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 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.     

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     

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     

Natural convection heat transfer along vertical rectangular ducts

Experimental investigations have been reported on steady state natural convection from the outer surface of vertical rectangular and square ducts in air. Seven ducts have been used; three of them have a rectangular cross section and the rest have square cross section. The ducts are heated using internal constant heat flux heating elements. The temperatures along the vertical surface and the peripheral directions of the duct wall are measured. Axial (perimeter averaged) heat transfer coefficients along the side of each duct are obtained for laminar and transition to turbulent regimes of natural convection heat transfer. Axial (perimeter averaged) Nusselt numbers are evaluated and correlated using the modified Rayleigh numbers for laminar and transition regime using the vertical axial distance as a characteristic length. Critical values of the modified Rayleigh numbers are obtained for transition to turbulent. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers and the area ratio for the laminar regimes. The local axial (perimeter averaged) heat transfer coefficients are observed to decrease in the laminar region and increase in the transition region. Laminar regimes are obtained at the lower half of the ducts and its chance to appear decreases as the heat flux increases.     

Oscillatory free convection heat transfer along a semi-infinite vertical plate

Summary The fluctuating free convection flow along a semi-infinite vertical plate is considered when the plate temperature is of the form T _p –T =(T ₀ –T ) where 0 < 1, denotes the frequency of oscillation and the mean temperature T ₀–T is proportional to ⁿ (0 n < 1). Flow and temperature fields have been obtained by means of two asymptotic expansions. For small values of the frequency parameter , a regular expansion is obtained while for large the method of matched asymptotic expansion is used. It is found that the skin friction and the rate of heat transfer obtained from two expansions overlap satisfactorily for a certain value of . For n=1 the flow governing equations to a semisimilar form, and have been solved by finite difference method. The results obtained from the series and the finite difference methods are in good agreement.

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Oszillierender Wärmeübergang an einer halbunendlichen senkrechten Platte bei freier Konvektion

Übersicht Betrachtet wird die fluktuierende freie Konvektionsströmung längs einer halbunendlichen senkrechten Platte, deren Temperatur dem Gesetz T _p –T =(T ₀–T ) [1+ sin {ie1-03}] folgt, wobei 0 < 1 gelte, {ie1-04} die Frequenz ist und der Temperatur-Mittelwert T ₀–T proportional zu ⁿ (0 n < 1) ist. Mit Hilfe zweier asymptotischer Entwicklungen werden die Strömungs- und Temperaturfelder gewonnen. Für kleine Werte des Frequenzparameters wird eine gewöhnliche Entwicklung benutzt, für große die Methode angepaßter asymptotischer Entwicklungen. Es stellt sich heraus, daß die Oberflächenreibung und die Wärmeübergangsrate aus zwei Entwicklungen für ein bestimmtes zufriedenstellend aufeinander fallen. Für n=1 werden die Grundgleichungen zueinander ähnlich und werden nach der Finite-Differenzen-Methode gelöst. Die Ergebnisse nach den Reihenentwicklungen und der Finite-Differenzen-Methode stimmen gut überein.

     

Natural convection heat transfer from a thin rectangular fin with a line source at the base — a finite difference solution

This paper presents an analysis of the problem of a thin fin of finite thermal conductivity, with an isothermal line source at the base, dissipating heat to the surrounding air by natural convection. The horizontal surface to which the fin is attached is adiabatic so that heat is dissipated only through the fin. The temperature and velocity distributions in the field, the temperature profile in the fin, local Nusselt numbers along the fin and the average heat transfer coefficient of the fin are obtained by solving the governing equations in the field and the heat transfer equation in the fin simultaneously, using an explicit unsteady Finite Difference formulation leading to the steady state result. Numerical experiments are performed to study the influence of parameters namely the fin height, temperature of the heating source and the fin material on the average heat transfer coefficient. Comparison is made with fins of infinite thermal conductivity and the vertical isothermal flat plate.     

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.

     

Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity

In order to understand the effect of the vertical heat transfer on thermocapillary convection characteristics in a differentially heated open shallow rectangular cavity, a series of two- and three-dimensional numerical simulations were carried out by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and the aspect ratio ranged from 12 to 30. Results show that thermocapillary convection is stable at a small Marangoni number. With the increase of the heat flux on the bottom surface, thermocapillary convection transits to the asymmetrical bi-cellular pattern with the opposite rotation direction. The roll near the hot wall shrinks as the Marangoni number increases. At a large Marangoni number, numerical simulations predict two types of the oscillatory thermocapillary flow. One is the hydrothermal wave, which is dominant only in a thin cavity. The other appears in a deeper cavity and is characterized by oscillating multi-cellular flow. The critical Marangoni number for the onset of the oscillatory flow increases first and then decreases with the increase of the vertical heat flux. The three-dimensional numerical simulation can predict the propagating direction of the hydrothermal wave. The velocity and temperature fields obtained by three-dimensional simulation in the meridian plane are very close to those obtained by two-dimensional simulation.     

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.     

Calculating mass transfer from vertical wet fabrics using a free convection heat transfer correlation

In this note, the evaporation rate from a vertical wet fabric sheet is calculated using a free convection heat transfer correlation. Chilton–Colburn analogy is used to derive a mass transfer correlation from a heat transfer correlation proposed by Churchill and Chu for free convection from a vertical isothermal plate. The mass transfer rate obtained from this expression has shown excellent agreement with experimental data.     

Three dimensional free convection flow and heat transfer along a porous vertical plate

The free convection flow along a vertical porous plate with transverse sinusoidal suction velocity distribution is investigated. Due to this type of suction velocity at the plate the flow becomes three dimensional one. For the asymptotic flow condition, the wall shear stress in the direction of main flow for different values of buoyancy parameter G is obtained. For G=0, the skin friction in the direction of free stream and the rate of heat transfer from the plate to the fluid are given. It is found that these results differ from those obtained by Gersten and Gross.     

A correlation for free convection heat transfer from vertical wavy surfaces

Free convection heat transfer along an isothermal vertical wavy surface was studied experimentally and numerically. A Mach-Zehnder Interferometer was used in the experiment to determine the local heat transfer coefficients. Experiments were done for three different amplitude–wavelength ratios of α = 0.05, 0.1, 0.2 and the Rayleigh numbers ranging from Ra _l = 2.9 × 10⁵ to 5.8 × 10⁵. A finite-volume based code was developed to verify the experimental study and obtain the results for all the amplitude–wavelength ratios between α = 0 to 0.2. It is found that the numerical results agree well with the experimental data. Results indicate that the frequency of the local heat transfer rate is the same as that of the wavy surface. The average heat transfer coefficient decreases as the amplitude–wavelength ratio increases and there is a significant difference between the average heat transfer coefficients of the surface with α = 0.2 and those surfaces with α = 0.05 and 0.1. The experimental data are correlated with a single equation which gives the local Nusselt number along the wavy surface as a function of the amplitude–wavelength ratio and the Rayleigh number.     

Experimental research on heat transfer of natural convection in vertical rectangular channels with large aspect ratio

This work presents the experimental research on the steady laminar natural convection heat transfer of air in three vertical thin rectangular channels with different gap clearance. The much higher ratio of width to gap clearance (60–24) and the ratio of length to gap clearance (800–320) make the rectangular channels similar with the coolant flow passage in plate type fuel reactors. The vertical rectangular channels were composed of two stainless steal plates and were heated by electrical heating rods. The wall temperatures were detected with the K-type thermocouples which were inserted into the blind holes drilled in the steal plates. Also the air temperatures at the inlet and outlet of the channel were detected. The wall heat fluxes added to the air flow were calculated by the Fourier heat conduction law. The heat transfer characteristics were analyzed, and the average Nusselt numbers in all the three channels could be well correlated with the Rayleigh number or the modified Rayleigh number in a uniform correlation. Furthermore, the maximum wall temperatures were investigated, which is a key parameter for the fuel’s integrity during some accidents. It was found that even the wall heat flux was up to 1500 W/m², the maximum wall temperature was lower than 350 °C. All this work is valuable for the plate type reactor’s design and safety analysis.     

Boundary effect on free convection flow in a porous medium at given heat transfer from a vertical surface

The system of momentum and energy conservation equations governing free convection flow near a vertical surface in a semi-infinite porous medium subject to the boundary conditions of the third kind is considered in the boundary layer approximation. Asymptotic expansions in the powers of the Darcy parameter Da are constructed. The dependence of flow parameters on the parameters Da and xGr is studied. Analytical solutions applicable throughout the entire flow region are constructed.     

Conjugate free convection of non-Newtonian fluids about a vertical cylindrical fin in porous media

Conjugate free convection along a vertical cylindrical fin in a non-Newtonian fluid-saturated porous medium has been investigated theoretically. The boundary layer equations based on the power lay model appropriate for the Darcy flows are solved numerically exploiting a very efficient finite difference method. Effects of the power-law index, conjugate convection-conduction parameter and the surface curvature parameter on the fin temperature distribution, local heat transfer-coefficient and local heat flux are studied and presented in graphical and tabular form.     

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 %.