Effect of wall emissivities on radiation heat transfer in glass tank forehearths

In an earlier work, we had proposed a two-band, nongrey radiative transfer model for heat transfer in forehearths with simultaneous optically thick and thin approximations for molten glass interiors and at boundaries. Here using the same model, the radiative interaction of the top-crown and bottomrefratory walls with interior layers of shallow molton glass is studied by varying the wall emissivities. The forehearth exit temperature profiles for higher wall emissivities (0.9) show better conditioning of the glass for white flint glasses (optically thin).     

The effect of radiation upon forced-convection heat transfer

Summary A study has been made to determine the influence of radiation heat transfer upon the forced-convection Nusselt number. The particular situation considered was that of flow of a fluid transparant to radiation across a flat plate having a constant surface heat rate per unit area. The analysis was restricted to first order radiation effects, and these results were in turn employed to estimate under what conditions radiation may be neglected. It was found that the radiation influence may be extremely severe for laminar flow, but is considerably less important with regard to turbulent forced convection.Nomenclature a _n constants - c _p specific heat at constant pressure - f Blasius stream function - h local convective heat transfer coefficient - k thermal conductivity - Nu local convective Nusselt number, hx/k - Pr Prandtl number, c _p /k - q heat transfer rate per unit area - Re Reynolds number, u x/ - T absolute temperature: T _e , environment temperature; T _w , surface temperature; T , free-stream temperature - u velocity component in x-direction - u free-stream velocity - v velocity component in y-direction - absorptivity of plate surface - total hemispherical emissivity of plate surface - dimensionless normal coordinate - _n functions of (n=1, 2, ..) - dummy variable of integration - absolute viscosity - kinematic viscosity - dimensionless axial coordinate - density - Stefan-Boltzmann constant     

Stagnation-point flow of couple stress fluid with melting heat transfer

Melting heat transfer in the boundary layer flow of a couple stress fluid over a stretching surface is investigated. The developed differential equations are solved for homotopic solutions. It is observed that the velocity and the boundary layer thickness are decreasing functions of the couple stress fluid parameter. However, the temperature and surface heat transfer increase when the values of the couple stress fluid parameter increase. The velocity and temperature fields increase with an increase in the melting process of the stretching sheet.     

Counterflow, crossflow and cocurrent flow heat transfer in heat exchangers: analytical solution based on transfer units

By means of analysis equations for heat transfer performance based on number of heat transfer units were found, that allow to solve in a simple way single-pass and multipass heat exchanger problems when there are counterflow, crossflow and cocurrent modes of flow in any combination. There is no need to use external information such as the effectiveness concept or the correction factor F. The analysis gives new results which are at variance with traditional heat exchanger analysis when crossflow or cocurrent flow is involved.     

Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow

A numerical method for calculation of strong radiation for 2D reactive air is developed. Governing equations are taken to be 2D, compressible Reynolds-average Navier–Stokes and species transport equations. Also, radiation heat flux is evaluated using a model of discrete ordinate method. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method.     

Thermohydrodynamic characteristics of combined double-diffusive radiation convection heat transfer in a cavity

This work deals with the numerical analysis of a radiating gas flow caused by both temperature and buoyancy concentration gradients in a square cavity; in this regard, the set of governing equations, including conservation of mass, momentum, species, and energy are solved by a numerical technique. In terms of radiation, since the fluid is considered as a semitransparent medium, the radiative term in the energy equation appears and is calculated by numerical solving of the radiative transfer equation (RTE). Furthermore, all of the surrounding cavity walls are considered to be opaque, gray, and diffuse with constant emissivity. All of the flow equations are solved by the finite difference method (FDM) and the RTE by the discrete ordinate one (DOM). In the present study, an attempt is made to verify the optical thickness effects on flow, thermal behavior, and mass transform in a cavity flow, such that reciprocating trends were seen in this manner. Our numerical results show that the thermal field in double-diffusive convection flow reaches very fast its steady-state situation in comparison to the concentration distribution. Besides, it is found that the thermohydrodynamic characteristics of a double-diffusive convection flow of a radiating gas are much affected by optical thickness.     

A New modelling strategy for phase-change heat transfer in turbulent interfacial two-phase flow

The paper presents a modelling strategy for phase-change heat transfer in turbulent interfacial two-phase flow. The computational framework is based on interface tracking ITM (level set approach), combined with large-scale prediction of turbulence, a new methodology known as Large-Eddy & Interface Simulation (LEIS), where super-grid scale turbulence and interfaces are directly solved, whereas the sub-scale parts are modelled. Because steady-state flow conditions are difficult to attain, recourse is made of the Very Large-Eddy Simulation (V-LES) instead of LES, where the flow-dependent cut-off filter is larger and independent from the grid. The computational approach is completed by a DNS-based interfacial phase-change heat transfer model built within the Surface Divergence (SD) theory. The original SD model is found to return better results when modified to account for scale separation, i.e. to segregate low-Re from high-Re number flow portions in the same flow. The model was first validated for an experiment involving a smooth to wavy turbulent, stratified steam-water flow in a 2D channel (Lim et al., 1984, Condensation measurement of horizontal concurrent steam-water flow, ASME J. Heat Transfer 106, 425–432.), revealing that the original SD model performs better for high interfacial shear rates. This screening phase also demonstrated that the most critical issue is the accurate prediction of the interfacial shear using ITM. The model was then applied successfully to predict condensing steam in the event of emergency core cooling in a Pressurized Water Reactor (PWR), where water is injected into the cold leg during a postulated loss-of-coolant-accident. The simulation results agree fairly well with the COSI (short for COndensation at Safety Injections) data (Janicot and Bestion, 1993, Condensation modelling for ECC injection, Nucl. Eng. Des. 145, 37–45).     

Coherent structures in trailing-edge cooling and the challenge for turbulent heat transfer modelling

The present paper tests the capability of a standard Reynolds-Averaged Navier–Stokes (RANS) turbulence model for predicting the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable target data and the mean velocity and eddy viscosity as input for the heat transfer model testing. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. The LES yielded coherent structures which were analysed, in particular with respect to their effect on the turbulent heat transfer. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness caused by the coherent structures becoming stronger. In contrast, the RANS turbulent heat transfer model failed in predicting this behaviour and yielded significantly too high cooling effectiveness. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes caused by large coherent structures, which were found to be responsible for the counter-intuitive decrease of the cooling effectiveness.     

The comparison of two approaches to numerical modelling of gas-particles turbulent flow and heat transfer in a pipe

The comparison of two theoretical approaches for the numerical investigation of turbulent gas–solid flows with heat transfer in a pipe are presented in this paper. The first approach is based on Eulerian–Eulerian modelling of investigated phenomena, the second one is formulated within the framework of the Eulerian–Lagrangian approach. The verification of numerical models under consideration. Their testing against available experimental data show good prognostic properties of the elaborated theoretical tool for research activities to study new physical fundamentals of turbulent gas-suspended particles flows in pipes and channels.     

Interaction of heat transfer by conduction and radiation in a nongray planar medium

This paper considers the problem of the steady energy transfer due to combined effects of conduction and radiation in a medium with frequency dependent properties. The particular problem studied is the one-dimensional energy transfer in an absorbing, emitting, and conducting medium capable of generating heat which is bounded by two black plates. The analysis is restricted to an absorption coefficient x_v of theMilne-Eddington type, i.e., x_v(T)=αv β(T), and the frequency dependence of α(v) is approximated by a rectangular model. Temperature distribution and heat fluxes are reported in the paper for two models of spectral absorption coefficient and are compared with those for the gray case.     

Effect of surface radiation heat transfer on the optimal distribution of discrete heat sources under natural convection

Experiments have been conducted for natural convection heat transfer from protruding discrete heat sources, mounted at different positions on a substrate, to determine the optimal configuration, and to study the effect of surface radiation on them, which reduces their temperature upto 12 %. The optimal configuration has been determined by a non-dimensional geometric distance parameter (λ). An empirical correlation has been proposed between the non-dimensional steady state temperature (θ) and λ, by taking into account the effect of surface radiation heat transfer.     

Numerical modelling of heat and mass transfer in adsorption solar reactor of ammonia on active carbon

 In this paper, we present a modelling of the performance of a reactor of a solar cooling machine based carbon–ammonia activated bed. Hence, for a solar radiation, measured in the Energetic Laboratory of the Faculty of Sciences in Tetouan (northern Morocco), the proposed model computes the temperature distribution, the pressure and the ammonia concentration within the activated carbon bed. The Dubinin–Radushkevich formula is used to compute the ammonia concentration distribution and the daily cycled mass necessary to produce a cooling effect for an ideal machine. The reactor is heated at a maximum temperature during the day and cool at the night. A numerical simulation is carried out employing the recorded solar radiation data measured locally and the daily ambient temperature for the typical clear days. Initially the reactor is at ambient temperature, evaporating pressure; P _ev =P _st (T _ev =0 ^∘C) and maintained at uniform concentration. It is heated successively until the threshold temperature corresponding to the condensing pressure; P _cond =P _st (T _am ) (saturation pressure at ambient temperature; in the condenser) and until a maximum temperature at a constant pressure; P _cond . The cooling of the reactor is characterised by a fall of temperature to the minimal values at night corresponding to the end of a daily cycle. We use the mass balance equations as well as energy equation to describe heat and mass transfer inside the medium of three phases. A numerical solution of the obtained non linear equations system based on the implicit finite difference method allows to know all parameters characteristic of the thermodynamic cycle and consider principally the daily evolution of temperature, ammonia concentration for divers positions inside the reactor. The tube diameter of the reactor shows the dependence of the optimum value on meteorological parameters for 1 m² of collector surface. Received on 10 January 2001     

Global heat transfer analysis in Czochralski silicon furnace with radiation on curved specular surfaces

Numerical analysis of global heat transfer with coupled thermal radiation and heat conduction is investigated in Czochralski silicon crystal growth furnace with curved diffuse and specular surfaces. The finite element method and the radiation element method are adopted to solve the global heat transfer and the radiative heat exchange, respectively. The emphasis focuses on the discussion of the influence of silicon surface radiative characteristics, i.e., either diffuse or specular, on the global heat transfer and the crystal growth process. When the specular character of the silicon crystal and melt surfaces is considered, it is found that the temperature of the melt is obviously decreased and the crystal pulling rate is enhanced. Received on 7 August 1998     

Free convection heat transfer around a horizontal ice cylinder formed through melting within an immiscible liquid

An experimental study has been performed to determine the melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid. Vegetable oil, which was contained within a horizontal heated copper tube, was adopted as a testing liquid. A bubble-free ice cylinder was situated at the center of the tube. The experiments were carried out for the heated tube temperatures ranging from 8.0 to 30.0 °C, while for the cooled tube temperatures from ч.0 to ⪡.0 °C. The flow pattern of the liquid and the ice-liquid interface shape of the ice cylinder being formed through melting were extensively observed and recorded photographically. The local/average heat transfer coefficient along the ice cylinder at steady state was determined as a function of the heated tube temperature as well as the cooled tube temperature. The measurements show that the ice layer profiles at steady state are quite similar irrespective of the thermal conditions. Zusammenfassung Die Experimentelle Untersuchung hatte zum Ziel, den Wärmeübergangsmechanismus beim Schmelzen eines horizontalen, in eine nichtmischbare Flüssigkeit eingetauchten Eiszylinders aufzuklären. In einem horizontalen, beheizten Kupferrohr befindliches Pflanzenöl diente als Versuchsflüssigkeit. Ein blasenfreier Eiszylinder befand sich in der Mitte des Rohres. Bei den Experimenten variierten die Temperaturen des Heizrohres zwischen 8.0 und 30.0 °C, die des gekühlten Innenrohres zwischen ч.0 und ⪡.0 °C. Das Strömungsmuster der Flüssigkeit und die sich während des Schmelzvorganges ausbildende Form der Eis-Flüssigkeitsgrenze am Eiszylinder wurden genauestens beobachtet und photographisch festgehalten. Der Lokale, den Eiszylinder entlang gemittelte Wärmeübergangskoeffizient wurde für den Stationärfall als Funktion der Heiz- und Kühlrohrtemperaturen bestimmt. Die Messungen zeigen, daß die Eisschichtprofile im Stationärfall - unabhängig von den thermischen Bedingungen - weitgehend ähnlich sind.     

Natural convection and radiation heat transfer of an externally-finned tube vertically placed in a chamber

A three-dimensional numerical study was made to investigate effects of fin angle, fin surface emissivity, and tube wall temperature on heat transfer enhancement for a longitudinal externally-finned tube placed vertically in a small chamber. The numerical model was first validated through comparison with experimental measurements and the appropriateness of general boundary conditions was examined. The numerical results show that the mean Nusselt number increases with Rayleigh number for all the fin angles investigated. The maximum heat transfer rate per mass occurs when the fin angle is about 60° for fin surface emissivity between 0.7 and 0.8 and 55° when the surface emissivity increases to 0.9. With increasing tube wall temperature, both the natural convection and radiation heat transfer are enhanced, but the fraction of radiation heat transfer decreases in the temperature range studied. Radiation fraction increases with increasing fin surface emissivity. Both convection and radiation heat transfer modes are important.     

The mathematical modelling of thermal radiation in high temperature fluidized bed

The aim of this study is composed of two parts. One of them is to calculate the radiation heat flux and the other is to determine the overall heat transfer coefficient for the gas-fluidized bed. The radiative heat transfer model is developed for predicting the total heat transfer coefficients between submerged surfaces and fluidized beds for several working temperatures. The role of radiation heat transfer in the overall heat transfer process at an immersed surface in a gas-fluidized bed at high temperatures is investigated. Analytical results are compared with the previously done experiments and a good agreement between the two, is obtained.

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Bestimmung der Wärmeübertragungs-Koeffizienten in Gas-Wirbelschichten

Zusammenfassung Diese Untersuchung besteht aus folgenden zwei Teilen: 1. Kalkulation des Radiationswärmeübergangs in Gas-Wirbelschichten. 2. Bestimmung des Wärmeübergangs-Koeffizienten in Gas-Wirbelschichten. Dieses Radiationswärmeübergangsmodell wurde entwickelt, um die Wärmeübertragungs-Koeffizienten zwischen der eingetauchten Oberfläche und der Wirbelschicht bei verschiedener Wärme schätzungsweise zu bestimmen. Es wurde das Verhältnis der Radiationswärmeübertragung in Gas-Wirbelschichten zum totalen Wärmeübergang untersucht. Die Meßwerte wurden mit theoretischen Resultaten verglichen.

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Nomenclature c (x) specific heat capacity of packet [J/kg K] - c _p specific heat capacity of particle [J/kg K] - c _pg specific heat capacity of gas [J/kg K] - d _p average diameter of the bed particles [m] - f ₀ the fraction of time that a unit surface exposed to the bubble phase - 1–f ₀ the fraction of time that a unit surface exposed to the packet phase - g acceleration due to gravity [m/s²] - h _b heat transfer coefficient for the surface in contact with bubble [W/m² K] - h _bc conduction heat transfer coefficient for the surface/bubble [W/m²K] - h _br radiation heat transfer coefficient for the surface/bubble [W/m²K] - h _p heat transfer coefficient for the surface in contact with packet [W/m²K] - h _pc conduction heat transfer coefficient for the surface/packet [W/m² K] - h _pr radiation heat transfer coefficient for the surface/packet [W/m² K] - h _T total heat transfer coefficient between bed and surface [W/m² K] - k ⁰ thermal conductivity of the emulsion phase for fixed bed [W/m K] - k(x) thermal conductivity of packet [W/m K] - k _e the logarithmic mean of conductivity for first layer in packet [W/m K] - k _g the logarithmic mean of conductivity for the first layer in packet [W/m K] - K extinction coefficient [1/m] - m mass [kg] - n number of layers - p air pressure [pa] - q _pc mean local conduction heat transfer for packet [kW/m²] - q _pr mean local radiation heat transfer for packet [kW/m²] - Q _p average heat flux during packet contact with surface [kW/m²] - Q _b average heat flux during bubble contact with surface [kW/m²] - R gas constant [287.04 J/kg K] - t time [s] - t _g residence time for gas bubble [s] - t _k residence time for packet [s] - T temperature [K] - T _b bed temperature [K] - T _W surface temperature [K] - V _mf minimum fluidization velocity [m/s] - v _t terminal velocity [m/s] - x distance [m] Greek symbols t time increment - x thickness of the layer - emissivity - thermal diffusivity [m²/s] - (x) voidage of fluidized bed - _mf void ratio of the bed at minimum fluidization - ₀ voidage of fixed bed - _g dynamic viscosity of gas [kg/m s] - _g kinematic viscosity of gas [m²/s] - (x) density of packet [kg/m³] - _p density of particles [kg/m³] - _g density of gas [kg/m³] - Stefan-Boltzmann constant [5.66·10^–8 W/m²K⁴] - geometric shape factor for particles Dimensionless numbers Ar Archimedes numberAr=g d _p ³ ( _p – _g ) _g / _g ² - Nu Nusselt numberNu=h·d/k - Re Reynolds numberRe=d _p ·V _mf / _g - Pr Prandtl numberPr=C _{pg g} /k _g