Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

Experimental investigation of heat transfer and flow pattern from heated horizontal rectangular fin array under natural convection

This paper presents results of the experimental study conducted on heated horizontal rectangular fin array under natural convection. The temperature mapping and the prediction of the flow patterns over the fin array with variable fin spacing is carried out. Dimensionless fin spacing to height (S/H) ratio is varied from 0.05 to 0.3 and length to height ratio (L/H) = 5 is kept constant. The heater input to the fin array assembly is varied from 25 to 100 W. The single chimney flow pattern is observed from 8 to 12 mm fin spacing. The end flow is choked below 6 mm fin spacing. The single chimney flow pattern changes to sliding or end flow choking at 6 mm fin spacing. The average heat transfer coefficient (h_a) is very small (2.52–5.78 W/m² K) at 100 W for S = 5–12 mm. The h_a is very small (1.12–1.8 W/m² K) at 100 W for 2–4 mm fin spacing due to choked fin array end condition. The end flow is not sufficient to reach up to central portion of fin array and in the middle portion there is an unsteady down and up flow pattern resulting in sliding chimney. The central bottom portion of fin array channel does not contribute much in heat dissipation for S = 2–4 mm. The h_a has significantly improved at higher spacing as compared to lower spacing region. The single chimney flow pattern is preferred from heat transfer point of view. The optimum spacing is confirmed in the range of 8–10 mm. The average heat transfer results are compared with previous literature and showed similar trend and satisfactory agreement. An empirical equation has been proposed to correlate the average Nusselt number as a function of Grashof number and fin spacing to height ratio. The average error for this equation is ?0.32 %.     

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 investigation of combined forced and free convection in horizontal and inclined tubes

Summary This investigation considers the effects of free convection on the laminar flow of water through a circular duct having essentially constant wall heat transfer rate per unit length of the duct and circumferentially uniform wall temperature. The effect of the Reynolds and Rayleigh number variations on heat transfer results has been analysed for both horizontal and inclined pipe. The experiment has covered the range of the inlet Reynolds number from 200 to 2300, and of the Rayleigh number from 6,000 to 70,000. The effect of pipe inclination has been investigated for slope angle values up to 60°, with laminar ascending flow.

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Sommario L'indagine é volta alla determinazione sperimentale dei coefficienti di scambio termico in regime di convezione mista per acqua in moto laminare entro un condotto a sezione circolare. Allo scopo di consentire il confronto dei risultati con le previsioni teoriche, l'esperienza è stata condotta cercando di approssimare le condizioni al contorno di flusso termico uniforme lungo l'asse del tubo e di temperatura uniforme in senso circonferenziale. La dipendenza dei coefficienti di scambio termico dai numeri di Reynolds e di Rayleigh è stata analizzata sia per condotto orizzontale che inclinato. La sperimentazione ha coperto il campo di valori compreso tra 200 e 2300 del numero di Reynolds all'ingresso, e tra 6000 e 70000 del numero di Rayleigh. L'influenza dell'inclinazione sullo scambio termico è stata esaminata, per moto laminare ascendente, tra 0 e 60° sull'orizzontale.

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Research supported by C.N.R., grant no. 81.002.77.07.     

Turbulent thermal convection in wide horizontal fluid layers

Turbulence in thermal convection is investigated for flows in which the production of turbulence energy is due solely to buoyancy, and the statistics of the flow are homogeneous in horizontal planes. New experimental results for high Rayleigh number unsteady turbulent convection in a horizontal layer heated from below and insulated from above are presented and compared to turbulent Rayleigh convection, convection in the planetary boundary layer, and laboratory penetrative convection. Mean temperature fields are correlated in terms of wall layer scales and convection scales. Joint statistics of turbulent temperature and horizontal velocity and vertical velocity through fourth order are presented for the core region of the convection layer.This paper was presented at the Ninth Symposium on Turbulence, University of Missouri-Rolla, October 1–3, 1984     

Analytical and numerical study of natural convection heat transfer in an inclined composite enclosure

Laminar natural convection heat transfer in inclined fluid layers divided by a partition with finite thickness and conductivity is studied analytically and numerically. The governing equations for the fluid layers are solved analytically in the limit of a thin layered system with constant flux boundary conditions. The study covers of the range of Ra from 10³ to 10⁷, from 0° to 180° and the thermal conductivity ratio of partition to fluid ratioK from 10^–2 to 10⁶. The Prandtl number was 0.72 (for air). Results are obtained in terms of an overall Nusselt number as a function of Rayleigh number, angle of inclination of the system, mid layer thickness, and mid layer thermal conductivity. The critical Rayleigh number for the onset of convection in a bottom-heated horizontal system is predicted. The results are compared with the numerical results obtained by solving the complete system of governing equations, using SIMPLER method, as well as with the limiting cases in the literature.     

Characterization of fluid flow patterns and heat transfer in horizontal channel mixed convection

Two mechanisms of roll initiation are highlighted in a horizontal channel flow, uniformly heated from below, at constant heat flux (Γ = 10, Pr = 7, 50 ≤ Re ≤ 100, 0 ≤ Ra ≤ 10⁶). The first mechanism is the classical one, it occurs for low Rayleigh numbers and is initiated by the lateral wall effect. The second occurs for higher Rayleigh numbers and combines the previous effect with a supercritical vertical temperature gradient in the lower boundary layer, which simultaneously triggers pairs of rolls in the whole zone in between the two lateral rolls. We have found that in the present configuration, the transition between the two roll initiation mechanisms occurs for Ra/Re ² ≈ 18. Consequently, the heat transfer is significantly enhanced compared to the pure forced convection case owing to the flow pattern responsible of the continuous flooding the heated wall with cold fluid.     

最大偏心圆环空间自然对流传热的数值分析

采用正切圆坐标变换 ,对不同直径比以及上、下、侧面三种偏心位置 ,偏心率达到最大值± 1的变壁温水平圆柱环形封闭空间内空气的自然对流传热进行了数学模拟 ,求出的二维空间温度分布与实验拍摄相应的温度干涉条纹图片吻合良好。计算结果同时给出流线分布及内、外壁面的局部传热系数、热流量。并与现有的偏心率小于 1的有关资料作对比分析。数值计算的范围是 :2 .0× 1 0 2 ≤ Ra≤ 3 .0× 1 0 5,1 .3≤ Do/Di≤ 3 .8,Pr=0 .70 6,|ε|=1 .     

Laminar natural convection heat transfer from vertical plate to power-law fluid

Summary Approximate solutions for laminar natural convection heat transfer between a vertical plate and a power-law fluid with high Prandtl number were obtained using an integral method for cases with various types of boundary conditions. The results were found in good agreement with available experimental evidence.Nomenclature a exponent defined by equations (28) and (29) - A, B, C, D, E constants defined by equations (15) to (19) - C ₁, C ₂, M ₁, M ₂ coefficients for Nusselt number expression defined by (32b), (33b) - f temperature difference, equal to T _s–T - f ⁺ dimensionless temperature difference - g gravitational acceleration - Gr Grashof number defined by (25), (50) and (66), respectively - H heat flux at plate surface - h _x local heat transfer coefficient - K consistency index for Power-law fluid - k thermal conductivity of fluid - K ₁, K ₂ constants defined by (50) and (51) - L height of plate - n flow behavior index for Power-law fluid - P a quantity defined by (54a) - T temperature - T _s plate temperature - T temperature of the bulk of fluid - s constant given by (35) - u velocity component along x-direction - u _x maximum velocity induced by natural convection current, (10) - v velocity component along y-direction - x distance measured along direction parallel to that of gravitational force - x ⁺ dimensionless quantity, defined as x/L - y distance measured away from plate - Nu _x local Nusselt number - Nu _av average Nusselt number - Pr Prandtl number defined by (24) - T temperature difference according to boundary conditions - thermal diffusivity of fluid - coefficient of thermal expression of fluid - boundary layer thickness - ⁺ dimensionless boundary layer thickness - dimensionless velocity profile - dimensionless variable, defined as y/ - dimensionless temperature difference     

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.

     

Experimental study of steady and transient natural convection heat transfer of mercury

An experimental investigation of transient and steady-state natural convection in a narrow vertical rectangular channel following a step-change in uniform wall-heat-flux is presented. The construction and instrumentation for two test sections are described. These test sections formed a rectangular channel 15.2×2.54×25.4 cm and consisted of: 1) both 15.2×25.4 cm faces heated uniformly by constant radiant heat flux with mercury as the fluid, and 2) the same boundary conditions as 1 but lead was used to thermally model the mercury. Initially the fluid was stagnant and at a uniform temperature. The transient was initiated by suddenly increasing the wall-heat-flux from zero to some constant, preselected value using radiant heating. Temperature-time histories were measured during the transient and steady-state regimes at several locations on the wall and in the fluid. Transient and steady-state heat transfer results are reported. The results show that when the wall-heat-flux on both faces is sufficiently large, the primary mechanism for energy transport in the fluid is molecular conduction. For lower values of imposed heat flux, natural convection, as well as conduction, contributed to the energy transfer.     

Prandtl number effects on natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli

The influence of various Prandtl numbers on the laminar convection flow between concentric and vertically eccentric cylinders is studied numerically. To overcome the difficulties associated with the complex physical domains a numerical transformation method is used to map this region on a rectangle. Although two independent computer programs which are based on different formulations of the governing equations were used, nearly identical results were obtained. Local heat transfer results are presented for a wide range of Rayleigh numbers for the first time. Local heat transfer rates are found to depend on the Prandtl number in addition to the Rayleigh number dependence.     

Experimental investigation of natural convection heat transfer between two oblate concentric and eccentric hemi-spheroids with different elliptical ratios

In this paper, natural convection between a pair of oblate hemi-spheroids with different elliptical ratios was depicted experimentally. The experimental tests study the effects of the orientation modes (horizontal, inclined, vertical, inclined revolved and vertical revolved) as well as the vertical eccentricity on the natural convection between each pair. Correlations among Nusselt number, Rayleigh number, elliptical ratio and eccentricity were deduced. A notable increase in the natural convection could be satisfied through the gaps among successive layers of hemi-spheroids having higher elliptical ratio rather than hemi-spherical ones. The positive vertical eccentricity shows remarked increase in natural convection rather than both concentric and negative eccentric cases. Also, the inclination of the minor axis of hemi-spheroids while keeping the major axis parallel to the horizontal plane produces a stronger upward plume rather than different inclination modes.     

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.     

Experimental and numerical study on unsteady natural convection heat transfer in helically coiled tube heat exchangers

Both of experimental and numerical investigations were performed to understand unsteady natural convection from outer surface of helical coils. Four helical coils with two different curvature ratios were used. Each coil was mounted in the shell both vertically and horizontally. The cold water was entered the coil and the hot water in the shell was cooling by unsteady natural convection. A CFD code was developed to simulate natural convection heat transfer. Equations of tube and shell are solved simultaneously. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It was revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, specific heat of fluids and geometrical parameters including length, inner diameter of the tube and the volume of the shell, and time.     

Thermal convection heat transfer of air/water layers enclosed in horizontal annuli with mixed boundary conditions

This paper presents a numerical study for thermal convection of air/water layers enclosed in a horizontal concentric/eccentric cylindrical annulus with the inner wall subjected to a constant heat flux and an isothermal condition at the outer wall. Results are generated for an annulus of radius ratio of 2.6 with three different vertically eccentric positions of the inner cylinder, the modified Rayleigh number up to 10⁷, and the modified Marangoni number varying from 0.0 to 10⁴. The heat transfer characteristics and fluid flow patterns driven by buoyancy and/or thermocapillary effects in air/water-filled annulus are illustrated by means of contour maps of healtline and streamline respectively. Under the mixed thermal boundary conditions considered, significant heat exchange across the air-water interface is found and appears to be unaffected by the thermocapillary convection.Es wird eine numerische Untersuchung der thermischen Konvektion von Luft/Wasser-Schichten, die von horizontalen konzentrischen/exzentrischen zylindrischen Ringkanälen umschlossen sind, deren innere Wand einer konstanten Wärmestromdichte und deren äußere Wand isothermen Bedingungen ausgesetzt sind, dargestellt. Ergebnisse werden für einen Ringkanal mit einem Radiusverhältnis von 2,6 mit drei verschiedenen senkrechten exzentrischen Positionen des inneren Zylinders, für die modifizierte Rayleigh-Zahl bis 10⁷ und für die modifizierte Marangoni-Zahl zwischen 0,0 und 10⁴ erhalten. Die Charakteristiken der Wärmeübertragung und des Fluid-Stromlinienbildes, hervorgerufen durch Auftriebskräfte und/oder thermokapillare Effekte in mit Luft/Wasser gefüllten Ringkanälen wurden mittels Schichtlinienplänen der Isothermen und der Stromlinien dargestellt. Bei den untersuchten gemischten thermischen Randbedingungen wurde ein signifikanter Wärmeaustausch über der Luft/Wasser-Grenzfläche gefunden, der scheinbar nicht durch die thermokapillare Konvektion gestört wird.