A transition phenomenon of ice formation in water flow between two horizontal parallel plates

Experiments have been performed to investigate the icetransition profiles and heat-transfer characteristics for water flows between two horizontal parallel plates. The experiments are carried out under the condition that upper plate is cooled at uniform temperature kept less than freezing temperature of water, while the lower plate is heated at uniform temperature kept higher than the temperature of water flow. The temperatures of the upper and lower plates range from ?8 to ?14°C and from 10 to 60 °C, respectively, with inlet-water temperature varied from 1.5 to 4.5 °C. The cooling and heating temperature ratios, θ_c and θ_h, are ranging from 1.78 to 9.33 and from 1.22 to 39, respectively. By using three kinds of heightH of 16, 30 and 40 mm between the horizontal parallel plates, the Reynolds and Grashof numbers are varied from 3.2 × 10² to 1.5 × 10⁴ and from 3.4 × 10³ to 8.97 × 10⁶, respectively. As a result of this investigation two ice-transition modes are observed. The first ice-transition mode is due to an interruption of upper and lower thermal boundary layers, while the second mode is due to an instability of laminar boundary layer formed on water-ice interface. In order to determine the kind of ice-transition mode, criterion correlation formulas including the Reynolds numberRe _H , Grashof numberGr _H , and heating temperature ratio θ_h are determined and may be written as follows: For thermal icetransition mode (th.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23<1.6×10^?3 and for hydrodynamical ice-transition mode (hy.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23>2.3×10^?3 By introducing the freezing parameterB _f , correlation equations for local and mean Nusselt numbers along the water-ice interface at steady-state condition are determined. From the current experimental results it is found that the local Nusselt number may be described as the following equation:Nu _x =0.835 Re _H ^0.278 · B _f ^0.834 ·x/H)^?0.139     

Turbulent heat-transfer characteristics along the heated convex wall of a rectangular cross-sectional return bend

The turbulent heat-transfer characteristics along the heated convex wall of a return bend which has rectangular cross section with large ratio have been examined for various clearances of the duct in detail. The experiments are performed under condition that the convex wall is heated at uniform heat flux while the concave wall is insulated. Water as a working fluid is utilized. Using four kinds of clearances of 15, 40, 60 and 80 mm, the Reynolds number in the turbulent range is varied from 8×10³ to 8×10⁴ with Prandtl number ranging from 6.5 to 8.5. In consequence, it is found that both the local and the mean heat-transfer rates are always smaller than those for straight parallel plates or for the straight duct. It is also found that the local heat-transfer characteristics in the outlet region of the return bend are more sensitively influenced by the variation of duct clearance than those in the inlet region.     

Fluid flow and heat transfer in transitional boundary layers: effects of surface curvature and free stream velocity

Velocity and wall temperature measurements, over flat plate, concave and convex walls, were experimentally investigated in a low-speed wind tunnel with inlet velocities of 4 and 12 m/s encompassing the transitional region with streamwise distance Reynolds numbers from 3.15×10⁵ to 1.04×10⁶. As the velocity profiles, recorded by a semi-circular pitot tube and a digital constant-temperature hot-wire anemometer, were compared to exact Blasius profile and (1/7)th power law, experimental local Stanton numbers to analytical flat plate solution and turbulent correlation formula. Intermittency factors, derived from velocities and local Stanton numbers, were presented both in streamwise and pitchwise directions. It was found that the convex curvature delayed transition up to Re _x =1.04×10⁶, with a mean intermittency value of 0.61 and a shape factor of 1.81, where the similar intermittency and shape factors were determined at Re _x of 8.33×10⁵ and 4.25×10⁵ for the flat plate and concave wall, indicating the enhancing role of concave curvature on the transition mechanism. The thinner boundary layers of the concave surface resulted in higher intermittency values, corresponding to higher skin friction and Stanton numbers; moreover the lowest gap between the measured and derived Stanton numbers were also obtained over the concave surface. Destabilising role of the concave wall caused Stanton numbers to increase up to 22%, whereas the convex wall, due to its stabilising character, produced lower Stanton numbers by 12% with respect to those of the flat plate.     

Flow structure and heat transfer characteristics of an unconfined impinging air jet at high jet Reynolds numbers

The flow and heat transfer characteristics of an unconfined air jet that is impinged normally onto a heated flat plate have been experimentally investigated for high Reynolds numbers ranging from 30,000 to 70,000 and a nozzle-to-plate spacing range of 1–10. The mean and turbulence velocities by using hot-wire anemometry and impingement surface pressures with pressure transducer are measured. Surface temperature measurements are made by means of an infrared thermal imaging technique. The effects of Reynolds number and nozzle-to-plate spacing on the flow structure and heat transfer characteristics are described and compared with similar experiments. It was seen that the locations of the second peaks in Nusselt number distributions slightly vary with Reynolds number and nozzle-to-plate spacing. The peaks in distributions of Nusselt numbers and radial turbulence intensity are compatible for spacings up to 3. The stagnation Nusselt number was correlated for the jet Reynolds number and the nozzle-to-plate spacing as Nu _st∝Re ^0.69(H/D)^0.019.     

Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures

Two-dimensional numerical studies of flow and temperature fields for turbulent natural convection and surface radiation in inclined differentially heated enclosures are performed. Investigations are carried out over a wide range of Rayleigh numbers from 10⁸ to 10¹², with the angle of inclination varying between 0° and 90°. Turbulence is modeled with a novel variant of the k–ε closure model. The predicted results are validated against experimental and numerical results reported in literature. The effect of the inclination of the enclosure on pure turbulent natural convection and the latter’s interaction with surface radiation are brought out. Profiles of turbulent kinetic energy and effective viscosity are studied to observe the net effect on the intensity of turbulence caused by the interaction of natural convection and surface radiation. The variations of local Nusselt number and average Nusselt number are presented for various inclination angles. Marked change in the convective Nusselt number is found with the orientation of enclosure. Also analyzed is the influence of change in emissivity on the flow and heat transfer. A correlation relevant to practical applications in the form of average Nusselt number, as a function of Rayleigh number, Ra, radiation convection parameter, N _RC and inclination angle of the enclosure, φ is proposed.     

Turbulent free convection in a vertical converging channel

This paper presents the results of experimental and numerical investigations of the problem of turbulent natural convection in a converging-plate vertical channel. The channel has two isothermally heated inclined walls and two adiabatic vertical side walls. The parameters involved in this study are the channel geometry represented by the channel width at exit, the inclination of the heated walls and the temperature difference between the heated walls and the ambient. The investigation covered modified Rayleigh numbers up to 10⁸ in the computational study and up to 9.3 × 10⁶ in the experimental work. The experimental measurements focused on the velocity field and were carried out using a PIV system and included measurements of the mean velocity profiles as well as the root-mean-square velocity and shear stress profiles. The experiments were conducted for an inclination angle of 30°, a gap width of 10 mm and two temperature differences (∆T=25.4°C and 49.8°C). The velocity profiles in the lower part of the channel indicated the presence of two distinct layers. The first layer is adjacent to the heated plate and driven by buoyancy forces while the second layer extends from the point of maximum velocity to the channel center plane and driven mainly by shear forces. The velocity profile at the upper portion of the channel has shown the merging of the two boundary layers growing over the two heated walls. The measured values of the Reynolds shear stress and root mean square of the horizontal and vertical velocity fluctuation components have reached their maximum near the wall while having smaller values in the core region. The computational results have shown that the average Nusselt number increases approximately linearly with the increase of the modified Rayleigh number when plotted on log–log scale. The variation of the local Nusselt number indicated infinite values at the channel inlet (leading edge effect) and high values at the channel exit (trailing edge effect). For a fixed value of the top channel opening, the increase of the inclination angle tended to reduce flow velocity at the inlet section while changing the flow structure near the heated plates in such a way to create boundary-layer type flow. The maximum value of the average Nusselt number occurs when θ = 0 and decreases with the increase of the inclination angle. On the other hand, the increase of the channel width at exit for the same inclination angle caused a monotonic increase in the flow velocity at the channel inlet.     

Local Nusselt number and temperature field in turbulent flow through a heated square-sectioned U-bend

Local heat transfer coefficients and temperature distributions within the fluid for air flow around a 180° square-sectioned bend have been measured. The ratio of bend radius to hydraulic diameter of the duct is 3.35:1 and the flow entering the bend is sensibly fully developed. Measurements of air and wall temperatures span a range of Reynolds numbers from 9.9 × 10³ to 9.2 × 10⁴ with the principal emphasis given to the case of Re ? 5.6 × 10⁴. This Reynolds number and geometric configuration coincide with that of a companion LDA study carried out by Chang et al¹ which provides detailed maps of the mean and turbulent velocity fields. The data show that by 45° into the bend the heat transfer coefficients on the inner convex wall of the bend drop markedly while those on the other walls increase. By 90° the ratio of the heat transfer coefficients at the mid positions of the concave and convex walls is more than 2:1. Nevertheless this ratio is less than would be anticipated from considering two-dimensional flow on weakly curved surfaces. There is a general consistency between the velocity and the temperatyre field data in the heated fluid     

Subcooled forced convection film boiling over a vertical flat plate embedded in a fluid-saturated porous medium

The problem of subcooled forced convection film boiling on a vertical flat plate embedded in a porous medium was attacked exploiting similarity transformations on the governing equations and boundary conditions in both vapor and liquid layers. Similarity solutions were obtained to investigate the effects of the vapor super-heating and liquid subcooling. The heat transfer groupingNu _x /Ra _x ^1/2 is expressed in terms of a function of three parameters associated with the degree of liquid subcooling (Sub), the degree of vapor superheating (Sup) and the vapor buoyancy effect relative to the liquid forced convection effect (R). It is found that the level ofNu _x /Ra _x ^1/2 increases asSup orR decreases and asSub increases. Furthermore, asymptotic expressions were reduced considering the physical limiting conditions, namely, thin and thick vapor films.     

Methodical investigation of free convection from vertical and horizontal plates

This paper attempts of review the literature on free convection from flat surfaces transferring heat in an unlimited space. Data from the references have been presented as final criterial relations both in tabular form and in graphic system, separately for the vertical plates and the horizontal ones. About 45 results of investigations on free convection have been examined and the following mean criterial relations have been calculated:Nu=0.550·(Ra)^0.250 for vertical plates,Nu=0.310·(Ra)^0.290 for horizontal plates. It has been observed for the vertical plates that divergence of these results relatively to the mean values is constant within the whole variability range of the Rayleigh number and amounts to about ± 15%. In the case of horizontal plates the divergencies are more considerable and vary within ± 50% for the laminar, and within ± 25% for the turbulent range. In the next step the attempt was made to determine the causes of these divergencies and errors. The work was performed because of two main reasons: imperfection of measuring methods and a lack of uniformity in the choice of the characteristic linear dimension.     

A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed. The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu _m at the bottom surface of both cavity models tends generally to increase with increasing Re_HorGr _w/Re _H ² . However, in the flow region ofRe _H & 500 for DOF-cavity, theNu _m for 0.4 ≦ D₂/D₁ ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe _H.     

Natural convection in inclined two dimensional rectangular cavities

Steady two-dimensional natural convection in fluid filled cavities is numerically investigated. The channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. The field equations for a Newtonian Boussinesq fluid are solved numerically for three cavity height based Rayleigh numbers, Ra = 10⁴, 10⁵ and 10⁶, and several aspect ratios. The calculations are in excellent agreement with previously published benchmark results. The effect of the inclination of the cavity to the horizontal with the angle varying from 0° to 180° and the effect of the startup conditions on the flow pattern, temperature distribution and the heat transfer rates have been investigated. Flow admits different configurations at different angles as the angle of inclination is increased depending on the initial conditions. Regardless of the initial conditions Nusselt number Nu exhibits discontinuities triggered by gradual transition from multiple cell to a single cell configuration. The critical angle of inclination at which the discontinuity occurs is strongly influenced by the assumed startup field. The hysteresis effect previously reported is not always present when the calculations are reversed from 90° to 0°. A comprehensive study of the flow structure, the Nu variation with varying angle of inclination, the effect of the initial conditions and the hysteresis effect are presented.     

An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows

Flow and heat transfer characteristics over flat, concave and convex surfaces have been investigated in a low speed wind tunnel in the presence of adverse and favourable pressure gradients (k), for a range of –3.6 × 10^–6 ≤ k ≤ +3.6 × 10^–6. The laminar near zero pressure gradient flow, with an initial momentum thickness Reynolds number of 200, showed that concave wall boundary layer was thinner and heat transfer coefficients were almost 2 fold of flat plate values. Whereas for the same flow condition, thicker boundary layer and 35% less heat transfer coefficients of the convex wall were recorded with an earlier transition. Accelerating laminar flows caused also thinner boundary layers and an augmentation in heat transfer values by 28%, 35% and 16% for the flat, concave and convex walls at k = 3.6 × 10^–6. On the other hand decelerating laminar flows increased the boundary layer thickness and reduced Stanton numbers by 31%, 26% and 22% on the flat surface, concave and convex walls respectively. Turbulent flow measurements at k = 0, with an initial momentum thickness Reynolds number of 1100, resulted in 30% higher and 25% lower Stanton numbers on concave and convex walls, comparing to flat plate values. Moreover the accelerating turbulent flow of k = 0.6 × 10^–6 brought about 29%, 30% and 24% higher Stanton numbers for the flat, concave and convex walls and the decelerating turbulent flow of k = –0.6 × 10^–6 caused St to decrease up to 27%, 25% and 29% for the same surfaces respectively comparing to zero pressure gradient values. An empirical equation was also developed and successfully applied, for the estimation of Stanton number under the influence of pressure gradients, with an accuracy of better than 4%.     

Turbulence Models and Large Eddy Simulations Applied to Ascending Mixed Convection Flows

Coolant flows in the cores of current gas-cooled nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be significantly modified from the forced convection condition by the action of buoyancy, and the thermal-hydraulic regime is no longer one of pure forced convection. These modifications are associated primarily with changes to the turbulence structure. Flow laminarization may occur, and in that event heat transfer rates may be as low as 40% of those in the corresponding forced convection case. The present work is concerned with the modelling of such ??mixed?? convection flows in a vertical heated pipe. All fluid properties are assumed to be constant and buoyancy is accounted for within the Boussinesq approximation. Six different Eddy Viscosity Models (EVMs) are examined against experimental measurements and the direct numerical simulation (DNS) data of You et?al. (Int J Heat Mass Transfer 46:1613?C1627, 2003). The EVMs selected for study embody distinct physical refinements with respect to the parent high-Reynolds-number k-?? model. Large Eddy Simulations employing the classical Smagorinsky sub-grid-scale model are also presented. It is found that the early EVM scheme of Launder and Sharma (1974) is the turbulence model in the closest agreement with direct simulation results for the ratio of mixed-to-forced convection Nusselt number, Nu/Nu ₀; the model in the poorest accord with the DNS data is a k-??-SST formulation. However, in relation to comparisons with both numerical and experimental data for forced convection Nusselt number, Nu ₀, the present work reveals that some of the more recent models perform better than the Launder-Sharma scheme. No single scheme is in consistently close agreement with the numerical simulation flow profiles.     

Transient natural convection cooling of a high Prandtl number fluid in a cubical cavity

This work presents a numerical analysis of the effects of thermal boundary conditions, fluid variable viscosity and wall conduction on transient laminar natural convection of a high Prandtl number (Pr=4×10⁴) fluid (Golden Syrup) in a cubical cavity. The simulations consider physical situations realizable at laboratory scale using a cavity with Plexiglas walls of 1 cm of thickness, and inside dimension of L=20 cm. The initial Rayleigh (Ra) number is 10⁶. The cavity is initially full of fluid at rest and at constant temperature (T _i =45°C) higher than the temperature of the walls (T _w =25°C). The time evolution of the flow patterns, the temperature contours, the mean temperature of the fluid and the Nusselt number (Nu) of eight different cases of cooling are presented and analyzed.     

Combined Laminar Mixed Convection and Surface Radiation using Asymptotic Computational Fluid Dynamics (ACFD)

This paper reports the use of the technique of combining asymptotics with computational fluid dynamics (CFD), known as asymptotic computational fluid dynamics (ACFD), to handle the problem of combined laminar mixed convection and surface radiation from a two dimensional, differentially heated lid driven cavity. The fluid under consideration is air, which is radiatively transparent, and all the walls are assumed to be gray and diffuse and having the same hemispherical, total emissivity (ɛ). The computations have been performed on FLUENT 6.2. The full radiation problem (i.e. all the walls are radiatively black corresponding to ɛ = 1) is first taken up and the method of “perturbing and blending” is used wherein, first, limiting solutions of natural and forced convection are perturbed, to obtain correlations for the weighted average convective Nusselt numbers for the full radiation case. These correlations are then blended suitably in order to obtain a composite correlation for the weighted average convective Nusselt number that is valid for the entire mixed convection range, i.e., 0 ≤ Ri ≤ ∞. This correlation is then expanded in terms of ɛ to obtain an expression for the average convective Nusselt number that is valid for any ɛ in the range 0 ≤ ɛ ≤ 1. In so far as radiation heat transfer is concerned, using asymptotic arguments, a new weighted average radiation Nusselt number is defined such that this quantity can be expanded just in terms of ɛ. Hence, by the use of ACFD, the number of solutions required to obtain reasonably accurate correlations for both the convective and radiative heat transfer rates and hence the total heat transfer rate (Nu _total = Nu _C + Nu _R), is substantially reduced. More importantly, the correlations for convection and radiation are asymptotically correct at their ends. The effect of secondary variables like aspect ratio and the case of unequal wall emissivities can also be included without significant additional effort.     

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     

Chimney effect due to different vertical position of an isothermal horizontal cylinder confined between two adiabatic walls

The variation of natural convection heat transfer from an isothermal horizontal cylinder confined between two adiabatic walls of constant height is investigated by Mach-Zehnder interferometry technique. This paper focuses on the chimney effect due to the vertical position changes of cylinder (Y) located between two walls with a constant distance of W measuring 1.5 cylinder diameter. The cylinder’s local and average Nusselt numbers are determined for ratio of vertical position to its diameter ranging from Y/D = (0 to 10), and the Rayleigh number ranging from 3.5 × 10³ to 1.4 × 10⁴. There is an optimum distance between the walls in which the Nusselt number is maximum. Results are indicated with a single correlation which gives the average Nusselt number as a function of the ratio of vertical position to cylinder diameter and the Rayleigh number. The experimental data shows that there is an optimum vertical position for the cylinder at which the Nusselt number has a maximum value at each Rayleigh number. This optimal vertical position is derived from the correlation and is presented by an equation. The value of the optimum vertical position increases as the Rayleigh number increases.     

Study of the aerodynamic characteristics of cone-sphere models in a hypersonic flow

The aerodynamic characteristics of cone-sphere models are studied at Mach numbers M = 6, 8.4, and 12 to 13 over a wide Reynolds number range. Models of a braking device (sphere) were connected with a load (frustum of a cone) by means of shrouds. The dependences of the aerodynamic coefficients C _x and C _y on the angle of attack α were obtained for different relative dimensions of the load and the braking device, shroud lengths, and Mach and Reynolds numbers. The effect of the above-mentioned parameters on the aerodynamic characteristics of the models is analyzed. The C _x (Re_D) dependences of load-parachutemodels in a symmetric flow are determined over the wide Mach and Reynolds number ranges 6 ≤ M ≤ 13 and 3 · 10³ ≤ Re_D ≤ 3 · 10⁶.     

Hysteretic heat transfer study of liquid–liquid two-phase flow in a T-junction microchannel

Liquid–liquid two-phase flow in microchannels is capable of boosting the heat removal rate in cooling processes. Formation of different two-phase flow patterns which affect the heat transfer rate is numerically investigated here in a T-junction containing water-oil flow. For this purpose, the finite element method (FEM) is applied to solve the unsteady two-phase Navier–Stokes equations along with the level set (LS) equation in order to capture the interface between phases. It is shown that the two-phase flow pattern in microchannels depends on the flow initial condition which causes hysteresis effect in two-phase flow. In this study, the hysteresis is observed in flow pattern and consequently in the heat transfer rate. The effect of wall contact angle on the hydrodynamics and heat transfer in the microchannel is investigated to gain useful insight into the hysteresis phenomenon. It is observed that the hysteresis is significant in super-hydrophilic microchannels, while it disappears at the contact angle of 75^°. The effect of water to oil flow rate ratio (Q_wat/Q_oil) on the heat transfer is also studied. The flow rate ratio has a negligible effect on the Nusselt number (Nu) in the dripping regime, while the Nu decreases with an increase of Q_wat/Q_oil in the co-flow regime. The thickness of the oil film, velocity, and temperature distribution are studied in the co-flow regime. It is revealed that the normalized slip velocity reduces at higher values of Q_wat/Q_oil, which causes a reduction in the averaged Nu. In dripping regimes, higher flow rate ratios lead to a more frequent generation of droplet/slugs at a smaller size. The passage of the slugs or droplets increases the local Nu. Larger droplets generated at lower flow rate ratios cause a larger increase in the local Nu than smaller droplets. The temperature and velocity field around the droplets are also illustrated to investigate the heat transfer improvement. The generated vortex at the tip of the oil jet causes an increase in the velocity and Nu on the water side.     

Free convective heat-transfer performance of a two-dimensional open thermosyphon with heat sources of cavity dotted along vertical wall

This paper is concerned with the heat-transfer characteristics in a vertical two-dimensional open thermosyphon whose heat sources are the heated cavities dotted along the vertical wall. Air is utilized for the measurement of heat transfer, while transformer oil for the observation of the flow patterns. Attention is particularly focussed on the effects of the depth of cavity and the clearance for main fluid-flow on the behavior of free convective heat transfer in the present open thermosyphon. Environmental temperature is maintained at 10°C, while temperature of the bottom-surface of cavity and the clearance of main fluid-flow are parametrically varied, as Rayleigh number ranging from 1.2×10¹ to 3.8×10⁶.It is found that the effect of the clearance on the heat-transfer characteristics in the two-dimensional open thermosyphon is unexpectedly large. Experimental results are finally given as plots of Nusselt number versus Rayleigh number. An experimental correlation is given for the Nusselt number as a function of the Rayleigh number and the clearance/length ratio of the open thermosyphon.

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Wärmeübertragungsverhalten bei freier Konvektion eines zweidimensionalen, offenen Thermosyphons mit längs der vertikalen Wand verteilten Hohlräume als Wärmequellen

Zusammenfassung Der Bericht befaßt sich mit dem Wärmeübertragungsverhalten in einem vertikalen, zweidimensionalen offenen Thermosyphon mit längs der vertikalen Wand verteilten, beheizten Hohlräumen als Wärmequellen. Zur Messung des Wärmeüberganges wird Luft, zur Strömungsbeobachtung Transformatorenöl verwendet. Besonderes Interesse gilt den Einflüssen der Hohlraumtiefe und der lichten Weite für den Hauptstrom auf das Verhalten des Wärmeüberganges bei freier Konvektion. Die Umgebungstemperatur wird auf 10°C gehalten, während die Hohlraumbodentemperatur und die lichte Weite für den Hauptstrom variiert werden mit Rayleigh-Zahlen zwischen 1.2×10¹ und 3.8×10⁶.Es wird festgestellt, daß der Einfluß der lichten Weite auf das Wärmeübertragungsverhalten unerwartet groß ist. Die experimentellen Ergebnisse werden in Diagrammen der Nusselt-Zahl über der Rayleigh-Zahl dargestellt. Ein Zusammenhang für die Nusselt-Zahl als Funktion von der Rayleigh-Zahl und dem Verhältnis von lichte Weite zu Länge wird gegeben.

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Nomenclature B distance between heated wall and opposing insulation wall,W+D - d _i diameter of inner tube - d ₀ diameter of outer heated tube - D depth of cavity along vertical wall, 0, 25, and 50 mm - g gravitational acceleration - H length of heated or un-heated wall, 100 mm - L length of thermosyphon, 500 mm for two-, 700 mm for three-, and 1100 mm for five-dotted heat sources - Nu _B Nusselt number based on B as reference length - Nu _x Nusselt number, defined in Eq. (1) - Pr Prandtl number, defined in Eq. (3) - q heat flux from heated wall - r equivalent heat-transfer radius - Ra _B Rayleigh number based on B as reference length - Ra _x Rayleigh number, defined in Eq. (2) - T _e temperature of entrance-fluid - T _w temperature of heated wall - T temperature difference between heated wall and entrance-fluid,T _w -T _e - W clearance for main fluid-flow - x reference length - X distance from bottom of thermosyphon Greek symbols coefficient of volumetric expansion - thermal diffusivity - thermal conductivity - kinematic viscosity