions, i.e. pure conduction regime, transition regime and convection regime. The average heat transfer results were correlated into two empirical equations. Comparison was made with the non-slotted case. It is found that slots of the internal cylinder can significantly enhance the heat transfer.

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Experimentelle Untersuchung des Wärmeübergangs bei natürlicher Konvektion zwischen einer horizontalen zylindrischen Außenhülle und einem konzentrischen, beheizten, quadratischen Prisma mit zwei Schlitzen

Zusammenfassung In der Arbeit werden die Ergebnisse einer experimentellen Untersuchung des Wärmeübergangs bei natürlicher Konvektion zwischen einer horizontalen zylindrischen Außenhülle und einem beheizten quadratischen Prisma mit zwei Schlitzen vorgestellt. Das Prisma selbst ist hohl und weist in der oberen und unteren Begrenzungsfläche je einen horizontalen Längsschlitz auf. Das Verhältnis von SchlitzweiteS zu SeitenhöheH beträgt 0,0612 und 0,3878, das des HülleninnendurchmessersD _o zur SeitenhöheH beträgt 2,653. Als Arbeitsmedium diente Luft. Die Rayleigh-Zahlen variierten zwischen 1,7·10² und 8,72·10⁶ fürS/H=0,0612 und zwischen 1,32·10² und 6,25·10⁶ fürS/H=0,3878. Die Ergebnisse belegen die Existenz dreier unterschiedlicher Wärmeübergangsregime in den verschiedenen Rayleigh-Zahl-Bereichen, und zwar reiner Leitungsbereich, Übergangsgebiet und Konvektionsbereich. Die Ergebnisse für den Wärmeübergang werden im Vergleich mit jenen für ein Prisma ohne Schlitze durch zwei Korrelationbeziehungen dargestellt. Es zeigt sich, daß durch Anbringung von Schlitzen am Innenprisma der Wärmeübergang wesentlich verstärkt werden kann.

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Nomenclature C _p specific heat at constant pressure, J/(kg·K) - D _i diameter of the related circular cylinder whose circumferential area is equal to that of the unslotted square cylinder, m - D _o internal diameter of the outer circular envelope, m - F _i surface area of the inner two slot cylinder, m - g gravitational acceleration, m/s² - H distance between the opposite sides of the square cylinder with two slots, m - K _eq dimensionless equivalent thermal conductivity - L axial length of the test section, m - m ratio of the area of the unslotted square cylinder surface to that of the slotted square cylinder - P pressure in the enclosure, Pa - Q total power input to the enclosure, W - Q _cond radial heat conduction, W - Q _conv convective heat transfer, W - Q _r radiation heat transfer, W - Q _los end heat dissipation, W - R air gas constant, J/(kg·K) - Ra Rayleigh number - S slot width, m - T _i wall temperature of the inner cylinder, K - T _o wall temperature of the outer envelope, K - T _m mean temperature, K - T temperature difference=T _i –T _o , K - W maximum gap width of the test annuli=(D _o –H)/2 for the square case, m Greek symbols ₀ black body radiation constant, W/(m²·K⁴) - _s equation system emissivity - air thermal conductivity, W/(m·K) - _eq equivalent thermal conductivity, W/(m·K) - air dynamic viscosity, kg/(m·s) This work was supported by the National Natural Science Foundation of China.     

Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries

This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - c_m mass concentration of microcapsules - c_p specific heat, kJ kg^–1 K^–1 - h_fs phase change material heat of fusion, kJ kg^–1 - h_m* modified convective heat transfer coefficient, W m^–2 K^–1 - k thermal conductivity, W m^–1 K^–1 - k_e effective thermal conductivity of slurry, W m^–1 K^–1 - k_b slurry bulk thermal conductivity, W m^–1 K^–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - q_wⁿ wall heat flux, Wm^–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r₀ duct radius, m - r₁ dimensionless radial coordinate - Ste Stefan number - T temperature, K - T₁ lower phase change temperature limit, K - T₂ upper phase change temperature limit, K - T_i slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x₁ dimensionless axial coordinate - thermal diffusivity, m²/s - dimensionless temperature - dynamic viscosity, N·s/m² - kinematic viscosity, m²/s - _t width of thermal boundary, m - degree of heat transfer enhancement, = h_m*/(h_m*)_single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid     

Delay in response of turbulent heat transfer against acceleration or deceleration of flow in a pipe

To predict the heat transfer enhancements that result from the application of a pulsating flow in a pipe, we experimentally investigated the turbulent heat transfer variations produced in response to sudden accelerations or decelerations to flows within a pipe. To accomplish this, the Reynolds numbers with the valve open (Re₁) and close (Re₀) were systematically varied in the range of 8,000 ≤ Re₁ ≤ 34,000 and 700 ≤ Re₀ ≤ 23,000, respectively, and in-pipe spatiotemporal heat transfer variations were measured using infrared thermography simultaneously with temporal variations to the in-pipe flow properties. Based on the experimental results, it was found that the heat transfer delays that occur in response to accelerations or decelerations can be characterized using the corresponding time lag Δt and first-order time constant τ. The values of Δt and τ can be expressed as non-dimensional forms of Δt/(ν/u_τ²) and τ/(R/u_τ), respectively, where u_τ is the pipe wall friction velocity, ν is the kinematic viscosity of the fluid, and R is the pipe radius.     

Double-diffusive convection for a heated cylinder submerged in a salt-stratified fluid layer

Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra _T , and the buoyancy ratio, R _ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder are the latter. The increase in Ra _T reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio. For the same Ra _T , the increase of R _ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number are between the pure conduction and natural convection modes and the variation is due to the evolution of layers. Received on 13 September 1996     

Turbulent heat transfer in a flat plate boundary layer disturbed by a cylinder

Augmentation of heat transfer from a flat plate using a turbulence promoter has been studied. A circular cylinder 8 mm in diameter was placed in the turbulent boundary layer detached from the flat plate. It was located parallel to the plate and perpendicular to the flow direction. Clearance, c, between the cylinder and the flat plate was varied in nine steps: c=0, 1, 2, 3, 4, 6, 11, 20 and 29.5 mm. Measurements were made of the local heat transfer coefficients, mean velocity profiles, turbulence intensity profiles, static pressure and skin friction. Experimental results showed that the heat transfer deterioration which occurs just downstream of the cylinder at c=0 mm can be removed by displacing the cylinder a small distance from the wall. The improvement in heat transfer is mainly due to the unsteadiness of the recirculating flow on the plate and the effect of intense turbulence arriving at the near wall region from the lower shear layer of the cylinder wake. Heat transfer augmentation is most effective when c=4 mm and becomes less effective when c is increased more than 6 mm. The enhancement disappears far downstream from the cylinder.     

Flow boiling heat transfer of R134a,R236fa and R245fa in a horizontal 1.030 mm circular channel

This research focuses on acquiring accurate flow boiling heat transfer data and flow pattern visualization for three refrigerants, R134a, R236fa and R245fa in a 1.030 mm channel. We investigate trends in the data, and their possible mechanisms, for mass fluxes from 200 to 1600 kg/m²s, heat fluxes from 2.3 kW/m² to 250 kW/m² at T_sat = 31 °C and ΔT_sub from 2 to 9 K. The local saturated flow boiling heat transfer coefficients display a heat flux and a mass flux dependency but no residual subcooling influence. The changes in heat transfer trends correspond well with flow regime transitions. These were segregated into the isolated bubble (IB) regime, the coalescing bubble (CB) regime, and the annular (A) regime for the three fluids. The importance of nucleate boiling and forced convection in these small channels is still relatively unclear and requires further research.     

Single-phase heat transfer characteristics of concentric-tube thermosyphon

An experimental study has been conducted to evaluate the influence of the presence of inner tube and the Rayleigh number on free convective heat transfer in an open thermosyphon. Water and fluorocarbon R-11 refrigerant as the working fluids were utilized. Heat transfer results using the concentric geometry were given for modified Rayleigh number from 3.6×10² to 4.1 × 10⁷ which encompasses the regions of similarity, impeded and boundary layer flow conditions. It was found that the presence of the inner tube markedly increases the overall heat transfer coefficient of open thermosyphon by a factor as large as 2 to 10 in the turbulent impeded and boundary layer regimes.

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Wärmeübergang in einem Thermosyphon aus konzentrischem Rohr bei einphasiger Strömung

Zusammenfassung Es wurde experimentell untersucht, wie der Einbau eines Innenrohres und wie die Rayleigh-Zahl auf die freie Konvektion in einem offenen Thermosyphon, gefüllt mit Wasser oder dem Kältemittel R 11, einwirkt. Der untersuchte Bereich bei konzentrischer Geometrie lag bei modifizierten Rayleigh-Zahlen von 3,6 · 10² bis 4,1 · 10⁷ und umfaßte damit die Regionen der Grenzschichtströmung. Es ergab sich, daß der Einbau eines Innenrohres den Gesamtwärmeübergang eines offenen Thermosyphons im Bereich der behinderten turbulenten Strömungen und Grenzschichtströmungen um den Faktor 2 bis 10 steigert.

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Nomenclature a inner radius of heated tube, D/2 - A_in sectional space area of inner tube, d _i ² /4 - A_an sectional space area of annulus, (D^2-d ₀ ² )/4 - C_p specific heat - d_i inner diameter of inner tube - d₀ outer diameter of inner tube - D inner diameter of heated tube - g gravitational acceleration - L tube length of thermosyphon - Nu_a Nusselt number based on inner radius of heated tube - Nu_r Nusselt number based on equivalent heattransfer radius - Nu_x Nusselt number, defined in equation (1) - Pr Prandtl number, defined in equation (3) - q heat flux from heated tube - r equivalent heat-transfer radius, defined in equation (4) - Ra_a modified Rayleigh number based on inner radius of heated tube - Ra_r modified Rayleigh number based on equivalent heat-transfer radius - Ra_x modified Rayleigh number, defined in equation (2) - T_e temperature of entrance-fluid - T_w temperature of heated surface - T temperature difference between heated wall and entrance-fluid, T_w-T_e Greek Symbols coefficient of volumetric expansion - thermal diffusivity - thermal conductivity - viscosity - kinematic viscosity     

A numerical and experimental study of natural convective heat transfer from an inclined isothermal square cylinder with an exposed top surface

Natural convective heat transfer from an isothermal inclined cylinder with a square cross-section which have an exposed top surface and is, in general, inclined at an angle to the vertical has been numerically and experimentally studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The numerical solution has been obtained by solving the dimensionless governing equations subject to the boundary conditions using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. Results have only been obtained for Prandtl number of 0.7. Values of inclination angle between 0° and 180° and a wide range of Rayleigh number and the dimensionless cylinder width, W = w/h, have been considered. The effects of Dimensionless widths, Rayleigh numbers, and inclination angles on the mean Nusselt number for the entire cylinder and for the mean Nusselt numbers for the various surfaces that make up the cylinder have been examined. Empirical equations for the heat transfer rates from the entire cylinder have been derived.     

Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers

In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 × 10⁴ < Ra < 5 × 10⁵) for different annulus gap widths (L/D _o = 0.23, 0.3, and 0.37) and different inclination of the annulus (α = 0°, 30° and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and (3) increasing Ra increases the heat transfer rate for any L/D _o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D _o and α. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.     

Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid

Effects of inclination angle on natural convection heat transfer and fluid flow in a two-dimensional enclosure filled with Cu-nanofluid has been analyzed numerically. The performance of nanofluids is tested inside an enclosure by taking into account the solid particle dispersion. The angle of inclination is used as a control parameter for flow and heat transfer. It was varied from  = 0° to  = 120°. The governing equations are solved with finite-volume technique for the range of Rayleigh numbers as 10³  Ra  10⁵. It is found that the effect of nanoparticles concentration on Nusselt number is more pronounced at low volume fraction than at high volume fraction. Inclination angle can be a control parameter for nanofluid filled enclosure. Percentage of heat transfer enhancement using nanoparticles decreases for higher Rayleigh numbers.