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.     

Mixed convection and conduction heat transfer in open cavities

A numerical study has been carried out on mixed convection and conduction in open cavities. The study covers the Rayleigh number from 10 to 10⁶, the Reynolds number from 1 to 10³ andk _r =k _w /k _a from 1 to 100 forPr=0.72 (air) and cavity aspect ratioB from 0.8 to 1.3. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. The controlvolume approach is used for solving the governing equations of conjugate heat transfer involving conduction in the walls. Streamlines and isotherms in the system are produced and the results are represented in terms of the Nusselt number as function of other parameters. Correlations are derived to calculate heat transfer through the cavity openings.     

A boundary value problem in extended thermodynamics - one-dimensional steady flows with heat conduction

Abstract. One-dimensional steady flows with heat conduction, treated by the 13-moment theory of extended thermodynamics are considered. The usual well-posed boundary conditions for the corresponding problems in the Navier-Stokes-Fourier (NSF) theory are insufficient to give unique solutions. In order to have unique physically sensible solutions, minimization of the deviation of iterative approximations from the exact solutions, proposed in [1], is used as a criterion. Moreover, the solutions are shown to be invariant with respect to change of consistent boundary conditions - a requirement abide by our physical intuition. In the problems of plane shearing flow and Couette flow, the minimization with respect to two uncontrollable parameters is involved. The examples are carried out numerically, and the results are compared with the classical results of NSF theory.Received: 16 August 2002, Accepted: 20 April 2003, Published online: 5 December 2003PACS: 83.20.Lr, 83.50.Ax Correspondence to: I-S. Liu Dedicated to Professor Ingo Müller on the occasion of his 65th birthday     

Laminar forced convection conjugate heat transfer over a flat plate

Coupled heat transfer between laminar forced convection along and conduction inside a flat plate wall is theoretically studied. The laminar convective boundary layer is analyzed by employing the integral technique. The energy equations for the fluid and the plate wall are combined under the condition of the continuity in the temperature and heat flux at the fluid-solid interface. The analysis results in a simple formal solution. Expressions have been obtained for calculating local Nusselt number, wall heat flux and temperature along the plate, all are functions of the local Brun number, Br _x , which is a measure of the ratio of the thermal resistance of the plate to that of the convective boundary layer. The results indicate that for Br _x ≥0.15, neglecting the plate resistance will results in an error of more than 5% in Nusselt number. Comparison of the present solution with other previous studies has been made. The solution may be of a considerable theoretical and practical interest. Received on 19 August 1998     

A simultaneous PIV and heat transfer study of bubble interaction with free convection flow

Whole field velocity and point temperature and surface heat flux measurements were performed to characterise the interaction of a single rising ellipsoidal air bubble with the free convection flow from a heated flat surface immersed in water at different angles of inclination. Two thermocouples and a hot film sensor were used to characterise heat transfer from the surface, while a time-resolved digital particle image velocimetry technique was used to map the bubble induced flow in a plane parallel to the surface. Heat flux fluctuations, preceding and following the bubble passage, were shown to correlate with the variation in both local flow velocities and fluid temperatures. The largest increases in heat transfer were recorded when both flow and temperature effects combined to enhance the convective cooling simultaneously. Such conditions were shown to be most likely met when the block was inclined at 45°, thus forcing the bubble to slide closer to the heated surface and hence to the thermal boundary layer.     

The steady state Stefan problem with convection

For steady-state Stefan problems with convection in the fluid phase governed by either the Stokes equations or the Navier Stokes equations, and with adherence of the fluid on all boundaries, the existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation together with application of various compactness arguments.This research was supported in part by the National Science Foundation and the Consiglio Nazionale delle Ricerche.     

共轭梯度法求解非线性多宗量稳态传热反问题

应用共轭梯度法求解非线性多宗量稳态热传导反问题。采用八节点的等参单元在空间上进行离散,建立了便于敏度分析的非线性正演和反演的有限元模型,可直接求导进行敏度分析。给出了相关的数值验证,对测量误差及测点数目的影响作了初步探讨,结果表明,采用的算法能够对非线性稳态热传导中导热系数和边界条件联合反问题进行有效的求解,并具有较高精度。     

Natural convection and conduction heat transfer in open shallow cavities with bounding walls

A numerical study has been carried out on inclined open shallow cavities, which are formed by a wall and horizontal fins. Constant heat flux is applied on the surface of the wall inside the cavity while its other surface was kept isothermal. The wall and the fins are conductive. Conjugate heat transfer by natural convection and conduction is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁶ to 10¹², conductivity ratio from 1 to 60, open cavity aspect ratio from 1 to 0.125, dimensionless end wall thickness from 0.05 to 0.20, horizontal walls from 0.01 to 0.15 and inclination of the end wall from 90° to 45°. It is found that the volume flow rate and Nusselt number are a decreasing function of the cavity aspect ratio, horizontal fin thickness and conductivity ratio. They are an increasing function of end wall thickness and inclination angle, except in the latter case optima exist at high Rayleigh numbers.     

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 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.     

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.     

A new approach to the analysis of turbulent free convection heat transfer

The principle of surface renewal is utilized in the analysis of fully turbulent free convection. The present analysis together with a previous surface renewal ased analysis of combined forced and free convection associated with supercritical fluids demonstrate the potential usefulness of the surface renewal approach in modelling buoyancy influenced turbulent convection processes.     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

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.

     

A new algorithm of global tightly-coupled transient heat transfer based on quasi-steady flow to the conjugate heat transfer problem

Concerning the specific demand on solving the long-term conjugate heat transfer(CHT) problem,a new algorithm of the global tightly-coupled transient heat transfer based on the quasi-steady flow field is further put forward.Compared to the traditional loosely-coupled algorithm,the computational efficiency is further improved with the greatly reduced update frequency of the flow field,and moreover the update step of the flow field can be reasonably determined by using the engineering empirical formula of the Nusselt number based on the changes of the inlet and outlet boundary conditions.Taking a duct heated by inner forced air flow heating process as an example,the comparing results to the tightly-coupled transient calculation by Fluent software shows that the new algorithm can significantly improve the computational efficiency with a reasonable accuracy on the transient temperature distribution,such as the computing time is reduced to 22.8% and 40% while the duct wall temperature deviation are 7% and 5% respectively using two flow update time step of 100 s and 50 s on the variable inlet-flow rate conditions.     

Influence of free convection on the heat transfer from hot-wire probes

The present paper is concerned with the experimental determination of the influence of free convection on the heat transfer from horizontal hot-wire probes in cross flow. Free convective flow can be minimized under microgravity conditions and its quantity can be determined by comparisons with terrestrial investigations. Using the developod experimental setups it is possible to investigate all three flow regimes, i.e. pure free, mixed, and pure forced convection (o Re 0.1). It was found that the influence of free convection is limited to Reynolds numberRe 0.0045, independent of the overheat ratio. Based on the findings of Collis and Williams [12], the influence of free convection can be neglected forRe > 0.58 ·Gr ^1/3. The fluid properties are computed at the film temperature. Two correlations are established for the regime of pure forced convection. End losses to the supports were determined in a vacuum experiment, thus allowing comparison with theoretical investigations. The difference between the analytical computations and the measurement data in the range 0 Re 0.02 is caused by the three-dimensional heat transfer occuring in the experimental investigation.Die vorliegende Untersuchung beschäftigt sich mit der experimentellen Bestimmung des Einflusses der freien Konvektion auf den Wärmeübergang bei quergeströmten Hitzdrahtsonden. Die freie Konvektionsströmung kann unter Schwerelosigkeit minimiert und ihre Größe durch den Vergleich mit terrestrischen Untersuchungen ermittelt werden. Mit den erstellten Experimentaufbauten ist es möglich, alle drei Strömungsbereiche von der rein freien über die gemischte bis zur rein erzwungenen Konvektion zu untersuchen (0 <>Re 0,1). Dabei wurde festgestellt, daß der Einfluß der freien Konvektion sich unabhängig von Überhitzungsverhältnis nur bis zu einer ReynoldszahlRe 0,0045 erstreckt. Zur Vernachlässigung der freien Konvektion kann in Anlehnung an Collins und Williams folgende Beziehung angegeben werden:Re > 0,58 ·Gr ^1/3. Die Stoffwerte werden bei der Filmtemperatur berechnet. Für den Bernich der rein erzwungenen Konvektion wurden zwei Korrelationer aufgestellt. Durch einen Vakuumversuch wurden die Endverluste in die Haltespitzen ermittelt und somit der Vergleich mit theoretischen Arbeiten ermöglicht. Der Unterschied zwischen den analytischen Berechnungen und den Meßdaten im Bereich 0 Re 0,02 ergibt sich durch den dreidimensionalen Wärmeübergang bei der experimentellen Untersuchung.The authors acknowledge the support of the Deutsche Agentur für Raumfahrtangelegenheiten (DARA) under grant number 50-QV 8898-1.     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.