Natural convection heat transfer in a uniformly heated horizontal pipe

Natural convection heat transfers inside horizontal pipes were measured. The Rayleigh numbers were varied from 6.8 × 10⁸ to 1.5 × 10¹², while the Prandtl number was fixed at 2,094. Based on the analogy concept, a copper sulfate electroplating system was adopted to measure mass transfer rates in place of heat transfer rates. Test results using single-piece electrodes were in good agreement with the work of Sarac and Korkut. The angle-dependent mass transfer rates, measured using piecewise electrodes, were compared with the results of studies on natural convection in concentric annuli, and showed similar trends. The experiments were expanded to the turbulent region, and a transition criterion was proposed. Angle-dependent natural convection heat transfer correlations for the laminar and turbulent regions were derived.     

Natural convection heat transfer from a horizontal ice cylinder

Heat transfer characteristics passing through the maximum density point around a horizontal ice cylinder immersed in water was studied both theoretically and experimentally. For the sake of a precise comparison, the stagnation point Nusselt number was measured and results then compared with those of the numerical computations that were obtained by solving the full Navier-Stokes equations. A fairly good agreement was seen between the theory and the experiment.At about 6°C of water temperature where the stagnation Nusselt number takes its minimum value, the instability of the flow was observed. It was found that two different computer solutions exist, which shows unstable aspects corresponding to the experimental result.     

The onset of natural convection in a horizontal air layer heated from below

In this work, the beginning of the instability (onset of convection) of an air layer of infinite width and depth heated from underneath with a constant heat flux is studied. In the theoretical part, the instability is studied using the quasi-static assumption. The functional relationship of Rayleigh number vs. horizontal wave number of the disturbance is obtained in a digital computer using Green's Fonctions for the case of Prandtl number equal to one. Furthermore in order to make a comparison with similar investigations, limiting cases of infinite and very small Prandtl numbers are also taken into consideration.-In the experimental part, Rayleigh numbers corresponding to the onset of manifest convection based on visual observations are investigated by optical methods under various heat fluxes. The average value measured is found to be 145.     

Laminar free convection heat transfer from a horizontal ring

The analytical solution of laminar free convective heat transfer in an unlimited space from an isothermal horizontal ring with an adiabatic plug is presented. The results of theoretical considerations are presented as relation of the Nusselt and Rayleigh numbers: $$Nu_D = 1.151 \cdot (Ra_D )^{1/5} \cdot \Phi (\phi _0 )$$ \] where Φ(φ₀) is a function of shape coefficient of the ring (φ₀=d/D). The solution presented has been verified experimentally with rings of constant external diameter (D=0.06 [m]) and various internal diameters (d=0, 0.01, 0.02, 0.04 and 0.05 [m]). The fluid tested was glycerin. The theoretical predictions agree well with the experimental results.     

Free convection heat transfer around a horizontal ice cylinder formed through melting within an immiscible liquid

An experimental study has been performed to determine the melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid. Vegetable oil, which was contained within a horizontal heated copper tube, was adopted as a testing liquid. A bubble-free ice cylinder was situated at the center of the tube. The experiments were carried out for the heated tube temperatures ranging from 8.0 to 30.0 °C, while for the cooled tube temperatures from ч.0 to ⪡.0 °C. The flow pattern of the liquid and the ice-liquid interface shape of the ice cylinder being formed through melting were extensively observed and recorded photographically. The local/average heat transfer coefficient along the ice cylinder at steady state was determined as a function of the heated tube temperature as well as the cooled tube temperature. The measurements show that the ice layer profiles at steady state are quite similar irrespective of the thermal conditions. Zusammenfassung Die Experimentelle Untersuchung hatte zum Ziel, den Wärmeübergangsmechanismus beim Schmelzen eines horizontalen, in eine nichtmischbare Flüssigkeit eingetauchten Eiszylinders aufzuklären. In einem horizontalen, beheizten Kupferrohr befindliches Pflanzenöl diente als Versuchsflüssigkeit. Ein blasenfreier Eiszylinder befand sich in der Mitte des Rohres. Bei den Experimenten variierten die Temperaturen des Heizrohres zwischen 8.0 und 30.0 °C, die des gekühlten Innenrohres zwischen ч.0 und ⪡.0 °C. Das Strömungsmuster der Flüssigkeit und die sich während des Schmelzvorganges ausbildende Form der Eis-Flüssigkeitsgrenze am Eiszylinder wurden genauestens beobachtet und photographisch festgehalten. Der Lokale, den Eiszylinder entlang gemittelte Wärmeübergangskoeffizient wurde für den Stationärfall als Funktion der Heiz- und Kühlrohrtemperaturen bestimmt. Die Messungen zeigen, daß die Eisschichtprofile im Stationärfall - unabhängig von den thermischen Bedingungen - weitgehend ähnlich sind.     

Melting heat transfer along a horizontal heated tube immersed in a fluidized liquid ice bed

An experimental study was performed to determine the melting heat transfer characteristics along a horizontal heated circular tube immersed in a solid-air-liquid three-phase fluidized liquid ice bed. A mixture of fine ice particles and ethylene glycol acqueous solution was adopted as the liquid ice for the test. Measurements were carried out for a range of parameters such as airflow rate, heated tube diameter, and initial concentration of acqueous binary solution. It was found that the heat transfer coefficient for the fluidized liquid ice bed might be more than 20 times as large as that for the fixed liquid ice bed.     

Experimental investigation of free convection above a heated horizontal wire

Results are presented of an experimental investigation of the convective plume above a fine horizontal wire, heated by a constant current in air and in water. The temperature distribution in the plume was investigated using the IAB-451 shadow instrument in the diffraction interferometry method. The experimental results are in good agreement with laminar convection theories above a linear heat source. In the air, a comparison was made with the experimental results of other authors.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhicheskoi Fiziki, Vol. 11, No. 2, pp. 169–173, March–April, 1970.The author wishes to express his indebtedness to V. D. Zimin and N. V. Eyzhanov for their assistance with numerical solutions of Eqs. (1.3).     

Forced convection heat transfer on a heated bottom surface of cavity with different wall-height

Experiments to obtain the heat transfer characteristics of cavity, in which the downstream wall-heightD ₂ was changed from zero toD ₁ of upstream wall-height, have been performed. The vortex flow inside cavity was varied complicatedly depending on aspect-ratio of cavity and main flow velocity, and the flow pattern for cavity ofD ₂/D ₁=0.8 was altered entirely at theRe _H of about 1.5×10⁴. Three heat transfer regions ofNu _m versusRe _H were recognized for the cavity of large aspect-ratio. A close relation between those heat transfer behavior and approaching boundary layer flow was found. Heat transfer correlation was partially obtained for every cavities.     

The effect of corona discharge on free convection heat transfer from a horizontal cylinder

Free convection heat transfer from an isothermal horizontal cylinder in the presence of DC positive corona discharge with a blade edge emitter electrode has been studied experimentally and numerically. A Mach–Zehnder interferometer was used to determine the local Nusselt numbers. The effect of corona discharge on heat transfer from the cylinder was investigated at Rayleigh numbers in the range between 1500 and 5000. To find the details of the flow patterns and to further verify the experimental results, numerical simulations were also performed. It was found that the numerical results are in good agreement with experimental data. By increasing the applied voltage up to 15.5 kV, the corona discharge generates a recirculation zone around the blade and below the lower stagnation point of the cylinder. The effect of the recirculation zone becomes stronger near the breakdown voltage (17 kV) and it is responsible for a local decrease in the cooling of the cylinder around the lower stagnation point. The results indicate that corona discharge has a significant effect on the average Nusselt number at lower Rayleigh numbers whereas it has smaller effect at higher Rayleigh numbers.     

Effect of surface tension on the onset of convection in a layer of liquid with a free surface

The problem of stability of a plane horizontal layer of liquid heated from below is considered with surface tension at the upper surface taken into account. The problem is stated in section 1, proof of the existence of stability threshold is given in section 2, while section 3 concerns the construction of neutral curves by numerical methods and with the stabilizing effect of surface tension on the state of equilibrium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 89–92, May–June, 1969.     

Computation of conjugate natural convection heat transfer from a rectangular fin on a partially heated horizontal base

In this study, a numerical investigation has been carried out to reveal the mechanism of fluid flow and heat transfer from a vertical rectangular fin attached to a partially heated horizontal base. The problem is a conjugate conduction-convection heat transfer problem with open boundaries. The governing equations for the problem are the conservation of mass, momentum and energy equations for the fluid and the heat conduction equation for the fin. The control volume technique based on the SIMPLEC algorithm with a nonstaggerred grid arrangement is employed to solve the governing equations. The effect of the heated base, on the mechanism of the fluid flow and heat transfer, is numerically investigated. Temperature distribution and flow patterns around the fin are plotted to support the discussion. Results are obtained for air at laminar and steady flow. Received on 15 May 1997     

Free convection heat transfer from an isothermal wavy surface in a porous enclosure

The coupled streamfuction–temperature equations governing the Darcian flow and convection process in a fluid-saturated porous enclosure with an isothermal sinusoidal bottom sun face, has been numerically analyzed using a finite element method (FEM). No restrictions have been imposed on the geometrical non-linearity arising from the parameters like wave amplitude (a), number of waves per unit length (N), wave phase (Φ), aspect ratio (A) and also on the flow driving parameter Rayleigh number (Ra). The numerical simulations for varying values of Ra bring about interesting flow features, like the transformation of a unicellular flow to a multicellular flow. Both with increasing amplitude and increasing number of waves per unit length, owing to the shift in the separation and reattachment points, a row–column pattern of multicellular flow transforms to a simple row of multicellular flow. A cycle of n celluar and n+1 cellular flows, with the flow in adjacent cells in the opposite direction, periodically manifest with phase varying between 0 and 360°. The global heat transfer into the system has been found to decrease with increasing amplitude and increasing number of waves per unit length. Only marginal changes in the global heat flux are observed, either with increasing Ra or varying Φ. Effectively, sinusoidal bottom surface undulations of the isothermal wall of a porous enclosure reduces the heat transfer into the system. © 1998 John Wiley & Sons, Ltd.     

Experimental analysis of unsteady free convection heat transfer from horizontal fin arrays

Experimental work has been carried out on horizontal fin arrays using the differential interferometric technique. The local variations of heat flux and temperature in the central fin of a three fin array have been studied in the transient heating and cooling regimes. The average values of heat transfer coefficients in the transient state have been calculated for three spacings of 10 mm, 15 mm and 25 mm and with two materials namely aluminum and mild steel under constant heat input to the system. The results have been compared with experimental findings in the cases of a single fin attached to a base and a vertical isothermal flat plate. Attempt has been made to explain the differences between these cases in relation to the physical mechanism of heat and fluid flow about a fin array.

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Eine experimentelle Untersuchung der Wärmeübertragung bei instationärer freier Konvektion an horizontalen Rippenanordnungen

Zusammenfassung Unter Anwendung der Differential-Interferometrie-Technik wurde eine experimentelle Arbeit auf dem Gebiet horizontaler Anordnungen von Kühlrippen durchgeführt. Die lokale Veränderung von Wärmestrom und Temperatur der mittleren Rippe einer Dreieranordnung wurde an transienten Heiz- und Kühlbereichen untersucht. Im transienten Zustand wurden die Durchschnittswerte der Wärmeübertragungskoeffizienten bei konstanter Wärmezuführ in das System für Aluminium und Flußstahl bei Zwischenräumen von 10 mm, 15 mm und 20 mm berechnet. Die Berechnungen wurden mit experimentellen Ergebnissen einer einzigen, auf einer Basis befestigten Rippe und einer vertikalen isothermen flachen Platte verglichen. Es wurde der Versuch gemacht, den Unterschied zwischen diesen Fällen, in bezug auf den physikalischen Mechanismus der Wärmeübertragung und Strömung über eine Rippenanordnung, zu erklären.

     

Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium

In this article nonsimilarity solution for mixed convection from a horizontal surface in a saturated porous medium was obtained for the case of variable surface heat flux. The entire mixed convection regime, ranging from pure forced convection to pure free convection, is considered by introducing a single nonsimilarity parameter. Heat transfer results are predicted by employing four different flow models, namely, Darcy's law, the Ergun model, and the Brinkman-Forchheimer-extended Darcy model with constant and variable porosity. The variable porosity effect is approximated by an exponential function. Effects of transverse thermal dispersion are taken into consideration in the energy equation, along with variable stagnant thermal conductivities. The formulation of the present problem shows that the flow and heat transfer characteristics depend on five parameters, that is, the power in the variation of surface heat flux, the nonsimilarity mixed-convection parameter, the inertia effect parameter, the boundary effect parameter, and the ratio of thermal conductivity of the fluid phase to that of the solid phase. Numerical results for the local Nusselt number variations, based on the various flow models, are presented for the entire mixed convection regime. The impacts␣of different governing parameters on the heat transfer results are thoroughly investigated. Received on 7 August 1997     

The onset of convection in a horizontal nanofluid layer of finite depth

This paper presents a linear stability analysis for the onset of natural convection in a horizontal nanofluid layer. The employed model incorporates the effects of Brownian motion and thermophoresis. Both monotonic and oscillatory convection for free–free, rigid–rigid, and rigid–free boundaries are investigated. The oscillatory instability is possible when nanoparticles concentrate near the bottom of the layer, so that the density gradient caused by such a bottom-heavy nanoparticle distribution competes with the density variation caused by heating from the bottom. It is established that the instability is almost purely a phenomenon due to buoyancy coupled with the conservation of nanoparticles. It is independent of the contributions of Brownian motion and thermophoresis to the thermal energy equation. Rather, the Brownian motion and thermophoresis enter to produce their effects directly into the equation expressing the conservation of nanoparticles so that the temperature and the particle density are coupled in a particular way, and that results in the thermal and concentration buoyancy effects being coupled in the same way.     

Natural convection heat transfer through an enclosed horizontal layer of supercritical carbon dioxide

In natural convection heat transfer through a thin horizontal layer of carbon dioxide, maxima in the equivalent thermal conductivities are obtained in the vicinity of the respective pseudocritical temperatures at pressures of 75.8, 89.6 and 103.4 bar. The maxima are the more pronounced, the closer the critical point is approached.Comparison of experimental results with Nusselt equations shows good agreement except for the immediate vicinity of the pseudocritical temperature.In visual observations a distinct change in flow structure appears in the immediate vicinity of the pseudocritical temperature. A steady state polygon pattern and a boiling-like action could not be observed in this geometry.

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Zusammenfassung Beim Wärmetransport durch freie Konvektion in einer dünnen waagerechten Schicht von Kohlendioxid ergaben sich Maxima der scheinbaren Wärmeleitfähigkeit in der Nähe der pseudokritischen Temperaturen bei Drükken von 75,8, 89,6 und 103,4 bar. Die Maxima sind um so ausgeprägter, je mehr man sich dem kritischen Punkt nähert.Ein Vergleich der Versuchsergebnisse mit Nusseltbeziehungen ergibt gute Übereinstimmung außer in unmittelbarer Umgebung der pseudokritischen Temperatur. Direkte Beobachtungen der Konvektionsmuster zeigen in unmittelbarer Umgebung der pseudokritischen Temperatur eine deutliche Strukturänderung. Ein stationäres Zellmuster und siedeähnliche Vorgänge konnten in dieser Anordnung nicht beobachtet werden.

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Nomenclature A area of the heating or cooling plate - C constant in the correlation - g acceleration of gravity - h heat transfer coefficient - k thermal conductivity of fluid in the gap - k _e equivalent thermal conductivity - m, n exponents of dimensionless numbers - q heat flux - T _C,PC absolute temperature; critical C, pseudocritical PC - Gr Grashof numberg ( _h– _c) ³/ ² - Nu Nusselt numberh/k - Pr Prandtl number/ - thermal diffusivity - coefficient of volume expansion - width of gap - _c,h temperature of cooling (c)-, heating (h)-plate - _m arithmetic mean temperature ( _c+ _h)/2 - kinematic viscosity - _c,h fluid density at the temperature of the cooling (c)- or heating (h)-plate - heat flow rate through the gap     

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.     

An experimental investigation on performance of fins on a horizontal base in free convection heat transfer

 Natural convection heat transfer in rectangular fin-arrays mounted on a vertical base was investigated experimentally. An experimental set-up was constructed and calibrated to test 15 different fin configurations. Fin length and fin thickness were kept fixed at 100 and 3 mm respectively, while fin spacing was varied from 4.5 to 58.75 mm and fin height was varied from 5 to 25 mm. Base-to-ambient temperature difference was also varied through a calibrated wattmeter ranging from 10 to 50 W. The results showed that fin spacing is the most significant parameter in the performance of fin arrays; and for every fin height, for a given base-to-ambient temperature difference, there exists an optimum value for the fin spacing for which the heat transfer rate from the fin array is maximized. It was seen that higher heat transfer enhancement are obtained with vertically oriented bases than with horizontally oriented bases for fin arrays of the same geometry. Received on 16 February 2000