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     

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 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 natural convection heat transfer in horizontal and inclined annular fluid layers

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

Measurements of heat dissipation from miniaturized vertical rectangular fin arrays under dominant natural convection conditions

Experiments have been conducted to investigate the effects of miniaturizing the base plate dimensions of vertically based straight rectangular fin arrays on the steady-state heat-dissipation performance under dominant natural convection conditions. The miniaturization process was initiated from a square-based array of 49×49 mm² (maximum base area) and terminated at a square-based array of 25×25 mm² (minimum base area) with rectangular-based arrays of varying intermediate areas in between. Two inter-fin separation distances of 3 and 11 mm were used. The effect of base plate orientation on the heat-dissipation performance was studied through comparison of present results with those of an earlier work, in which the arrays were miniaturized with the base horizontally oriented. A correlation for miniaturized vertically based straight rectangular fin arrays, which employed the fin length as the prime geometric parameter, has been presented on the basis of the experimental conditions of this investigation.     

Analysis of natural convection melting inside isothermally heated horizontal rectangular capsule

Melting characteristics of phase change material by natural convection heat transfer inside horizontal rectangular capsules are examined experimentally. The capsules are heated isothermally and three kinds of aspect ratios (qH/W=3, 1 and 1/3) are provided. Octadecane and ice are used, respectively, as the phase change material. A method of analysis applying the empirical correlations for natural convection heat transfer in a vertical or horizontal enclosure to the melting in the rectangular capsules is presented. The predicted results show good agreement with the experimental data. For the melting of octadecane and ice, it is found that the effect of aspect ratio on the melting process is not significant for the range ofB=1/3 to 3.     

MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure

This study looks at MHD natural convection flow and heat transfer in a laterally heated enclosure with an off-centred partition. Governing equations in the form of vorticity–stream function formulation are solved using the polynomial differential quadrature (PDQ) method. Numerical results are obtained for various values of the partition location, Rayleigh, Prandtl and Hartmann numbers. The results indicate that magnetic field significantly suppresses flow, and thus heat transfer, especially for high Rayleigh number values. The results also show that the x-directional magnetic field is more effective in damping convection than the y-directional magnetic field, and the average heat transfer rate decreases with an increase in the distance of the partition from the hot wall. The average heat transfer rate decreases up to 80% if the partition is placed at the midpoint and an x-directional magnetic field is applied. The results also show that flow and heat transfer have little dependence on the Prandtl number.     

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.     

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).     

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 studies on steady free convection heat transfer from fins and fin arrays

This paper deals with an experimental study of free convective heat transfer from fins and fin arrays attached to a heated horizontal base. The technique of differential interferometry has been utilised and experiments have been carried out under steady state conditions. Local values of heat flux, temperature, heat transfer coefficients, local and overall Nusselt numbers have been estimated. An attempt has been made to discuss in detail the flow and heat transfer mechanisms for three cases namely an isothermal vertical flat plate, a single fin attached to a heated horizontal base and a fin array in the light of the experimental findings. Correlations are presented relating the overall Nusselt number with the relevant non-dimensional parameters in these cases.Diese Abhandlung beschäftigt sich mit einer experimentellen Studie über freie konvektive Wärmeübertragung von Rippen und Rippenfeldern, die an eine erwärmte horizontale Grundfläche angebracht sind. Es wurde die Technik der differentiellen Interferometrie verwendet. Die Versuche sind unter konstanten Zustandsbedingungen ausgeführt worden. Lokale Werte des Wärmestroms, der Temperatur, des Wärmeübertragungskoeffizienten sowie lokale und mittlere Nusseltzahlen sind bestimmt worden. Der Strömungs- und Wärmeübertragungsmechanismus wurde an drei Fällen detailliert untersucht: nämlich eine isotherme vertikale ebene Platte; eine einzelne Rippe, angebracht an einer beheizten horizontalen Grundfläche und ein dem Strahlengang entsprechend angeordnetes Rippenfeld. Für diese drei Fälle werden die Berechnungen der mittleren Nusseltzahl in Abhängigkeit der relevanten dimensionslosen Parameter dargestellt.     

Experimental and numerical investigation of transition to turbulent flow and heat transfer inside a horizontal smooth rectangular duct under uniform bottom surface temperature

In this study, steady-state turbulent forced flow and heat transfer in a horizontal smooth rectangular duct both experimentally and numerically investigated. The study was carried out in the transition to turbulence region where Reynolds numbers range from 2,323 to 9,899. Flow is hydrodynamically and thermally developing (simultaneously developing flow) under uniform bottom surface temperature condition. A commercial CFD program Ansys Fluent 12.1 with different turbulent models was used to carry out the numerical study. Based on the present experimental data and three-dimensional numerical solutions, new engineering correlations were presented for the heat transfer and friction coefficients in the form of $ {\text{Nu}} = {\text{C}}_{2} {\text{Re}}^{{{\text{n}}_{ 1} }} $ and $ {\text{f}} = {\text{C}}_{3} {\text{Re}}^{{{\text{n}}_{3} }} $ , respectively. The results have shown that as the Reynolds number increases heat transfer coefficient increases but Darcy friction factor decreases. It is seen that there is a good agreement between the present experimental and numerical results. Examination of heat and mass transfer in rectangular cross-sectioned duct for different duct aspect ratio (α) was also carried out in this study. Average Nusselt number and average Darcy friction factor were expressed with graphics and correlations for different duct aspect ratios.     

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.     

Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above

A two-dimensional numerical simulation of natural convection in a rectangular enclosure heated from below and cooled from above has been conducted with non-Newtonian phase-change-material (PCM) microcapsulate slurry with latent heat capacities. The formulation of the mathematical model in dimensionless co-ordinates and discretization of the governing equations have been done using the finite volume method. Both natural convection and heat transfer characteristics are discussed about natural convection with PCM microcapsulate slurry, which exhibits the pseudoplastic non-Newtonian fluid behavior and a peak value in the specific heat capacity with latent heat. The viscosity of the present PCM microcapsulate slurry is assumed to follow the Ostwald-de Waele power law fluid model with the power-law index n and the consistency coefficient K. The effects of phase-change material, the mass concentration, and the aspect ratio Ar on the natural convection heat transfer are described, respectively. By comparing with the results of microcapsule slurry without phase change, the enhancement in heat transfer is found in microcapsule slurry with phase change during the phase change temperature range. Numerical simulations are performed in the following parametric ranges: the width–height aspect ratio of the enclosure Ar from 2 to 20, the mass concentrations C _m of the slurry from 10 to 40%, power law index n of the slurry from 0.89 to 1.0 and Rayleigh numbers Ra ranges from 10³ to 10⁷.     

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

This paper reports an experimental study of free convection heat transfer from rectangular fin-arrays on a horizontal base. An experimental set-up was constructed and calibrated, 15 sets of fin-arrays and a base plate without fins were tested in atmosphere. Fin height was varied from 6 mm to 26 mm, fin spacing was varied from 6.2 mm to 83 mm. The base-to-ambient temperature difference was also varied independently and systematically with the power supply to heater ranging from 8 W to 50 W. Fin length and fin thicknesses were fixed at 100 mm and 3 mm, respectively. The experimental program was conducted so as to clearly delineate the separate roles of fin height, fin spacing and base-to-ambient temperature difference. It was found that for a given base-to-ambient temperature difference the convection heat transfer rate from fin-arrays takes on a maximum value as a function of fin spacing and fin height. For a given base-to-ambient temperature difference the enhancement of the convection heat transfer rate of fin-arrays relative to that for base plate without fins is strongly dependent on the fin spacing to fin height ratio and number of fins. A correlation was also presented relating the convection heat transfer rate of fin-arrays relative to that for base plate without fins with the relevant non-dimensional parameters. Received on 7 August 1997     

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

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

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

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

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

Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.