Distinctive features of heat transfer in the region of a gas curtain formed on injection of extraneous gas

New effects on a permeable surface on gas injection are detected on the basis of the numerical modeling of a turbulent boundary layer. It is shown, in particular, that in the gas curtain region the surface temperature can be considerably lower than the injected gas temperature. This effect manifests itself particularly strongly for gas mixtures with low Prandtl numbers.     

Radiative and convective heat transfer in a plane layer of absorbent curtain

An examination is made of the thermal state of a plane layer of gray gas injected into a turbulent stream of high temperature gas flowing over a permeable flat plate.Similarity-type formulations of problems are encountered both in examination of flow near a stagnation point, and also in analysis of the lifting of the boundary layer by intense injection through a porous plate [1]. The examination described relates to the following idealized formulation of the problem (Fig. la).In a plane layer of gray absorbing medium, formed by plane-parallel diffusely radiating surfaces (1-porous plate; 2-boundary of high temperature turbulent gas stream), heat transfer is accomplished by radiation and convection of the layer normal to the surfaces and by molecular heat conduction. All the physical and optical properties of the medium and of the boundary surfaces are assumed to be constant, independent of temperature.The temperature of the wetted surface of the specimen and also that of the fictitious surface determining the upper bound of the lift-off region, are given.Also assumed given is the velocity of the injected medium, which is constant throughout the entire lift-off layer. This idealization appreciably facilitates our examination without in principle changing its features.A very simplified examination of this problem was given in [2]. The special case of a medium with low optical thickness was examined in [3,4].The problem was examined in [5] under the assumption that molecular heat conduction in the medium is negligibly small.In the formulation considered the generalized energy equation has the form     

Laminar heat transfer in the entrance region of ducts

A finite difference technique is used for the evaluation of the rate of heat transfer in the thermal entrance region of ducts with axial conduction. The velocity profile is fully developed and flow in a tube and between parallel plates is studied. Local and average Nusselt numbers and mixing temperatures are presented as a function of the Péclet number. A criterion is also established which proves useful for predicting the conditions under which axial conduction may be ignored.Nomenclature C transformation constant - c _v specific heat, constant volume - D _h hydraulic diameter - h local convective film coefficient, Eq. (15) - h* local convective film coefficient, Eq. (16) - h _m ^* mean convective film coefficient, Eq. (17) - k thermal conductivity - Nu local Nusselt number, hD _h/k - Nu* local Nusselt number, h*D _h/k - Nu _m ^* mean Nusselt number, hQD _h/k - Pe Péclet number, D _h v _m/ - q rate of heat transfer - r radial coordinate - r _o tube radius - R nondimensional radial coordinate, r/r _o - S transformed axial coordinate, Eq. (10) - T temperature - T _e entrance temperature - T _m mixing temperature, Eq. (18) - T _w wall temperature - v _z axial velocity - v _m mean axial velocity - V nondimensional axial velocity, v _z /v _m - y transverse coordinate in parallel plate flow - y _o half width of parallel plate duct - Y nondimensional transverse coordinate, y/y _o - z axial coordinate - Z nondimensional axial coordinate, z/r _o or z/y _o - Z ⁺ nondimensional axial coordinate divided by Peclet number, Z/Pe - thermal diffusivity - nondimensional temperature, (T–T _w)/(T _e–T _w) - mean nondimensional temperature, - _m nondimensional mixing temperature, Eq. (22) - density - i axial position index - j radial or transverse position index     

Law of friction in the region of a gas screen behind a permeable section

The results are given of measurements of friction behind a permeable section in a subsonic turbulent boundary layer at blowing intensity j = 0.003–0.04. Methods are proposed for calculating the local coefficients of friction in the region of a gas screen and the Reynolds number determined from the momentum loss thickness; these are in satisfactory agreement with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 159–162, March–April, 1979.     

Heat transfer from a sphere in the intermediate dynamics region of a rarefied gas

The results are given of the experimental study of convective heat transfer from a sphere in a low-density subsonic stream. Generalizing the results obtained and earlier known data for sub-and supersonic velocities, we suggest approximate formulas for calculating heat transfer from a sphere under any streamline flow conditions of a rarefied gas.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 170-172, March-April, 1972.     

Self-similar channel flow of a viscous gas with heat transfer

We examine self-similar flows of a viscous gas in long, smooth channels with a special heat transfer law at the wall, corresponding to the same Mach number profile at all cross sections.     

Local heat transfer coefficients on the circumference of a tube in a gas fluidized bed

A heated horizontal heat transfer tube was installed 14.8 cm above the distributor plate in a square fluid bed measuring 30.5 × 30.5 cm. Four different Geldart B sized particle beds were used (sand of two different distributions, an abrasive and glass beads) and the bed was fluidized with cold air. The tube was instrumented with surface thermocouples around half of the tube circumference and with differential pressure ports that can be used to infer bubble presence. Numerical execution of the transient conduction equation for the tube allowed the local time-varying heat transfer coefficient to be extracted. Data confirm the presence of the stagnant zone on top of the tube associated with low superficial velocities. Auto-correlation of thermocouple data revealed bubble frequencies and the cross-correlation of thermal and pressure events confirmed the relationship between the bubbles and the heat transfer events. In keeping with the notion of a “Packet renewal” heat transfer model, the average heat transfer coefficient was found to vary in sympathy with the root-mean square amplitude of the transient heat transfer coefficient.     

Laminar flow heat transfer in the entrance region of circular tubes

Summary The asymptotic solution of laminar convective heat transfer in the entrance region of a circular conduit where velocity and temperature profiles are developing simultaneously, is obtained for fluids with high Prandtl numbers. Numerical values of local and average Nusselt numbers as functions of Pr and dimensionless longitudinal distances have been evaluated and presented in graphical forms.Nomenclature A ₀, A ₁ ... A _k coefficients defined by (40) - B ₀, B ₁ ... B _k coefficients defined by (39) - C _p heat capacity of fluid - I _n (x) = i ^–n J _n (ix) where J _n is the n ^th order Bessel function - k thermal conductivity of fluid - Nu _z local Nusselt number defined by (41) - Nu _av average Nusselt number defined by (44) - P pressure - Pr Prandtl number of fluid defined as C _p /k - q heat flux - Re Reynold number, defined as PR/ - R radius of pipe - r radial distance - r ⁺ dimensionless radial distance defined by (8) - T temperature of fluid - T ₀ initial temperature of fluid - T _w wall temperature - T ⁺ dimensionless temperature defined by (11) - T ₀ ⁺ , T ₁ ⁺ , ... T _k ^/+ ... functions related to T ⁺ by (22). - u dimensionless variables defined by (20) - v _r radial component of velocity - v _z z-component of velocity - v ⁺ dimensionless velocity defined by (10) - y ⁺ dimensionless distance defined by (8) - X dimensionless parameter defined by (38) - z longitudinal distance - z ⁺ dimensionless longitudinal distance defined by (9) - thermal diffusivity - dimensionless parameter defined by (12) - a parameter appearing in (46) - (x) gamma function - density - dimensionless variable defined by (28) - parameter defined by (19) - dimensionless variable defined by (32) - viscosity of fluid - kinematic viscosity of fluid     

Convective heat transfer in the thermal entrance region of finned double-pipe

Numerical simulation of the steady and laminar convection in the thermal entry region of the finned annulus is carried out for the case of hydrodynamically fully developed flow when subjected to uniform heat flux thermal boundary condition. Finite difference based marching procedure is used to compute the numerical solution of the energy equation. The results to be presented include Nusselt number, as a function of dimensionless axial length and thermal entrance length for various configurations of the finned double-pipe. The numerical results show that Nusselt number has complex dependence on the geometric variables like ratio of radii, fin height, and number of fins. A comparison of the computed results for certain limiting cases with the results available in the literature validates the numerical procedure used in this work.     

Flow and heat transfer for gas flowing in microchannels: a review

 Microchannels are currently being used in many areas and have high potential for applications in many other areas, which are considered realistic by experts. The application areas include medicine, biotechnology, avionics, consumer electronics, telecommunications, metrology, computer technology, office equipment and home appliances, safety technology, process engineering, robotics, automotive engineering and environmental protection. A number of these applications are introduced in this paper, followed by a critical review of the works on the flow and heat transfer for gas flowing in microchannels. The results show that the flow and heat transfer characteristics of a gas flowing in microchannels can not be adequately predicted by the theories and correlations developed for conventional sized channels. The results of theoretical and experimental works are discussed and summarized along with suggestions for future research directions. Received on 26 June 2000 / Published online: 29 November 2001     

Boiling heat transfer region with independence of the wall temperature

 Extensive measurements of the intensive cooling of hot-rolled wires with temperatures between 1000 ^°C and 1100 ^°C are analysed. The analysis proves the existence of a convection-controlled boiling region, which has been previously observed by few authors in the case of high mass fluxes and high liquid subcooling. This region is characterised by an independence of the heat flux of the surface temperature. The heat flux depends essentially on the Reynolds number, the main influence parameter of the single phase convection, and on the liquid subcooling. Received on 13 September 1999     

Convective heat transfer in the thermal entrance region of parallel-flow noncircular duct heat exchanger arrays

Convective heat transfer properties of a hydrodynamically fully developed flow, thermally developing flow in a parallel-flow, and noncircular duct heat exchanger passage subject to an insulated boundary condition are analyzed. In fact, due to the complexity of the geometry, this paper investigates in detail heat transfer in a parallel-flow heat exchanger of equilateral-triangular and semicircular ducts. The developing temperature field in each passage in these geometries is obtained seminumerically from solving the energy equation employing the method of lines (MOL). According to this method, the energy equation is reformulated by a system of a first-order differential equation controlling the temperature along each line.Temperature distribution in the thermal entrance region is obtained utilizing sixteen lines or less, in the cross-stream direction of the duct. The grid pattern chosen provides drastic savings in computing time. The representative curves illustrating the isotherms, the variation of the bulk temperature for each passage, and the total Nusselt number with pertinent parameters in the entire thermal entry region are plotted. It is found that the log mean temperature difference (T _LM), the heat exchanger effectiveness, and the number of transfer units (NTU) are 0.247, 0.490, and 1.985 for semicircular ducts, and 0.346, 0.466, and 1.345 for equilateral-triangular ducts.

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Konvektiver Wärmeübergang im thermischen Einlaufgebiet von Gleichstromwärmetauschern mit nichtkreisförmigen Strömungskanälen

Zusammenfassung Die Untersuchung bezieht sich auf das konvektive Wärmeübertragungsverhalten eines Gleichstromwärmetauschers mit nichtkreisförmigen Strömungskanälen bei hydraulisch ausgebildetet, thermisch einlaufender Strömung unter Aufprägung einer adiabaten Randbedingung. Zwei Fälle komplizierter Geometrie, nämlich Kanäle mit gleichseitig dreieckigen und halbkreisförmigen Querschnitten, werden bezüglich des Wärmeübergangsverhaltens bei Gleichstromführung eingehend analysiert. Das sich entwickelnde Temperaturfeld in jedem Kanal von der eben spezifizierten Querschnittsform wird halbnumerisch durch Lösung der Energiegleichung unter Einsatz der Linienmethode (MOL) erhalten. Dieser Methode entsprechend erfolgt eine Umformung der Energiegleichung in ein System von Differentialgleichungen erster Ordnung, welches die Temperaturverteilung auf jeder Linie bestimmt.Die Temperaturverteilung im Einlaufgebiet wird unter Vorgabe von 16 oder weniger Linien über dem Kanalquerschnitt erhalten, wobei die gewählte Gitteranordnung drastische Einsparung an Rechenzeit ergibt. Repräsentative Kurven für das Isothermalfeld, den Verlauf der Mischtemperatur für jeden Kanal und die Gesamt-Nusseltzahl als Funktion relevanter Parameter im gesamten Einlaufgebiet sind in Diagrammform dargestellt. Es zeigt sich, daß die mittlere logarithmische Temperaturdifferenz (T _LM), der Wärmetauscherwirkungsgrad und die Anzahl der Übertragungseinheiten (NTU) folgende Werte annehmen: 0,247, 0,490 und 1,985 für halbkreisförmige Kanäle sowie 0,346, 0,466 und 1,345 für gleichseitig dreieckige Kanäle.

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Nomenclature A cross sectional area [m²] - a characteristic length [m] - C _c specific heat of cold fluid [J kg^–1 K^–1] - C _h specific heat of hot fluid [J kg^–1 K^–1] - C _p specific heat [J kg^–1 K^–1] - C _r specific heat ratio,C _r=C _c/C_h - D _h hydraulic diameter of duct [m] - f friction factor - k thermal conductivity of fluid [Wm^–1 K^–1] - L length of duct [m] - m mass flow rate of fluid [kg s^–1] - N factor defined by Eq. (20) - NTU number of transfer units - Nu _{x, T} local Nusselt number, Eq. (19) - P perimeter [m] - p pressure [KN m^–2] - Pe Peclet number,RePr - Pr Prandtl number,/ - Q _T total heat transfer [W], Eq. (13) - Q ideal heat transfer [W], Eq. (14) - Re Reynolds number,D _h/ - T temperature [K] - T _b bulk temperature [K] - T _e entrance temperature [K] - T _w circumferential duct wall temperature [K] - u, U dimensional and dimensionless velocity of fluid,U=u/u - , dimensional and dimensionless mean velocity of fluid - w generalized dependent variable - X dimensionless axial coordinates,X=D _h ² /a ² x* - x, x* dimensional and dimensionless axial coordinate,x*=x/D _hPe - y, Y dimensional and dimensionless transversal coordinates,Y=y/a - z, Z dimensional and dimensionless transversal coordinates,Z=z/a Greek symbols thermal diffusivity of fluid [m² s^–1] - * right triangular angle, Fig. 2 - independent variable - T _LM log mean temperature difference of heat exchanger - effectiveness of heat exchanger - generalized independent variable - dimensionless temperature - _b dimensionless bulk temperature - dynamic viscosity of fluid [kg m^–1 s^–1] - kinematic viscosity of fluid [m² s^–1] - density of fluid [kg m^–3] - heat transfer efficiency, Eq. (14) - generalized dependent variable