Non-gray radiative convective conductive modeling of a double glass window with a cavity filled with a mixture of absorbing gases

Coupled radiation and natural convection heat transfer occurs in vertical enclosures with walls at different temperatures filled with gas media. In glass window thermal insulation applications in hot climates, infrared absorbing gases appear as an alternative to improve their thermal performance. The thermal modeling of glass windows filled with non-gray absorbing gases is somewhat difficult due to the spectral variation of the absorption coefficients of the gases and the phenomena of natural convection. In this work, the cumulative wavenumber (CW) model is used to treat the spectral properties of mixtures of absorbing gases and the radiative transport equation is solved using CW model and the discrete ordinates method. Due to the range of temperature variation, the mixture of gases is considered as homogeneous. The absorption coefficients were obtained from the database HITRAN. First, the natural convection in a cavity with high aspect ratio is modeled using a CFD code and the local and global Nusselt numbers are computed and compared with available empirical correlations. Also, the flow pattern for different Rayleigh numbers is analyzed. Then, the heat transfer in the gas domain is approximated by a radiative conductive model with specified heat flux at boundaries which is equivalent to convective transport at the walls surroundings. The energy equation in its two-dimensional form is solved by the finite volume technique. Three types of gas mixtures, highly absorbing, medium and transparent are investigated, to determinate their effectiveness in reducing heat gain by the gas ambient. Reflective glasses are also considered. The numerical method to solve radiative heat transport equation in gray and non-gray participant media was validated previously. The temperatures distributions in the gas and the glass domain are computed and the thermal performance of the gas mixtures is evaluated and discussed. Also, comparison with pure radiative conductive model is shown.     

Performance analysis of a solar glass tube collector

The thermal performance and thermal processes of a glass tube collector have been analysed in this paper. Its thermal performance can be improved by changing the thermal processes to take advantage of the glass tube's ability to transmit sunlight; that makes it possible for the working fluid to directly absorb part of solar radiation. Its thermal performance is even better in most parts of the working region than that of a steel tube collector, even when the structure, meteorological conditions and thermodynamic properties of the working fluid are exactly the same.An equation of steady-state instantaneous efficiency of a glass tube collector has been derived in the paper. Calculations of various operating conditions have been made with a computer, and the calculated results are quite agreeable with the experimental results. Thus the equation and the calculation method can be used in the design of glass tube collectors and for comparison calculations. The calculations also show some other important features of a glass tube collector.     

Heating/melting of a fused silica particle by convection and radiation

The effect of internal absorption and emission of radiation on the heating/melting process of small fused silica particles is analyzed. The particle is considered to be semitransparent to radiation, and the radiative transfer theory is used to predict the local volumetric absorption/emission rate. The transient energy equation with conduction and radiation accounted for is solved to predict the temperature distribution in the particle and the solid–liquid interface position after the melting has started. The radiative transfer calculations are carried out on the spectral basis using published spectral optical property data for fused silica. Results of parametric calculations for different diameter particles, surroundings temperatures and external flow conditions are reported and discussed.     

Experimental verification of thermal remote sensing method for recovering temperature distribution in glass

The thermal remote sensing method for recovering the temperature distribution in glass from spectral emission data is examined experimentally. An analytical model is formulated and the desired temperature distribution is obtained using an optimization scheme which determines the temperature profile in the form of a polynomial or a set of discrete points. In order to evaluate the accuracy and validity of the thermal remote sensing method, the recovered temperatures are compared with independent measurements using surface thermocouples and a Mach-Zehnder interferometer. Experimental results are reported for fused silica (Corning Code 7940) glass samples using a Perkin-Elmer spectrometer to measure the spectral radiant energy emerging from the layer of glass. Opaque (high and low emittance) boundary conditions at the heated surface of the glass were considered. Temperatures in the range from 500 to about 900 K were examined. Spectral emission data between 3.3 and 4.8 μm were used in recovering the temperature distribution in the glass samples. The results showed that the recovered and interferometrically measured temperature profiles agreed well, with the maximum deviation never exceeding approximately 2 per cent.     

Combined non-gray radiative and conductive heat transfer in solar collector glass cover

A rigorous approach for the radiative heat transfer analysis in solar collector glazing is developed. The model allows a more accurate prediction of thermal performance of a solar collector system. The glass material is analysed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in the one-dimensional case using the Radiation Element Method by Ray Emission Model (REM by REM).This method is used to analyse the combined non-gray convective, conductive and radiative heat transfer in glass medium. The boundary surfaces of the glass are specular. The spectral dependence of the relevant radiation properties of glass (i.e. specular reflectivity, refraction angle and absorption coefficient) are taken into consideration. Both collimated and diffuse incident irradiation are applied at the boundary surfaces using the spectral solar model proposed by Bird and Riordan. The optical constants of a commercial ordinary clear glass material have been used. These optical constants (100 values) of real and imaginary parts of the complex refractive index of the glass material cover the range of interest for calculating the solar and thermal radiative heat transfer through the solar collector glass cover. The model allows the calculation of the steady-state heat flux and temperature distribution within the glass layer. The effect of both conduction and radiation in the heat transfer process is examined. It has been shown that the real and imaginary parts of the complex refractive index have a substantial effect on the layer temperature distribution. The computational time for predicting the combined heat transfer in such a system is very long for the non-gray case with 100 values of n and k. Therefore, a simplified non-gray model with 10 values of n and k and two semi-gray models have been proposed for rapid computations. A comparison of the proposed models with the reference non-gray case is presented. The result shows that 10 bandwidths could be used for rapid computation with a very high level of accuracy.     

Online determination of transient thermal stresses in critical steam turbine components using a two-step algorithm

The article presents a novel algorithm for robust calculation of thermal stresses in steam turbine components during transient operating conditions. Stress calculations are performed in 2 steps: in the first step an unsteady radial temperature distribution in the component model is computed, and based on this thermal stresses at critical locations are determined in the second step. The radial temperature distribution is obtained by solving the Fourier-Kirchhoff equation for a cylinder or sphere by means of a finite difference method. The thermal stresses are computed using the Duhamel integral and Green functions evaluated with a constant heat transfer coe?cient and used with an equivalent steam temperature obtained from the surface heat flux.     

PCM glazing systems

This paper presents a different approach for thermal effective windows, i.e. windows that reduce the energy transmitted into or out of a room. The idea is to use a double sealed glass filled with a phase change medium (PCM) whose fusion temperature is determined by solar–thermal calculations. The PCM used is polypropylene glycol. The investigation includes modelling of the heat and radiation transfer through a composite window and optical investigation of conventional and PCM filled windows, testing of the window and comparison with numerical simulations. A one-dimensional model for the composite glass window is developed to predict the thermal performance as a function of the geometrical parameters of the panel and the PCM used. Optical measurements were realized using photo-spectrometry to determine the transmittance, reflectance and absorptance. The specimens used include single glass of different thicknesses, double glass of different gap spacing and thicknesses filled with air or PCM, and finally coloured PCM. The results indicate big reductions in the energy transmitted, specially in the infra-red and ultraviolet regions, while maintaining a good visibility. © 1997 by John Wiley & Sons, Ltd.     

Predication of nonlinear heat transfer in a convective-radiative fin with temperature-dependent properties by the collocation spectral method

ABSTRACT

The applicability of the collocation spectral method (CSM) for solving nonlinear heat transfer problems is demonstrated in a convective-radiative fin with temperature-dependent properties. In this method, the fin temperature distribution is approximated by Lagrange interpolation polynomials at spectral collocation points. The differential form of the energy equation is transformed to a matrix form of algebraic equations. The computational convergence of the CSM approximately follows an exponential decaying law; and thus, it is a very simple and effective approach for a rapid assessment of nonlinear physical problems. The effects of temperature-dependent properties such as thermal conductivity, surface emissivity, heat transfer coefficient, convection-conduction parameter, and radiation-conduction parameter on the fin temperature distribution and efficiency are discussed.     

THERMAL STRESS ANALYSIS IN THERMOPIEZOELASTIC STRIP WITH AN EDGE CRACK

The analysis of thermal stresses becomes important when the piezoelectric material has to be operated in either extremely cold or hot temperature environments. Hence, it is essential to know the interaction of mechanical defects with temperature changes. This investigation is concerned with a strip problem of transversely isotropic thermopiezoelastic material containing an edge crack under partial thermal and electric loading conditions. Thermopiezoelastic stresses are analyzed by introducing potential functions and Fourier transforms. The problem reduces to solving a singular integral equation, and the singular integral equation is solved. Numerical calculations of the thermal stress intensity factors are carried out for a cadmium selenide material.     

U-values, optical and thermal coefficients of composite glass systems

This paper presents a different approach for thermal effective windows, i.e. windows which reduce energy transmitted into or out of the room. The idea is to use a double-sealed glass filled with pcm whose fusion temperature is determined by solar-thermal calculations. The investigation is divided into two main parts: modeling of the heat and radiation transfer through the composite window and the optical investigation of the pcm-filled window. A one-dimensional thermal model for the composite window was developed to predict the resulting effects due to variation of the geometrical and pcm thermal properties. Optical investigations using photo-spectrometry were realized on single glass, double glass filled with air, and double glass filled with pcm. The transmittance and reflectivity tests indicate large reductions in the infrared and ultraviolet radiations while maintaining the good visibility. The effects of thickness of glass and spacing were also analyzed.     

A simplified approach for the thermoelastic large deflection in the thin clamped annular sector plate

The present article is concerned with analysis of large deflection of a heated thin annular sector plate with clamped edges under transient temperature distribution using Berger’s approximate methods. The prescribed surface temperature is at the top face of the plate whereas the bottom face is kept at zero temperature. In this study, the Laplace transform as well as the classical method have been used for the solution of heat conduction equation. The thermal moment is derived on the basis of temperature distribution, and its stresses are obtained using resultant bending moment and resultant forces per unit length. The calculations are obtained for the aluminium plate in the form of an infinite series involving Bessel functions, and the numerical results for temperature, deflection, resultant bending moments, and thermal stresses have been illustrated by graphs.     

Absorption of thermal radiation in large semi-transparent particles at arbitrary illumination of the polydisperse system

An approximate theoretical model for nonuniform absorption of the external thermal radiation in a large semi-transparent spherical particle is suggested. As applied to heat transfer problems with diffuse radiation in the wide spectral range, the asymmetric illumination of single particle is considered at each spectral interval as a uniform illumination from backward and forward hemispheres (with respect to the direction of spectral radiation flux). The Mie theory is employed in calculations for particles illuminated from a hemisphere. The modified differential approximation suggested earlier by the author is used in the case of spherically symmetric illumination. Approximate analytical relations for distribution of absorbed radiation power inside a particle are obtained. Results of calculations for typical polydisperse sprays of water and diesel fuel droplets are presented.     

Development of a model for calculating the longwave optical properties and surface temperature of a curved venetian blind

This article is about the development of a mathematical model for calculating the longwave optical properties of a curved venetian blind. The calculated optical properties are used to determine the performance of the glass window installed with a venetian blind in terms of thermal comfort. The blind, whose optical properties are considered nonspecular, is modeled as an effective layer. The effect of slat curvature is included in the developed model. A six surface enclosure formed by two consecutive slats is used to analyze for the longwave optical properties of the effective layer. The longwave optical properties, transmittance, reflectance, absorptance and emittance are developed by using the radiosity method. The steady state energy balance method along with the developed longwave optical properties are used to determine the surface temperature of the effective layer. The empirical expression for the total heat flux from the indoor glass window surface with an adjacent venetian blind is adopted in the developed model. The surface temperature of the blind, which is the key parameter for calculating the thermal performance of glass windows with venetian blinds with respect to thermal comfort, is chosen as the parameter used for the model validation. The predicted surface temperature of the venetian blind is compared with the surface temperature of the venetian blind obtained from the measurement. The agreement between the predicted temperature and the measured temperature is good.     

Comparison of long-term flat-plate solar collector performance calculations based on averaged meteorological data

The use of averaged meterological data for collector performance calculations is studied. To this end, a steady state, two-dimensional, nodal, heat transfer analysis is developed for a flat-plate solar collector. The analysis accounts for the temperature gradients in the fluid flow and vertical directions in the collector, the physical and thermodynamic properties of the materials in the collector, the collector location, the orientation and dimensions of the collector, the number of cover plates and any thin film selective coatings on the cover plates or absorber. Also accounted for are the time dependent variations in the meteorological conditions, insolation, and collimated and diffuse solar irradiation. The spectral nature of radiation heat transfer in the collector is modeled by two spectral bands, solar and thermal, with 3.0 μm as the cutoff frequency between the solar and thermal bands of radiation. The results indicate that long term collector performance calculations based on averaged meteorological data will not correlate with calculations based on hourly data if the weather is highly variable. When the weather variations are mild, averaged data can give results very close to those based on hourly data.     

Heat transfer aspects of an elevated linear absorber

This paper describes aspects of the design methodology and heat transfer calculations for an elevated north–south oriented linear absorber. The absorber is part of a direct steam generation solar thermal concentrating system based on the Australian compact linear Fresnel reflector (CLFR) concept. The basic absorber design is an inverted air cavity with a glass cover enclosing a selective surface. This arrangement has been shown previously to offer good optical and thermal performance from measurements on a 4 kW_thermal outdoor test apparatus. Two main design aims are discussed here: Firstly to maximise the heat transfer between the absorbing surface and the steam pipes, and secondly, to ensure that the absorber surface temperature is sufficiently uniform so as not to cause thermal degradation of the selective surface. Results are given of the absorber temperature distribution obtained from finite element analysis. Sufficiently low temperature differences between the fluid surface and the absorbing surface (<20 K) can be achieved with satisfactory pipe separations and sizes, and with practical absorber plate thicknesses.     

Study of thermal radiative properties of antireflection glass for flat-plate solar collector covers

An analytical study is presented to evaluate thermal radiative properties of soda-lime sheet glasses covered with 0·087 μ m thick MgF₂ coatings. Glass specimens analyzed in the work consist of single and double layers of glass with either coated or uncoated surfaces. Equations for bulk and system properties are given which are used in conjunction with the measured absorption coefficient to determine glass spectral properties. Glass system properties are evaluated for five combinations of glass consisting of double layers of coated or uncoated glass plates. The evaluated spectral properties are integrated to yield total solar properties at different incidence angles. Analytical results show clearly there are advantages in using coated glass as solar collector covers; not only is the transmitted energy to the collector increased at normal incidence condition, but also the energy loss by reflection at large incidence angles is substantially reduced. This characteristic might be worthy of consideration in the future design of the flat-plate solar energy collector.     

Modeling of Flow and Heat Transfer in a Molten Glass Mini-Film for High Temperature Heat Collection in a Falling-Film Solar Central Receiver

ABSTRACT

In concentrating solar power plants, there is a strong incentive to increase the collection temperature and the overall exergy efficiency of the system. Some molten glass mixtures are attractive working fluids for high temperature solar thermal heat collection because optimized glass mixtures can be more stable, less-toxic, and less-corrosive than, for example, molten salts at high temperatures (≥1000°C). A specific phosphorous pentoxide glass mixture is considered in this study to explore its performance in a molten glass falling film central receiver design for collection of heat at conditions resulting in a mini-film with a thickness less than 3mm. In our falling molten glass thin film, the phosphate glass flow is treated as a laminar, Newtonian and gravity-driven flow over a slightly inclined flat plate using an explicit finite difference scheme to evaluate its heat transfer performance for a direct absorption receiver concept. One of the main challenges of modeling transport in the molten glass is the strong dependence of its viscosity on temperature. To incorporate this effect in our numerical analysis, a temperature-dependent viscosity model is used in the momentum equation to model the fluid behavior as it flows down the surface and is progressively heated. An exponential function is used to model the viscosity as it changes with temperature to properly fit the measured the viscosity data provided by Halotechnics. Also, a variable film thickness model analysis is implemented to treat the variation in film thickness that results from the viscosity variation with temperature. In order to avoid stability issues, the finite difference scheme is organized in terms of nondimensional parameters that include all important properties that govern the system. The results of our model indicate that thinning of the film as it flows over the heated surface enhances the heat transfer performance on the lower portion of the receiver system. The heat transfer coefficient increases instead of remaining constant (as normally expected for fully developed laminar flows) on the lower portion of the heated surface. The results further indicate that using a thin mini-film of molten glass for solar thermal heat collection provides high heat transfer performance and enhances the exergy collection.     

APPLICATION OF SPECTRAL METHODS TO THERMAL ANALYSIS OF NANOSCALE ELECTRONIC DEVICES

The transient thermal characteristics of nanoscale electronic devices operating at very high frequencies are studied by spectral methods. At such scales microscopic phenomena resulting from phonon collisions and phonon scattering become important. A device, consisting of an array of MOSFET transistors on silicon substrate, is considered as a test case. Thermal transport is represented by a reduced form of the Boltzmann transport equation: the thermal wave model or hyperbolic heat equation. The results indicate that spectral methods can be used effectively for the accurate prediction of the short-time transient effects in nanoscale devices. Such effects are amplified by a sharp increase in the operating voltage and the corresponding heat generation rate.     

Thermal advantages for solar heating systems with a glass cover with antireflection surfaces

Investigations elucidate how a glass cover with antireflection surfaces can improve the efficiency of a solar collector and the thermal performance of solar heating systems. The transmittances for two glass covers for a flat-plate solar collector were measured for different incidence angles. The two glasses are identical, except for the fact that one of them is equipped with antireflection surfaces by the company SunArc A/S. The transmittance was increased by 5–9%-points due to the antireflection surfaces. The increase depends on the incidence angle. The efficiency at incidence angles of 0° and the incidence angle modifier were measured for a flat-plate solar collector with the two cover plates. The collector efficiency was increased by 4–6%-points due to the antireflection surfaces, depending on the incidence angle. The thermal advantage with using a glass cover with antireflection surfaces was determined for different solar heating systems. Three systems were investigated: solar domestic hot water systems, solar heating systems for combined space heating demand and domestic hot water supply, and large solar heating plants. The yearly thermal performance of the systems was calculated by detailed simulation models with collectors with a normal glass cover and with a glass cover with antireflection surfaces. The calculations were carried out for different solar fractions and temperature levels of the solar heating systems. These parameters influence greatly the thermal performance associated with the antireflection surfaces.     

Pressure- and temperature-dependent combustion reactions

In combustion systems, many reactions are simple thermal unimolecular isomerizations or dissociations, or the reverse thereof. It is well understood that these reactions typically depend on temperature, pressure and the nature of the bath gas. These kinds of reactions are a subset of the more general behavior that can be described as free radical association reactions that produce highly energized intermediates, which can isomerize or dissociate via multiple chemical pathways. Each reaction rate depends on excitation energy and all of the competing reactions occur in competition with collisional activation and deactivation. These complicated multi-well, multi-channel reaction systems can only be simulated accurately by using master equation techniques. In this paper, master equation calculations are discussed for several examples of reactions important in combustion (and atmospheric chemistry). Current master equation codes are based on statistical RRKM reaction rate constants (including quantum mechanical tunneling) and simplified models for collisional energy transfer. A pragmatic semi-empirical approach is adopted in order to compensate for limited knowledge. The reaction energies needed for RRKM calculations are usually obtained from quantum chemistry calculations, which are often of limited accuracy and may be adjusted empirically. Energy transfer cannot be predicted accurately and must be parameterized by fitting experimental data. For combustion modeling, the master equation results are usually expressed as chemical reactions with rate constants fitted to empirical algebraic equations. However, the results may be expressed more accurately by interpolating from look-up tables. Several current research issues are also mentioned, including the effects of angular momentum conservation, vibrational anharmonicity, slow intramolecular vibrational energy redistribution, and assumptions surrounding the details of collisional energy transfer.