Natural convection heat transfer from round horizontal plate

A new approach to the model of natural convection from a horizontal, isothermal round plate and a simplified analytical solution of this model have been presented. In this model two separate regions with different fluid motions have been distinguished. In the first region, inside the boundary layer, the fluid flows concentrically towards the centre of the plate, while in the second one (stagnation region) the fluid is motionless. The presented theory has been verified experimentally.Ein neuer Lösungsweg für das Modell der freien Konvektion an einer isothermen, kreisförmigen, horizontalen Platte und eine vereinfachte analytische Lösung für dieses Modell werden hier vorgestellt. An diesem Modell wird zwischen zwei Bereichen mit verschiedenen Fluidbewegungen unterschieden. Im ersten Bereich, innerhalb der Grenzschicht, strömt das Fluid konzentrisch in Richtung Plattenmitte, während im zweiten Bereich (Stau-Bereich) die Flüssigkeit in Ruhe ist. Diese Theorie wurde experimentell überprüft.     

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.     

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.     

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.     

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.     

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.     

Mixed convection heat transfer from a horizontal channel with protruding heat sources

A numerical investigation is carried out to study fluid flow and heat transfer characteristics of conjugate mixed convection from a two dimensional horizontal channel with four protruding heat sources mounted on one of the finite thick channel walls. The flow is assumed as laminar, hydrodynamically and thermally developing. Water and FC70 are the fluids under consideration. The geometric parameters such as spacing between the channel walls (S), size of protruding heat sources (L_h×t_h), thickness of substrate (t) and spacing between heat sources (b) are fixed. Results are presented to show the effect of parameters such as Re_S, Gr_S^*, Pr, k_p/k_f and k_s/k_f on fluid flow and heat transfer characteristics. Using the method of asymptotic expansions, correlations are also presented for the maximum temperature of heat source.     

Analysis of buoyancy-aided convection heat transfer from a horizontal cylinder in a vertical duct at low Reynolds number

This paper reports a numerical study on buoyancy-aided steady convection heat transfer from a horizontal cylinder situated in a vertical adiabatic duct. Numerical results have been generated forH ₁/D=2.5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6, 20Re60, andRi up to 4. The placing of a horizontal cylinder in a vertical duct of smaller width results in significantly enhanced pure forced convection due to the blockage effect, but degrades appreciably the extent of buoyancy-aided enhancement in the heat transfer rate. Nevertheless, the presence of a vertical duct leads to an overall enhancement of mixed convection heat transfer coefficient relative to that without the confining duct. Moreover, the average Nusselt number is rather insensitive to the variation of either the position of the cylinder in the duct or the duct height in the investigated ranges of these geometric parameters.Dieser Artikel beschreibt eine numerische Studie über auftriebsunterstützte konvektive Wärmeübertragung von einem horizontalen Zylinder der in einem vertikalen adiabaten Kanal positioniert ist. Die numerischen Ergebnisse sind fürH ₁/D=2, 5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6 sowie 20Re60 undRi bis 4 berechnet worden. Die Anordnung des horizontalen Zylinders in einem schmaleren vertikalen Kanal führt auf Grund des Blockierungs-effektes zu einem deutlichen Anstieg der reinen Zwangskonvektion. Aber sie verschlechtert deutlich den Betrag der auftriebsbedingten Steigerung in der Wärmeübergangsrate. Trotzdem führt die Anwesenheit des vertikalen Kanals insgesamt zu einer Steigerung des Wärmeübergangskoeffizienten bei Mischkonvektion im Vergleich zur Abwesenheit des begrenzenden Kanals. Des weiteren ist die durchschnittliche Nusseltzahl von der Variation der Zylinderposition im Kanal oder der Kanalhöhe abhängig.     

Natural convection heat transfer from sinusoidal wavy surfaces

This paper presents the results of an experimental study of the natural convection heat transfer characteristics of sinusoidal wavy surfaces on vertical plates maintained at a constant temperature. Local heat transfer coefficients were obtained with a Mach-Zehnder interferometer. The heat transfer from the wavy surfaces, compared to a plane plate of equal projected area, increased with increasing amplitude-to-wavelength ratio. The heat transfer was increased by about 15 percent at an amplitude-to-wavelength ratio of 0.3; for this case a flow instability was detected. A quantitative comparison with a previously published numerical investigation is also presented. In general, there is agreement between the two studies.     

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     

Natural convection flow from an isothermal horizontal circular cylinder with temperature dependent viscosity

Free convection flow from an isothermal horizontal circular cylinder immersed in a fluid with viscosity proportional to an inverse linear function of temperature is studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity equations which are solved numerically by a very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity and viscosity profiles of the fluid as well as heat transfer characteristics, namely the local heat transfer rate and the local skin-friction coefficients for a wide range of viscosity parameter (= 0.0, 0.5, 1.0, 2.0, 3.0,4.0) and the Prandtl number Pr (= 1.0, 7.0, 10.0, 15.0, 20.0, 30.0).     

Condensation heat transfer in a rotating horizontal cylinder with a scraper

A dryer used in the drying process of paper production is usually a rotating horizontal cylinder in which steam condenses. This study concerns some experiments and analyses of condensate flow and heat transfer in a dryer with a scraper.

A laminar film model and a solid film model are introduced for the theoretical analyses. In the former the condensate flow is assumed to be laminar. In the latter the condensate film is assumed to adhere to the cylinder wall. In the analysis with the laminar film model, the film thickness diverges at relatively slow rotations. A criterion for the critical condition at which the divergence commences is proposed. From the solid film model, analytical expressions can be derived for the film thickness and the heat transmission coefficient through the condensate film and the cylinder wall.

The experiments are conducted with an acrylic resin cylinder and a stainless steel cylinder. The experimental result on heat transmission agrees with the analytical result for the solid film model if a condensate film about 25 μm thick remains in spite of scraping.     

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     

Radiation-conduction interaction on mixed convection from a horizontal circular cylinder

A mixed convection flow of an optically dense viscous incompressible fluid along a horizontal circular cylinder has been studied with the effect of radiation when the surface temperature is uniform. Using appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity form. Solutions of the governing equations are obtained employing the implicit finite difference method. Effects of varying the pertinent parameters, such as, the Planck number, R _w the surface temperature parameter, θ_w and the buoyancy parameter, α on the local skin-friction and local heat transfer coefficients are shown graphically as well as in tabular form against the curvature parameter ξ, while taking Prandtl number Pr = 1.0. It is found that an increase of R _d,θ_w or α leads to increases in the values of the local skin-friction and the local rate of heat transfer coefficients. At the stagnation point asymptotic solutions for large value of α are also obtained and the effect of the other pertinent parameters on the formation of the flow separation are studied. Received on 28 July 1998