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An analysis is presented for the steady non-linear viscous flow of an incompressible viscous fluid over a horizontal surface of variable temperature with a power-law velocity under the influences of suction/blowing, viscous dissipation and thermal radiation. Numerical results are illustrated by means of tables and graphs. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation. The effects of the stretching parameter n, suction/blowing parameter b, Prandtl number ¿, Eckert number E c(E c *) and radiation parameter N R are discussed. Two cases are studied, namely, (i) Prescribed surface temperature (PST case) and, (ii) Prescribed heat flux at the sheet (PHF case). © 2011 Springer Science+Business Media B.V.

We model a lava flow as a one-dimensional flow of a pseudoplastic fluid with viscous dissipation. The flow is horizontally unbounded and is driven downslope by the gravity force. We consider a power-law constitutive equation and we take into account the temperature dependence of the rheological parameters. Given an effusion rate and an initial temperature at the eruption vent, the flow is assumed to cool down by heat radiation. We calculate the heat produced by viscous dissipation as a function of lava temperature and effusion rate. The cooling rate is calculated as a function of the surface temperature and flow rate. Viscous dissipation reduces the cooling rate by an amount which is independent of flow rate. We evaluate the effect of viscous dissipation on the flow thickness and velocity. The effect of dissipation is to decrease the flow thickness and to increase the flow velocity. The effect on flow thickness is greater for smaller flow rates, while the effect on velocity is greater for larger effusion rates. In principle, the model provides a method for estimating the flow rate from in-field measurements of distances and temperatures.

International audience; A Multi-Spectral Reordering (MSR) scheme is introduced to improve the performances of the Spectral-Line Moment-Based (SLMB) modeling for the handling of full spectrum radiative heat transfer calculations in nonuniform media. Using this simultaneous reordering of the spectrum for several thermophysical conditions together with employing approximate formulations to evaluate path-averaged transmission functions for nonisothermal and nonhomogenous gaseous paths, a novel full spectrum gas radiation modeling method in nonuniform gaseous mixtures is constituted. The method is presented in details as well as the building of associated databases for CO2and H2O at atmospheric pressure and for the temperature range of 300-2700 K. The new model is validated against line-by-line reference computations for a series of existing bench-marks and for a flame configuration. The MSR-SLMB modeling is shown to perform accurately and better than the standard SLMB one, while involving reasonable additional computational costs.

In order to research the spread of a fire and the distribution of temperature and gas in high-rise building fires, setting the CCTV North Building Fire as the background, the fire was simulated and analyzed by FDS. The experiment indicates that the basic spread law of fire that mainly spreads on one hand through combustible material on the surface of buildings and then comes to inside, on the other hand spreads from the kindling point to the interior of building and then through lift and corridor from downstairs and finally inside out. The air temperature and gas concentration firstly increase with increasing distance from the fire surface, and then decrease. By changing the maximum combustion temperature and transmit power of the surface decoration materials, it can reduce the influence of surrounding buildings which comes from thermal radiation.

This paper presents a study of the flow and heat transfer of an incompressible Ostwald de-Waele power-law fluid past an infinite porous plate, subject to suction at the plate. The power-law index n satisfies 0 < n< 1 (shear-thinning fluid only) provided that there is suction at the plate. Three cases are studied, namely, (i) the plate with constant surface temperature (CST case), (ii) the plate with prescribed surface temperature (PST case), and (iii) the plate with prescribed heat flux (PHF case). The effects of viscous dissipation and thermal radiation are also considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated. © 2010 The Institution of Chemical Engineers.

This study involves a screening-level risk assessment of the impairment of human health and life related to hydrogen explosion and chemical release during the operation of a hydrogen refueling station (HRS) that uses organic hydride. First, twenty-one accident scenarios were identified involving the leakage of hydrogen, toluene and methylcyclohexane (MCH) in the HRS. Next, the leakage frequency for each scenario was estimated using a hierarchical Bayesian model. Simulations were then performed of the blast-wave pressure and heat radiation after a hydrogen leak and of atmospheric dispersion of evaporated chemicals after leaks of liquid MCH and toluene. The consequences were estimated for each scenario according to leak size using the existing probit functions and threshold values. Finally, the risk due to explosion, heat radiation, and acute toxicity was estimated by multiplying the consequence by the leakage frequency. The results show that the mortality risk of explosion and acute effect is less than 10−6 per year, which is a negligible level of concern. However, the mortality risk of heat radiation in the scenarios involving hydrogen leakage from the pipe connected to the cylinders and compressors exceeds 10−4 per year inside the HRS, thereby requiring additional steps if a more-detailed risk assessment is needed.

This paper reports the production of nanoaluminum particles using the wire explosion process at our laboratory. Electrical energy is applied to the aluminum wire in an argon atmosphere to yield spherical particles around 50 nm in size. The material is also characterized by a number of methods. The nano-Al is included in bimodal ammonium Perchlorate composite solid propellants, and their burning rates are compared with those containing normal micron- sized aluminum and nonaluminized propellants in a total of 21 formulations in the 1-12 MPa pressure range. Nanoaluminized propellants show ?100% increase in burning rate relative to nonaluminized or microaluminized ones, but only when large-sized coarse ammonium Perchlorate particles are used. Burning-rate plateaus observed in non- and microaluminized propellants are washed out with the addition of nano-Al, but the burning rates of nanoaluminized propellants register low pressure exponents in the elevated pressure range. The results suggest that the heat feedback from the diffusion-limited combustion of nano-Al particles near the propellant burning surface controls the propellant burning rate when sufficiently large parts of the burning surface are made up of the nanoaluminized fine ammonium-perchlorate/binder matrix.

Numerical and experimental investigations highlighting the heat and mass transfer phenomena in a laminar co-flowing jet diffusion flame have been carried out. The fuel under consideration is ethylene, with ambient air as the co-flowing oxidizer. The diffusion flame is modeled using a 17-step reduced reaction mechanism with finite rate chemistry and the effects of soot on the radiative heat transfer of the flame have been demonstrated. Soot growth and oxidation processes are studied using a two-equation transport model, while the radiative heat transfer is modeled using the P1 approximation. An in-house finite volume code has been developed to solve the axi-symmetric Navier-Stokes equations in cylindrical coordinates, along with the soot mass fraction, soot number density, energy and species conservation equations. Comparison of predictions with experimental results shows reasonable agreement with regard to the flame height and temperature distribution. A parametric study is also presented, which illustrates the effects of the fuel jet Reynolds number and the flow rate of co-flow air. � 2008 Elsevier Ltd. All rights reserved.

This paper presents a multilayer differential discrete ordinate method to solve the radiative transfer equation for an absorbing, emitting and scattering inhomogeneous plane parallel medium. This method reduces the integro-differential equation into a set of coupled first order ordinary differential equations with two point boundary conditions on using a suitable quadrature scheme. These equations are then solved numerically. Numerical validation of the method for gray medium is done by comparing the results obtained with benchmark cases available in the literature. Validation for a non-gray medium is done by considering a problem concerning radiative transfer from the atmosphere. The brightness temperature at the top of the atmosphere is calculated at various frequencies and validated with those obtained by several other numerical methods. � 2008 Elsevier Ltd. All rights reserved.

An inverse conduction-radiation problem for simultaneous estimation of the conduction-radiation parameter, the optical thickness and the boundary emissivity from a knowledge of the measured temperature profile for combined conduction and radiation in a plane parallel participating medium is presented. A finite volume method is used to solve the "forward" problem, wherein the temperature profile is determined by a solution of the governing equation for a given set of parameters. The inverse problem is treated as an optimization problem, wherein, we minimize the sum of square of residuals between the measured and estimated temperatures. Genetic algorithms are used for the search. The effects of "measurement" errors on the estimated parameters, which are introduced through a random perturbation, are investigated. � 2006 Elsevier Ltd. All rights reserved.

The existing literature on CFD-based coal combustion modelling is applicable mainly for coals of low ash content and the calculations are done on an ash-free basis. In Indian coals, the ash content may be significantly higher, up to 40% or more. Studies reported in the literature show that the mineral matter in the coal may have a number of effects on the combustion characteristics. In the present study, a sensitivity analysis is performed, using the CFD code CFX of AEA Technology, on the likely effect of ash content on the char reactivity, oxygen diffusion rate for char combustion and on the radiative heat transfer parameters. The results show that the effect of enhanced char reactivity is negligible whereas reduced oxygen diffusion rates due to a thicker ash layer may result in a significant reduction in char oxidation rates with a resultant decrease in the peak temperature in the furnace. The global parameters such as the peak temperature and the flue gas temperature remain relatively insensitive to the presence of high ash content. These results are consistent with the experimental observations of Kurose et al. [R. Kurose, M. Ikeda, H. Makino, Combustion characteristics of high ash coal in pulverized coal combustion, J. Fuel 80 (2001) 1447-1455]. � 2006 Elsevier Inc. All rights reserved.

The heating of containerized liquid using microwave radiation is investigated numerically. The numerical model is validated with an earlier experimental study. Unlike previous studies, the turntable rotation is taken into account. The effects of turntable rotation, natural convection, power sources, and aspect ratio of container on the temperature profiles are studied. Detailed results of temperature profiles, stream functions and time evolution of flow field are presented. An attempt is made to physically explain the complex flow pattern due to the effects of rotational and gravitational forces and spatially non-uniform internal heat generation typical in microwave heating. A correlation, for the transient changes of temperature is arrived at. Current studies indicate that turntable rotation does not aid in achieving uniform heating in case of a symmetric heat source. � 2006 Elsevier Ltd. All rights reserved.

Постановка проблемы. Данные Министерства здравоохранения и Международной организации труда свидетельствуют, что смертность от травм и профзаболеваний в мире занимает третье место после сердечно-сосудистых и онкологических заболеваний. По состоянию на 2014 г. в Украине свыше 3,4 млн лиц работают в условиях, не удовлетворяющих санитарно-гигиеническим нормам. Особенно сложными остаются условия труда на производствах, связанных с выделением или применением тепловых источников. Влиянию высоких температур подвергаются работники на предприятиях строительной индустрии (производство кирпича, стекла, полимеров).Цель статьи ‑обоснование применения средств для измерения теплового излучения на рабочих местах.Вывод. Установлено, что существующие приборы отечественного и зарубежного производства не позволяют исследовать условия труда на рабочих местах горячих производств из-за значительного диапазона тепловых излучений ‑от 50 до 24000 Вт/м2, что вносит большую погрешность в измерения. Впервые установлено, что для измерения как малых, так и значительных по величине тепловых потоков необходимо использовать низкопредельные, но высокочувствительные датчики, при этом дозируя время доступа теплового потока. Установлены закономерности изменения отражательной способности от вида материала и длины спектра излучения. На основании проведенных исследований влияния интенсивности избыточного теплового излучения на рабочие места горячих производств и установившейся при этом температуры нагрева поверхностей установлено распределение максимума длины волны ИК-излучения, подтверждаемое законом Голицына‑Вина. Предложен экспресс-метод оценки отражательной способности материалов, который позволяет оперативно получать информацию на начальной стадии исследований и разработки защитных средств от ИК-излучения. Усовершенствован стенд для проведения исследований отражательной и пропускной способности материалов с учетом изменяемого угла падения излучения, состояния поверхности и ее поляризационной способности, погрешность при этом не превышает 5‑7 %. Предложен новый подход к созданию эффективных защитных средств с учетом спектральной составляющей ИК-излучения. Данная методика измерений позволяет оценить влияние на рабочих местах не только первичных, но и вторичных источников излучения. На основе проведенного анализа существующих отечественных датчиков для измерения интенсивности тепловых потоков произведен выбор датчиков и исследование их характеристик с учетом влияния на них температурной составляющей., Постановка проблеми. Дані Міністерства охорони здоров'я і Міжнародної організації праці свідчать, що смертність від травм і профзахворювань у світі посідає третє місце після серцево-судинних і онкологічних захворювань. Станом на 2014 р. в Україні понад 3,4 млн осіб працюють в умовах, що не відповідають санітарно-гігієнічним нормам. Особливо складними залишаються умови праці на виробництвах, пов'язаних із виділенням або вживанням теплових джерел. Впливу високих температур піддаються працівники на підприємствах будівельної індустрії (виробництво цегли, скла, полімерів).Мета статті ‑ обґрунтування вживання засобів для вимірювання теплового випромінювання на робочих місцях.Висновок. Установлено, що існуючі прилади вітчизняного і зарубіжного виробництва не дозволяють досліджувати умови праці на робочих місцях гарячих виробництв через значний діапазон теплових випромінювань від ‑50 до 24000 Вт/м2, що вносить значні похибки у виміри. Вперше встановлено, що для вимірювання як малих, так і значних за величиною теплових потоків необхідно застосовувати низькомежові, але високочутливі датчики, при цьому є можливість дозувати час доступу теплового потоку. Встановлено закономірності зміни відбивної здатності від виду матеріалу і довжини спектра випромінювання. На підставі проведених досліджень інтенсивності впливу надлишкового теплового випромінювання на робочі місця гарячих виробництв і температури нагріву поверхонь установлено розподіл максимуму довжини хвилі ІЧ-випромінювання, що підтверджується законом Голіцина-Віна. Запропоновано експрес-метод оцінювання відбивної здатності матеріалів, який дозволяє оперативно отримувати інформацію на початковій стадії досліджень і розробляти захисні засоби від ІЧ-випромінювання. Удосконалено стенд для проведення досліджень відбивної і проникної здатності матеріалів з урахуванням змінного кута падіння випромінювання, стану поверхні та її поляризаційної здатності, похибка, при цьому не перевищує 5‑7 %. Запропоновано новий підхід до створення ефективних захисних засобів з урахуванням спектральної складової ІЧ-випромінювання. Дана методика вимірюваннь дозволяє оцінити вплив на робочих місцях не лише первинних, а і вторинних джерел випромінювання. На основі проведеного аналізу існуючих вітчизняних датчиків для вимірювання інтенсивності теплових потоків розроблено вибір датчиків і досліджено їх характеристики з урахуванням впливу на них температурної складової., Problem statement. The data of the Ministry of Health and the International Labour Organization indicate that mortality from injuries and occupational diseases in the world ranked third after cardiovascular diseases and cancer. As of 2014 in Ukraine, more than 3,4 million persons are working in conditions that do not meet sanitary standards. Especially difficult are the conditions at work associated with the release or use of heat sources. Workers at the enterprises of the construction industry (production of bricks, glass, polymers) are exposed to influence of high temperature.Purpose Justification of the use of means for measuring thermal radiation in the workplace.Conclusion. It was found that the existing instruments of domestic and foreign production does not allow us to investigate working conditions at the workplace of hot productions due to a significant range of thermal radiation from 50 to 24,000 W/m2, which makes a significant error in the measurement. For the first time, it found that the measurement of both small and large heat flows low limit and highly sensitive sensors must be used, thus, dosing time of heat flow access. It was disclosed regularities of changes in the reflectivity of the material type and length of the radiation spectrum. Based on conducted researches of the excess thermal radiation intensity at workplaces of hot productions and steady temperature of the heating surface, it was identified distribution of maximum wavelength of the infrared radiation, supported by law of Golitsyn-Vin. It was proposed rapid method for assessing the reflectivity of materials, which allows to receive information at an early stage of research and development of protective equipment from infrared radiation. Stand for research reflection and transmittance of materials in response to changing the angle of incidence of the radiation, surface condition and its polarizing ability is improved, the error in this case, does not exceed 5 to 7%. New approach in the creation of effective protective measures, taking into account the spectral component of the infrared radiation is suggested. On the basis of the first conducted researches, this measurement technique allows to estimate the impact on the workplace, not only primary, but also secondary sources of radiation. Based on the analysis of existing domestic sensors to measure the intensity of the heat flows, the choice of sensors and study their characteristics, taking into account their influence on the temperature component, is made.

Сформулированы условия декомпозиции зоны интенсивного горения (ЗИГ) на три компонента – топочный газ, факельный континуум и твердое ограждение – и определены их границы. Разработана схема тепловых потоков и определены их параметры и характеристики с целью определения результирующего теплового потока на факельный континуум. Определены три режима радиационного теплообмена в ЗИГ: равномерно распределенный и направленные (прямой и косвенный), сформулированы условия их существования и основные особенности. The conditions of decomposition for intensive burning zone (IBZ) on three component (furnace gas, flame continuum, solid fencing) are formulated in this article. The limits of these components are defined. The scheme of heat flows is developed. The parameters of flows and their characteristics are defined. The purpose of that development is definition of resultant heat flow onto the flame continuum. Three regime of heat radiation in the IBZ are defined. That are uniformly distributed and directed (direct and indirect). The conditions of their existing and main features are formulated. Торопов Евгений Васильевич, профессор, д-р техн. наук, профессор кафедры «Промышленная теплоэнергетика», Южно-Уральский государственный университет; toropovev@susu.ac.ru. Осинцев Константин Владимирович, канд. техн. наук, доцент, заведующий кафедрой «Промышленная теплоэнергетика», Южно-Уральский государственный университет; osintcevkv@susu.ac.ru. E.V. Toropov, toropovev@susu.ac.ru, K.V. Osintsev, osintcevkv@susu.ac.ru South Ural State University, Chelyabinsk, Russian Federation

International audience; This paper investigates the influence of electrical and thermal human tissue parameters on the heating of a body illuminated by a millimeter plane electromagnetic wave. A stochastic approach is considered with a three-layer model of the body: it is found that the parameters of skin play a major role.

Günümüzde teknolojinin gelişmesi hızlanmaktadır, gelişen teknoloji ile birlikte günlük işlerimizi daha kolay hale getirecek ürünlerde piyasaya sürülmektedir. Bu ürünlerin teknik özellikleri de yeni teknolojiler ile birlikte gelişmektedir. Son kullanıcı tarafından yeni özellikler dikkate alınsa da aynı zamanda ürünlerin tükettikleri enerji de önemli görülmektedir. Oluşturulan tasarruf ve enerji verimliliği bilinci son zamanlarda daha çok düşük enerji tüketen ürünlerin piyasaya sürülmesi ihtiyacını doğurmuştur. Aynı zamanda gerek Avrupa Birliği yasaları gerekse sivil toplum örgütlerinin çalışmaları ile birlikte üreticiler üzerinde de ürünlerin enerji verimli hale getirilmesinde pozitif güç oluşturmaktadır. Enerji verimliliğinin artırılması başlığı altında gerçekleştirilen çalışmalar, enerji verimliliğinin etkili olduğu sistemlerde yenilikçi fikirlerin, uygulamaların ve optimizasyonların geliştirilmesi zorunluluğunu doğurmaktadır.Bu yüksek lisans tez çalışmasında ev tipi fırınlarda enerji verimliliğini arttırmak için parametreler belirlenmiştir. Bu parametrelerin enerji tüketimine etkisi deneysel çalışmalarla araştırılmıştır. Kurumsal bir yazılım olan fırın simülasyon programı ile deneysel çalışmalar karşılaştırılmıştır. Fırın simülasyon programındaki mevcut modüllerde geliştirme amaçlı çalışmalar yürütülmüştür.Tez çalışması yedi ana bölümden oluşmaktadır. Birinci bölümde çalışmaya başlama nedenleri, çalışmaların bitiminde hedeflenen sonuçlar, çalışmalarda izlenilen yöntem ve problemin kısıtları genel hatlarıyla açıklanmıştır.İkinci bölümde, söz konusu konu ile ilgili olarak gerçekleştirilen literatür araştırmaları ve çalışmanın literatüre katkısı gösterilmektedir. Yapılan literatür araştırması sonucunda daha önce yapılan çalışmaların çoğunlukla fırın enerji tüketimine etki eden parametreler ayrı ayrı olacak şekilde araştırılmıştır. Literatürde yer alan sayısal analiz çalışmalarında da tez çalışması kapsamında kullanılan simülasyona rastlanılmamıştır.Üçüncü bölümde fırın enerji tüketiminin tespit edilme yöntemi tarif edilmiştir. Enerji tüketiminin doğru ölçülmesi için gerekli kısıtlar anlatılmış ve standartta yer alan gerekli bilgiler aktarılmıştır. Dördüncü bölümde, tez çalışmasında kullanılan kurumsal bir yazılım olan fırın simülasyon programı tanıtılmıştır. Bu bölümde programın çalışma prensipleri anlatılmış ve kullanıcı arayüzü tariflenmiştir.Beşinci bölümde bu yüksek lisans çalışması çerçevesinde gerçekleştirilmiş deneysel çalışmalar yer almaktadır. Bu bölümde, test parametreleri ve parametrelere ait değerler yer almakta, bu parametrelerin enerji tüketimine etkisi belirlenmiştir.Altıncı bölümde, kurumsal bir yazılım olan fırın simülasyon programının geliştirilen modülleri anlatılmıştır ve arka planındaki matematiksel modeller aktarılmıştır.Yedinci ve son bölümde sonuçlar ve değerlendirmeler yer almaktadır. Development of technology is accelerating in todays. Product that makes easy our routine job is presented the market with developed technology. These products' technical specification is also developed with new technology. End user is considering both new technical specification and energy consumption of the product in the market. The generated energy saving and energy efficiency awareness is needed to arise recently low energy consumption products in the market. On the other hand, both Europian Union Law and civil society is working at the same purpose for decreasing of energy demand. So producers have to presented to the market energy efficient product with these positive pressure. Producers' research and development activities are focused to producing energy efficient product with new technology, innovative idea.In this study, for increasing the efficiency of domestic oven, the effective parameters were specified. The effects of these parameters on energy consumption were investigated by experimental studies. The experimental studies test results were compared with the corporate software `Domestic Oven Simulation Program`. Development activities of existing modules in Oven Simulation Program were conducted.This thesis study is composed of seven main chapters. In chapter one, motivation and aim of this study were explained in general terms as an introduction.In the second chapter, literature researches about thesis were outlined. As a result of this research were presented. After the literature research, it was noticed that, the research is generally represents the parameters that effects on energy consumption of domestic built-in oven separately. Furthermore, the oven simulation studied in this thesis was not observed in numerical analysis studies in literature.In the third chapter, the method used for determining the energy consumption of oven is described step by step. Required criteria for correct measurement of energy consumption was discussed and required information contained in the standard were shared. In the fourth chapter, the corporate software `Domestic Oven Simulation Program` was introduced. In this chapter, an operation principle of the software was described and user interface was characterized.In chapter five, experiments were done within this thesis were described. In this chapter, test parameters and values of these parameters were shown. The effects of these parameters on energy consumption were defined.In the sixth chapter, improved modules of corporate software `Domestic Oven Simulation Program` were discussed and mathematical models running behind the software were shared.In the final chapter, results of this study have been evaluated and suggestions have been proposed. 113

A numerical investigation of conjugate convection with surface radiation from horizontal channels with protruding heat sources has been carried out. The flow is assumed to be steady, laminar, incompressible, hydrodynamically and thermally developing. Air is considered as the working fluid. The geometric parameters such as spacing between the channel walls, size of the protruding heat sources, thickness of the substrate and the spacing between the heat sources are fixed. Results are presented to show the effect of parameters such as ReS, Gr S ∗ , kp/kf, ks/kf, ep and es on the fluid flow and heat transfer. A correlation for the non-dimensional maximum temperature is also developed using the method of asymptotic expansions.

In this study, apart from the other studies related to thermal comfort, it is combined that the fundamental equations given in the steady-state energy balance and the empirical relations expressing effects of the thermoregulatory control mechanisms of the body. In the first section of this simulation, body core temperature is calculated by using the equations expressing thermoregulatory control mechanism, the required skin temperature and sweat rate values. Variation of the calculated body core temperature is investigated with the activity level based on required skin temperature and sweat rate values. In the second section of the simulation, heat losses from the body (convection, radiation, evaporation, and respiration) and ratio of the each heat loss mechanism to total heat loss are calculated and discussed in detail.

The effect of chemical reaction, heat and mass transfer on boundary layer flow over a porous wedge with heat radiation has been studied in the presence of suction or injection. An approximate numerical solution for the steady laminar boundary-layer flow over a wall of the wedge in the presence of species concentration and mass diffusion has been obtained by solving the governing equations using numerical technique. The fluid is assumed to be viscous and incompressible. Numerical calculations are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow field is influenced appreciably by the chemical reaction, the buoyancy ratio between species and thermal diffusion and suction/injection at wall surface. Effects of these major parameters on the transport behaviors are investigated methodically and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, and concentration distributions, as well as the skin friction, rate of heat transfer and mass transfer. Comparisons with previously published works are performed and excellent agreement between the results is obtained. .

In this work, the possibility of combining the method of matched asymptotic expansions with Computational Fluid Dynamics (CFD), a technique called ACFD, has been explored, for a new class of problems that involve interaction of radiation with convection. A specific problem of natural convection with surface radiation from an open cavity has been considered to demonstrate the efficacy of the ACFD approach. The work clearly demonstrates the adequacy of the approach and it appears to be an attractive option in the analysis of such multi-mode problems in heat transfer. ? 2003 Elsevier Science Ltd.

In this dissertation a detailed research was conducted into the unsteady flow in a plane, dynamic, temperature and diffusion MHD boundary layer of an incompressible electrically conducting fluid in the presence of source/sink of heat, radiation heat, chemical reactions, suction/blowing of fluid through the porous contour, and the effect of buoyancy force and transverse homogeneous magnetic field in the model of non inductive approximation. The outer flow velocity, temperature and concentration on the body, as well as velocity of suction/blowing, are arbitrary, differentiable functions of the longitudinal coordinate and time. To study the movement of a conductive fluid around the body of arbitrary shape, a system of basic partial differential equations was derived, as well as a system of equations for dynamic, temperature and diffusion MHD boundary layers. The derived system of equations is of general nature, because these equations contain a number of different influences. Thus, dynamic equations include the impact of nonstationary force, pressure force, Lorentz force and buoyancy forces, which are the result of differences in temperature and concentration as well as the influence of porosity of the surface. Energy and diffusion equations contain the impact of the heat which is the result of the viscous friction, fluid expansion, Joule heat, brought or taken heat by the source/sink of heat, radiation heat, and the impact of source/sink impurities, resulting from a homogeneous first order chemical reaction. Furthermore, corresponding integral equations are derived for the dynamic, temperature and diffusion boundary layer, which also have a general character, since they are reduced, by rejecting certain individual members, to a series of simpler physical tasks. Based on the presentation and analysis of the papers in which MHD flow boundary layers are studied, the universal parametric method of generalized similarities of Professor Loitsianskii L.G. was used for the resolution of the obtained system of MHD equations derived in this dissertation. Following the introduction of the similarity variables for the transverse coordinate, for the stream function, for temperature and concentration, and a series of infinite sets of similarity parameters, dynamic and magnetic, suction/blowing, temperature and diffusion, buoyancy force of temperature and diffusion, chemical reaction parameters and the parameters of source/sink of heat, a system of universal MHD equations was derived. This system of equations represents a generalized system of MHD boundary layer equations, which, with the rejection of certain members, becomes like many previously known systems. The universal system of MHD equations, after the formulation of the initial boundary conditions, defining the functions FS and TS, was numerically solved in a two-parameter, repeatedly localized approximation. With the implementation of finite difference method, iteration and linearization of non-linear coefficient, the resulting algebraic system of finite difference equations addressed the gathering points of indirect network integration, using the tridiagonal method. The obtained universal results provide an analysis of the impact of introduced parameters on the development of dimensionless quantities of velocity, temperature, concentration, and on the development of integral and differential characteristics of the considered MHD boundary layers, that is, the ability to manage the boundary layers was demonstrated. By applying the results of universal equations and solving the momentum equation, the effects of heat and mass transfer in MHD boundary layers were discussed in the example of convection flow horizontal circular cylinder at a constant velocity values of sucking / blowing, and for several values of the parameters introduced and the number of similarities r P , c E and c S . At the end of the dissertation, the initial system of equations of MHD dynamic, temperature and diffusion boundary layer was solved using a new approach, which can, to some extent, be divided into new methods for solving MHD boundary layer equations. Thus obtained system of equations, which also has the characteristic of universal approach, was applied to consider the effects of mass and heat transfer in mixed convection task, and the convection flow past a horizontal circular cylinder. Flow analysis was performed via the introduced dimensionless quantity for the class of deceleration and acceleration flow. The results of typical values of boundary layers, as well as the dimensionless function of the ratio of velocity, temperature and concentration, are shown graphically and confirm the conclusions on the expected tendencies of changes of these values in relation to the presence of different influences.

The paper proposes assessment of working conditions for operators HDTV ous authors developed a technique by which revealed the "hidden" sources of additional exposure , showing the real parameters of the production environment . Based on the research results revealed that the operator exposed to intense thermal radiation more 350V t/m 2 (exposure to 25 % of body surface) over 2/3 of the working period , which should be considered when determining the work and rest in accordance with applicable health standards ., В статье предложена оценка условий труда операторов ТВЧ по разработанной авторами методики, с помощью которой были выявлены скрытые источники дополнительного облучения, отображающие реальные параметры производственной среды. На основе полученных результатов исследований установлено, что оператор подвергаются интенсивному тепловом у облучению более 350В т/м2 (облучение до 25% поверхности тела) более 2/3 рабочей смены, что необходимо учитывать при определении режима труда и отдыха в соответствии с действующими гигиеническими нормативами., У статті запропонована оцінка умов праці операторів ТВЧ по розробленою авторами методики, за допомогою якої були виявлені «приховані» джерела додаткового опромінення, що відображають реальні параметри виробничого середовища. На основі отриманих результатів досліджень встановлено, що оператор піддаються інтенсивному тепловому опроміненню більш 350В т/м2 (опромінення до 25 % поверхні тіла) більш е 2/3 робочої зміни, що необхідно враховувати при визначенні режиму праці та відпочинку відповідно до діючих гігієнічним и нормативами.

Date of Conference: 6-9 Oct. 2014 Conference name: 44th European Microwave Conference, 2014 This paper presents a high power amplifier at K-band (20.2-21.2 GHz). The AlGaN/GaN CPW MMIC amplifier is realized with 0.25 μm HEMT process on 2-inch semi-insulating SiC substrate. The amplifier has a small signal gain over 20 dB for Vds=15V and measured output power of over 31 dBm at 20.2 Ghz. PAE of the amplifier is around 22% for desired frequency band. Initial radiation hardness tests indicate a suitable stability of the technology in space. © 2014 European Microwave Association.

Подведены некоторые итоги экспериментального и численного моделирования вихревых топочных процессов и эмиссии токсичных выбросов при сжигании низкокачественных углей в парогенераторе с вихревой топкой Н.В. Голованова. Исследования турбулентной аэродинамики вихревых топок на физических и математических моделях дали возможность установить их основные габаритно-компоновочные соотношения, а результаты моделирования лучистого теплообмена, горения топлива, химкинетики образования токсичных выбросов явились базовой информацией по определению их энергоэкологических параметров. Выполненный на современном уровне комплекс научно-исследовательских работ позволил выработать рекомендации по дальнейшему усовершенствованию конструктивных и режимных характеристик парогенератора с вихревой топкой на березовском угле Канско-Ачинского бассейна, а также лег в основу проектов реконструкции котла ТП-87 на кузнецких углях и БКЗ-320 на березовском угле. The author has summed up the results of experimental and numerical simulation of vortex combustion processes and emission of toxic discharge at combustion of low-grade coal, in particular, in the steam generator with a vortex furnace of N. V. Golovanov from scientific production association CKTI, with which IT SB RAS has long scientific cooperation. The study of turbulent aerodynamics of the vortex furnaces with the use of physical and mathematical models made it possible to determine their main dimension and assembling relations, and simulation of radiant heat transfer, fuel combustion, and chemical kinetics of toxic emission formation was the basic information for determining their energy and ecological parameters. A set of modern level research work resulted in recommendations for further improvement of design and operation characteristics of the steam generator with a vortex furnace on Berezovsk coals of Kansk-Achinsk deposit, and formed the basis for the projects of TP-87 boiler reconstruction at Novokuznetsk TPP on Kuznetsk coals and BKZ -320 (Barnaul Boiler Plant) and Novosibirsk TPP-3 on Berezovsk coals.

International audience; Radiative heat transfer calculations are conducted in two laboratory-scale axisymmetric methane pool fires generated on a burner of 038 m diameter with heat release rates (HRR) of 34 and 176 kW by using the `exact' Line-By-Line (LBL) method, the narrow band correlated-k (NBCK) model, the full-spectrum correlated-k (FSCK) model, the multi-scale full-spectrum k-distribution (MSFSK) model, and a grey wide-band model (WBM). For each radiative model the corresponding absorption coefficients for carbon dioxide, water vapor, carbon monoxide and methane are generated from the same high-resolution spectroscopic database. Model results show that the contribution of carbon monoxide can be neglected whereas that of methane increases with HRR. In addition, the grey approximation for soot holds for these weakly sooting flames. Comparisons with LBL solutions show that WBM fails to predict accurately the radiative heat transfer through the fuel rich core. The FSCK model presents the best compromise in terms of accuracy and computational efficiency for the 34 kW pool fire. However, significant discrepancies are observed for the 176 kW pool fire where the strong attenuation of radiation by methane invalidates the `correlated' assumption of the absorption coefficient. MSFSK and NBCK models provide very accurate predictions, with the MSFSK model being more efficient when overlap parameters are tabulated as a function of temperature and composition. (C) 2014 Elsevier Masson SAS. All rights reserved.

Simulations and experiments have been conducted to study the effect of radiative cooling on natural convection in a horizontal layer of a participatingmedium enclosed between isothermal opaque wall and radiatively transparent wall and exposed to a cold background. The study is of relevance to a nocturnal boundary layer under clear and calm conditions. The focus of the study is to capture the onset of convection caused by radiative cooling. The experiments have been designed to mimic the atmospheric radiative boundary conditions, and hence decoupling convection and radiation boundary conditions. Planck number Pl and optical thickness of the layer ?H are the two important parameters that govern the interaction between radiation and convection. The radiation-convection coupling is a strong function of length scale. Convection sets up within first few seconds for all the experiments. Strong plume like convection is observed for the experimental conditions used in the present study. Both simulations and experiments confirm that radiative cooling increases substantially with decrease in emissivity of the bottom wall. Radiative cooling is strongly influenced by the nongray nature of the participating medium, especially when strong emission from the medium escapes to space, in the window region of the atmosphere. Accurate representation of radiative properties is critical. Linear stability analysis of onset of convection indicates that radiation stabilizes convection as Pl decreases. The observations are similar to the case of Rayleigh B�nard convection in a radiating gas. However, for both experimental and numerical conditions, the observed Rayleigh numbers are much greater than the critical Rayleigh number. To conclude, the role of radiation is to drive and sustain convection in the unstable layer. � 2014 AIP Publishing LLC.

The heat transfer across an air-filled partitioned square enclosure is studied experimentally using a differential interferometer. The partition was located centrally inside the enclosure, parallel to the two isothermal differentially heated vertical walls, and extended the full height of the enclosure. The top and bottom horizontal walls of the enclosure were maintained adiabatic. A parametric study has been carried out using different partitions, focusing attention on the effect of partition thermal resistance as well as the interaction of surface radiation and natural convection, and on the total heat transfer between the vertical walls, inside the enclosure. Correlations, valid for the laminar range, are proposed.The heat transfer across an air-filled partitioned square enclosure is studied experimentally using a differential interferometer. The partition was located centrally inside the enclosure, parallel to the two isothermal differentially heated vertical walls, and extended the full height of the enclosure. The top and bottom horizontal walls of the enclosure were maintained adiabatic. A parametric study has been carried out using different partitions, focusing attention on the effect of partition thermal resistance as well as the interaction of surface radiation and natural convection, and on the total heat transfer between the vertical walls, inside the enclosure. Correlations, valid for the laminar range, are proposed.

We introduce briefly some nonlocal models for heat transfer in conducting and radiating media. The goal is to give an idea of the general mathematical structure and related existence results for such models.

The reliable results of an insulated oval duct considering heat radiation are obtained basing on accurate oval perimeter obtained by integral method as well as one-dimensional Plane Wedge Thermal Resistance (PWTR) model. This is an extension study of former paper of insulated oval duct neglecting heat radiation. It is found that in the practical situations with long-short-axes ratio a/b 43% at t/R2=0) and thin-insulated (E>4.5% while t/R2, {"references":["F. J. Schulenberg, Finned elliptical tubes and their application in\nair-cooled heat exchanger, Transactions of the ASME 88, 1966,\npp.179-190.","T. Ota, H. Nishiyama and Y. Taoka, Heat transfer and flow around an\nelliptic cylinder, International Journal of Heat and Mass Transfer, 27-10,\n1984, pp.1771-1779.","Y. Chen, M. Fiebig and N. K. Mitra, Heat transfer enhancement of finned\noval tubes with staggered punched longitudinal vortex generators,\nInternational Journal of Heat and Mass Transfer, 43, 2000, pp. 417-435.","M. K. Kim , J. S. Shin, and C. W. Bullard, Heat Transfer and Pressure\nDrop Characteristics During R22 Evaporation in an Oval Micro-fin Tube,\nJournal of Heat Transfer, 123-2, 2001, pp. 301-308.","J. S. Leu, M. S. Liu, J. S. Liaw, and C. Chuan, A numerical investigation\nof louvered fin-and-tube heat exchangers having circular and oval tube\nconfigurations, International Journal of Heat and Mass Transfer, 44,\n2001, pp. 4235-4243.","S. Tiwari, D. Maurya, G. Biswas, and V. Eswaran, Heat transfer\nenhancement in cross-flow heat exchangers using oval tubes and multiple\ndelta winglets, International Journal of Heat and Mass Transfer, 46, 2003,\npp.2841-2856.","A. Hasan, and K. Siren, Performance investigation of plain circular and\noval tube evaporatively cooled heat exchangers, Applied Thermal\nEngineering, 24, 2004, pp.777-790.","J. E. O'Brien, M. S. Sohal, and P. C. Wallstedt, Local heat transfer and\npressure drop for finned-tube heat exchangers using oval tubes and vortex\ngenerators, Journal of Heat Transfer, 126-5, 2004, pp. 826-835.","K. L. Wong, W. L. Chen, T. L. Hsien, and H. M. Chou, The critical heat\ntransfer characteristics of an insulated oval duct, Energy Conversion and\nManagement, 51, 2010, pp.1442-1448.\n[10] H. M. Chou, and K. L. Wong, Heat Transfer Characteristics of an\nInsulated Regular polygonal duct by Using a Wedge Thermal Resistance\nModel, Energy Conversion and Management, 44, 2003, pp.629~645.\n[11] K. L.Wong, H.M. Chou, and Y. H. Li, Complete Heat Transfer Solutions\nof an Insulated Regular Polygonal duct by Using a PWTR Model, Energy\nConversion and Management, 45, 2004, pp.1705~1724.\n[12] K. L. Wong, T. L. Hsien, P. Richards, and B. S. Her, The reliable simple\none-dimensional 64-CPWTR model applied to the two-dimensional heat\ntransfer problem of an insulated rectangular duct in an air conditioning or\nrefrigeration system, International Journal of Refrigeration, 28, 2005,\npp.1029-1039.\n[13] K. L. Wong, A. Al-Jumaily, and T. H. Lu, Reliable one-dimensional\nCPWTR models for two-dimensional insulated polygonal ducts,\nInternational Journal of Refrigeration, 30, 2007,pp. 254-266.\n[14] W. L. Chen , K. L. Wong, T. L. Hsien, C. T. Huang, Reliable\none-dimensional approximate solution of insulated oval duct, Energy\nConversion and Management, Volume 49, Issue 8, 2008, pp. 2214-2224\n[15] T. L. Hsien, K. L. Wong, and S. J. Yu, The inaccuracy of heat transfer\ncharacteristics of insulated and non-insulated circular duct while\nneglecting the influence of heat radiation, Energy Conversion and\nManagement, Volume 50, Issue 11, 2009, pp. 2856-2863.\n[16] K. L. Wong, M. T. Ke, and S. S. Ku, The log mean heat transfer rate\nmethod of heat exchanger considering the influence of heat radiation,\nEnergy Conversion and Management, Volume 50, Issue 11, 2009, pp.\n2693-2698.\n[17] K. L. Wong, J. L. Salazar, L. Prasad, and W. L. Chen, The inaccuracy of\nheat transfer characteristics for non-insulated and insulated spherical\ncontainers neglecting the influence of heat radiation, Energy Conversion\nand Management, 52, 2011, pp.1612-1621.\n[18] H. B.William, CRC standard mathematical table, 25th edition, Chemical\nRubber Pub., Cleveland, 1978, pp.14\n[19] J. P. Holman, Heat transfer, Eighth SI Metric Edition, McGraw-Hill Inc.,\n2001, pp.7~39 and pp.638~642."]}

Bu yüksek lisans tezinde, baca, taze hava için conta açıklıkları ve nem kaynağı bulunan evsel bir fırın içerisindeki türbülanslı, daimi olmayan, ışınımla ısı transferinde bulunan akış sayısal olarak incelenmiş ve sayısal sonuçlar da deneysel sonuçlar ile doğrulanmıştır. Sayısal çalışmalar ticari Hesaplamalı Akışkanlar Dinamiği yazılımı olan Fluent ile yapılmış ancak problemin kompleks yapısı nedeniyle zamana bağlı sınır şartı verilebilmesi, transport denklemlerine kaynak terimi eklenmesi için C programlama dilinde UDF yani Kullanıcı Tarafından Tarif Edilen Fonksiyon yazılmıştır.Çalışmanın ilk aşamasında, kavite içerisindeki havanın nemine bağlı olarak farklı iki ışınım modeli (Radiosity-Irradiosity ve Discrete Ordinates) denenmiş ve sonuçları karşılaştırılmıştır. Deneysel sonuçlar ile doğrulanan bu sayısal sonuçlar temel alınarak, ileriki aşamalarda çalışmalarda ışınım modellenmiştir. Sonraki aşamada ise, kavite içerisinde bir nem kaynağı bulunmadığı durum için sayısal çalışmalar gerçekleştirilmiş, deneyler ile doğrulanmış ve kavite içerisindeki akış detaylıca incelenmiştir. Nem kaynağı olmadan yapılan bu çalışmalar, nem kaynağı olan çalışmalara hazırlık çalışması olmuş olup ayrıca kavite içerisindeki momentum ve ısı transferini iyileştirmek için sunulmuş bazı önerilere ilk adım olmuştur.Üçüncü aşamada da, nem kaynağının bulunduğu durum için sayısal çalışmalar yapılmış. Enerji ve su buharı transport denklemlerine de kaynak terimleri eklenerek akış modellenmiştir. Bu tez çalışmasının son aşamasında da evsel fırının pişirme performansının iyileştirilmesi için düşük yayma oranlı yüzeyler kullanılmıştır. Sayısal sonuçlarda görülen iyileştirme deneysel olarak da gözlemlenmiştir. In this M.Sc. thesis, non-stationary, turbulent flow interacting with radiative heat transfer in a domestic oven with chimney and gasket openings has been numerically investigated. Numerical results have been validated by experimental results.Numerical studies have been performed by the commercial Computational Fluid Dynamics programme Fluent but due to the complexity of problem, UDF's in C programming language have been written to define transient boundary conditions and source terms to transport equations.The first part of study covers a comparative study based on the mass fraction of water wapour in cavity has been carried out for two different radiation models. In further studies, modeling of radiation has been conducted by taking the consideration of these results which are validated by experiments.In the next part of the study, numerical studies have been performed for the case of without moisture source. Numerical results have been validated and the flow within the cavity has been investigated in details. The numerical studies for the case without moisture source provided a basis for the studies with moisture source and enhancement proposals for energy efficieny in cavity.In the third part, source terms have been added to energy equation and species transport equation by the means of UDFs and numerical studies have been performed for the case with moisture source.At the final stage, in order to improve the baking performance of domestic oven, low emissivity surfaces have bene used. The enhancement provided by numerical studies have also been observed by experiments. 107

Literatürde üzerinde çok fazla çalışma yapılmayan bir konu olan ışınımla ısı geçişi, bilhassa yüksek sıcaklıklara çıkıldığında baskın bir mekanizma haline gelmekle birlikte, özellikle enerji verimliliğinin azaltılması açısından önemli bir bileşen durumundadır. Bu çalışma kapsamında, kapalı hacimler içerisindeki ışınımla ısı geçişi hakkında yapılan teorik arka plan araştırması ışığında geliştirilen modeller uygulama alanı olan ev tipi ankastre fırınlar üzerinde incelenmiştir. Tez çalışmasının ilk bölümünü oluşturan giriş bölümü boyunca ışınımla ısı geçişini oluşturan temel kavramlar tanıtılmıştır. Yüzey ışınımıyla ilgili olarak sunulan kavramsallaştırmalar ideal yüzeyleri tanımlamakta kullanılan siyah cisimleri tarif ettikten sonra, gerçek (gri) yüzeyler üzerinde durmuştur. Gri yüzeyler arasındaki yüzey ışınımını çözümlemekte kullanılan yöntemlerden bazıları sıralandıktan sonra, gaz ışınımı mekanizması ile ilgili temellerden bahsedilmiştir.İkinci bölümde ise çalışmaların yürütüldüğü laboratuar olan `Yüksek Sıcaklıkta Isı Geçişi Laboratuarı? bünyesinde yürütülen 111M048 numaralı TÜBİTAK 1001 projesi kapsamında yapılan çalışmalarla eş zamanlı olarak yürütülen tez çalışması esnasında ele alınan uygulama olan ev tipi ankastre fırının standart hale getirilmiş enerji tüketim deneylerinin yapıldığı tesisat tanıtılmıştır. Bölümü takiben, mevcut ev tipi fırın üzerinde yüzey ışınımı etkinliği incelenmiştir. Yapılan inceleme ilk olarak fırının boş olması durumunda, sonrasında ise standart deneylerde yiyeceği modelleyen tuğlalı hal için sunulmuştur. Bu incelemeler mevcut fırında yapılacak iyileştirmeler için zemin oluşturmaktadır. İlerleyen iki alt başlık kapsamında ışınımla ısı geçişini doğrudan etkileyen iki parametre olan şekil faktörü ve yayma oranı incelenmiştir. Şekil faktörü incelemeleri esnasında ilk olarak kavite hacmi üzerinde değişiklik yapılmış fırın ele alınmış ve enerji tüketimi değerleri ile ışınımla ısı geçişi performansı ilişkilendirilmiştir. Sonrasında ise, standart deneylerde merkezde yer alan tuğla farklı pozisyonlara yerleştirilerek sıcak yüzeyler ile yük arasındaki etkileşim mercek altına tutulmuştur. Yayma oranı ile ilgili olarak yapılan çalışmalar ilk olarak literatürde de üzerinde sıkça durulan `düşük yayma katsayılı fırın? üzerinde yoğunlaşmıştır. Destekçi kuruluş tarafından temin edilen bir prototip üzerinde yapılan incelemeler göstermiştir ki düşük yayma oranına sahip fırın yüzey sıcaklıklarını düşürmekte ve dolayısıyla ısıl kayıpların önüne geçmektedir. Bu bölümde yapılan incelemeler ışığında elde edilen sonuçlar bir sonraki bölümde düşük yayma katsayılı fırın tasarımına eleştirel olarak bakılmasının önünü açmıştır. Yapılan analizler sonucunda ışınım yayan yüzeylerin yüksek, ışınım toplayan yüzeylerin ise düşük yayma katsayısına sahip olduğu hibrid tasarımların performansı artıracağı öngörülmüştür. Yapılan öngörüler tasarlanan deney düzeneğinde test edilmiş ve öngörülerle paralel sonuçlar elde edilmiştir.Tez çalışmasının son bölümünde ise içeriğinde su buharı bulunduran bir ortam olan kavite hacmi içerisindeki gaz ışınımı mekanizmasının etkileri üzerinde durulmuştur. İlk olarak ortalama yayma katsayısını belirleyen mühendislik yaklaşımı sayesinde fırın içerisindeki gaz ışınımının mertebesi ortaya konmuştur. Elde edilen sonuçlar bu mertebenin hiç de azımsanamayacak düzeyde olduğunu göstermektedir. Son olarak ise, gaz ışınımı mekanizmasını göz önüne alan bir sayısal model olan Discrete Ordinates (DO) yöntemi ile yüzey ışınımını gözeten Surface to Surface (S2S) sayısal modelleri nemli hava içeren bir kapalı hacim içerindeki doğal taşınımın modellenmesinde kullanılmış ve elde edilen sonuçlar arasında karşılaştırmaya gidilmiştir. Radiation heat transfer, eventhough is not a popular subject in literature, is a dominant heat transfer mechanism especially in high temperatures thereby improving energy efficiency. In this study, models provided by theorical background on radiation heat transfer in enclosures applied on household built-in ovens.In the firt section of the thesis, the main concepts that constitute radiation heat transfer is introduced. Surface radiation has been divided into to sections: at first idealized surfaces that called `black body? than the real ones (gray surfaces). Here, the methods that are used to solve surface radiation between gray surfaces before mentioning fundamentals about gas radiation. The second section is referred to the application of the study and the experimental setup in `High Temperature Heat Transfer Laboratuary? that the studies carried with the 1001 project 111M048 supported by TUBITAK. Afterwards, the surface radiation in the original oven is investigated. At first, the cavity set empty, than the brick is been placed in the center to be studied to provide the basis for improvements. In the following two subtitle, the radiation exchange factor and emissivity are determined as parameters. At first, the prototype that the size of the cavity is changed is investigated to determine the effect of exchange factor relationship. Moreover, the standart position of the test brick is set to different locations to link energy consumption of the oven and position of the brick. As it is noticed that the energy resources of our planet is alarming, the researches have started to give their attention to decrease the consumptions. For that purpose, the household appliances are one of the important field to focus. Thanks to these studies, the efficiency levels are improving. During 90?s the energy efficiency of a domestic oven was in approximetely 12-13%, nowadays the levels are lift up to 25%. Nevertheless, the standardization of the energy consumption experiments has become to be identified more detailed by the commities. European Committee for Electrotechnical Standardization (CELENEC) has announced in 1996 and, give its final version in 2005 as EN 50304 for the energy consumption experiments for domestic ovens.The complexity of analytical solution of radiation problems have pave the way for numerical solutions beside them. Radiosity Irradiosity Method (RIM), Discrete Transfer Method (DTM), Discrete Ordinate Method (DOM), Finite Volume Method and Monte Carlo Method are some of the most popular numerical methods in radiation problems. Monte Carlo Method, which is used in this study, is a statistical method that models a physical problem. Markhov chain and random numbers set a base for this method which gives rapid results. Monte Carlo aprroach has been adapted to radiation problems by Howell . These models have been used oftenly in industrial cases. These studies and a large literature summary are present in. On the other hand, numerical studies in domestic ovens have been conducted by various studies including the effects of radiation in addition to natural convection.In the present work, such an analysis including the effects of radiation and convection in domestic ovens has been performed by the means of S2S radiation model and k-epsilon turbulence model. Three different enclosure models have been designed in a built-in oven in order to improve the efficiency of radiation. The main goal was to improve efficiency by improving the contribution of view factor effect. The experimental study has been carried out in order to compare the models from the view points of energy consumption and cooking time. By the way, the computational study focused on the mechanism of heat transfer in cavity.During the study on the emissivity of the oven the concept `low emissivity oven? examined at first. The studies carried on a prototype supplied by supporter firm that showing reducing emissivity reduces temperature gradient thus decreasing heat loses. The results obtained by this section pave the way for a critical view on the concept. Therefore, it has been stated as a projection that the emitter plates should be high and collector plates should have low emissivity. The projection has been validated by experimental results that the energy consumption can be reduced so.Finally, in the last section of the thesis, the effect of moist air in the cavity on the gas radiation mechanism is being searched. Firstly, by the view of engineering aspect the order of the gas radiation in the oven is stated. Results have shown that gas radiation cannot be neglected. Secondly, two different numerical models one considering gas radiation (Disrete Ordinates) the other only surface radiation (S2S) are compared for a cavity that filled with moist air. Due to many engineering applications, like ovens, combustion chambers, condensers etc. there are many researches devoted to coupled heat and mass transfer in enclosures. For high temperature applications, radiative heat transfer should be taken into account hence there are also some paper covered heat/mass transfer with radiation. However, it is possible to claim that radiative heat transfer plays a non-negligible role in heat transfer even in very low temperature differences .In addition to computational studies, including radiative heat transfer or not, it is also an important factor that whether radiation is treated as a surface phenomenon or a whole-domain phenomenon. A numerical study on this issue has shown that it is possible to obtain completely different results by using different treatments. Therefore, for the ones who are willing to conduct a numerical study on the radiation phenomena, it is vital to determine which type of treatment would be sufficient to obtain an agreement between experimental and numerical results. Briefly the object of this study is to investigate the coupled heat/mass transfer with radiation in an enclosure and proposing a limitation for participating medium assumption with a comparative study on two radiation models. In this study, the governing equations are solved by means of finite-volume approach with a commercial CFD program (FLUENT). All equations are temporally discretized by first order implicit time integration method. An implicit scheme may provide unconditionally stable numerical solution, however the time-steps are selected under the consideration of turbulent temporal scales. Previous studies in turbulent buoyant flows in enclosures have shown that under convenient discretization methods and grid resolutions, it is possible to obtain satiSfying numerical results which are on agreement with experimental results. Therefore, realizable k-? turbulence model is chosen for the modeling of turbulence. Convective terms of transport equations are discretized by upwind scheme whereas the diffusion terms are discretized by standard central differencing. Velocity and pressure are coupled by the means of SIMPLE method. Ideal gas formulation has been used for the variation of density.For modeling of radiation, two different models have been used. One of them is well-known Radiosity - Irradiosity Method (RIM) which can be used to account radiation exchange in an enclosure with gray surfaces. Radiation exchange with surfaces is accounted by a geometric function ?view factor? which can be determined by a ray tracing or a hemicube method. In this study, RIM method has been implemented on the basis of view factors calculated by ray tracing method. However, when the medium is participating, RIM model, which treats radiation as a surface phenomena, fails to provide a numerical result that would be validated by experimental results. Therefore, Discrete Ordinates Method (DO) which considers the fluid within the cavity as radiation exchanging domain. RTE is solved by means of finite volume techniques. RTE can be solved by using finite volume discretizations not only for structured meshes but also for unstructured meshes. In this study, radiation intensity field is obtained on a structured mesh. 103

Given the increased radiosensitivity of children, our aim is to evaluate the risk of solid cancer and leukaemia associated with long-term medical exposure received during childhood. Two cohort studies were performed by the Laboratory of epidemiology, Institute of Radiation Protection and Nuclear Safety (IRSN). The first one, the "Cohort Child Scanner" includes all children born after 01/01/1995 and exposed to ionising radiation during medical scans performed between 2000 and 2013. The other one focuses on children exposed to ionising radiation during interventional cardiology procedures before the age of 10 years between 2000 and 2013. For each cohort, a retrospective assessment of individual exposure will be conducted by the Medical Radiation Protection Expertise Unit of the IRSN. A passive follow-up in terms of solid cancer and leukaemia will be carried out using data from paediatric cancer registries and from mortality data. The "Cohort Child Scanner" consists of over 80 000 children and is part of the European project EPI-CT, which will gather data from 9 national cohorts. The cohort of children in interventional cardiology will include more than 8 000 children. These cohort studies, with extended follow-up, will contribute to the assessment of the health impact of radiation exposure received during childhood. © 2012 EDP Sciences.; Abstract Given the increased radiosensitivity of children, our aim is to evaluate the risk of solid cancer and leukaemia associated with long-term medical exposure received during childhood. Two cohort studies were performed by the Laboratory of epidemiology, Institute of Radiation Protection and Nuclear Safety (IRSN). The first one, the “Cohort Child Scanner” includes all children born after 01/01/1995 and exposed to ionising radiation during medical scans performed between 2000 and 2013. The other one focuses on children exposed to ionising radiation during interventional cardiology procedures before the age of 10 years between 2000 and 2013. For each cohort, a retrospective assessment of individual exposure will be conducted by the Medical Radiation Protection Expertise Unit of the IRSN. A passive follow-up in terms of solid cancer and leukaemia will be carried out using data from paediatric cancer registries and from mortality data. The “Cohort Child Scanner” consists of over 80 000 children and is part of the European project EPI-CT, which will gather data from 9 national cohorts. The cohort of children in interventional cardiology will include more than 8 000 children. These cohort studies, with extended follow-up, will contribute to the assessment of the health impact of radiation exposure received during childhood. Key words: epidemiology / radiation / children / medical exposure / cancer © EDP Sciences, 2012 Table of Contents Article AbstractPDF (210.6 KB)References Metrics Show article metrics Services Same authors - Google Scholar - EDP Sciences database - PubMed Recommend this article Send to my Kindle Download citation Related Articles L’optimisation avec réduction de l’exposition du patient lors des procédures en scanographie TDM/TAP : cas des patients cancéreux au nord du Maroc Radioprotection 2018, 53(2), 115–122

A TPV-system consists of a hot surface emitting heat radiation on a solar cell with a narrow bandgap. A unit consisting of a boiler and a TPV-system has been constructed for testing of the performance of TPV cells. The emitter is heated by a fuel consisting of RME-oil. The radiation is collected and concentrated through two reflecting cones formed like a Faberge-egg, with an edge-type optical filter between the cones. The Faberge-egg is treated with electro-polishing in order to obtain a high reflectance of radiation. The edge filter transmits radiation of short wavelengths towards the solar cells and reflects long wavelengths back to the emitter. This increase the temperature of the emitter to prevent the TPV-cells to be overheated. The construction made was working as expected and can be used for further experiments. The performance of the TPV-cells were however very poor because of a low emitter temperature. The main problem was to obtain a good heat transport from the flame to the emitter. It is required that the emitter temperature is considerably increased for justifying a continued work on TPV-systems in combination with boilers.

[No abstract available]

El calor de radiación depende de la emisividad del cuerpo y de la temperatura a la que éste se encuentra. En el caso de los productos que se generan por combustibles líquidos, se considera la emisividad luminosa, causada por la flama, y la emisividad no luminosa, producida por los gases. Se establece una comparación entre el cálculo de la emisividad no luminosa descrita por Michael Modest en su libro Radiative heat transfer y los cálculos propuestos por Prabir Basu, Cen Kefa y Louis Jestin, en su libro Boilers and burnes, design and theory. Además, se contrasta el total de la energía de radiación calculada por ambos métodos. The heat radiation emissivity is characterized by having the body and the temperature at which this is. In the case of products generated by liquid fuels should be considered luminous emissivity caused by the flame, and no light emissivity by gases. A comparison between the calculation of the non-luminous emissivity described by Michael Modest in his book Radiative heat transfer and the calculations proposed by Prabir Basu, Cen Kefa y Louis Jestin in their book Boilers and burnes, design and theory, is established. Furthermore, the total radiation energy calculated by both methods contrasts.

In this paper, a temperature field described by a fractional heat subconduction equation with a boundary temperature control is considered. The foundation of an optimal boundary control to take the thermal stress under constraints is purposed. Problem is formulated in terms of Caputo time-fractional derivative. The solution is found by applying Laplace and finite Fourier sine transforms. In addition, linear approximation is used to get the numerical solution. Consequently, the graphics of numerical results obtained by MATLAB are illustrated.

In this work a flame-spread model is formulated in three dimensions to simulate opposed flow flame spread over thin solid fuels. The flame-spread model is coupled to a three-dimensional gas radiation model. The experiments [1] on downward spread and zero gravity quiescent spread over finite width thin fuel are simulated by flame-spread models in both two and three dimensions to assess the role of radiation and effect of dimensionality on the prediction of the flame-spread phenomena. It is observed that while radiation plays only a minor role in normal gravity downward spread, in zero gravity quiescent spread surface radiation loss holds the key to correct prediction of low oxygen flame spread rate and quenching limit. The present three-dimensional simulations show that even in zero gravity gas radiation affects flame spread rate only moderately (as much as 20% at 100% oxygen) as the heat feedback effect exceeds the radiation loss effect only moderately. However, the two-dimensional model with the gas radiation model badly over-predicts the zero gravity flame spread rate due to under estimation of gas radiation loss to the ambient surrounding. The two-dimensional model was also found to be inadequate for predicting the zero gravity flame attributes, like the flame length and the flame width, correctly. The need for a three-dimensional model was found to be indispensable for consistently describing the zero gravity flame-spread experiments [1] (including flame spread rate and flame size) especially at high oxygen levels (>30%). On the other hand it was observed that for the normal gravity downward flame spread for oxygen levels up to 60%, the two-dimensional model was sufficient to predict flame spread rate and flame size reasonably well. Gas radiation is seen to increase the three-dimensional effect especially at elevated oxygen levels (>30% for zero gravity and >60% for normal gravity flames). � 2012 Copyright Taylor and Francis Group, LLC.

2 renkli pirometre, temassız sıcaklık tespitinde kullanılan, radyasyon, optik yasalarına ve cisimlerin yayınırlık katsayılarına dayanan optik bir ölçüm cihazı olup hedef objenin yüzeyinden iki farklı dalga boyunda ölçülen monokromatik ışınım sinyallerinin oranı yardımı ile sıcaklık ölçümü gerçekleştirilmesi temeline dayanır. Gazlaştırma ve yanma işlemlerinde pirometre kullanımı, hareket halinde küçük objeleri ölçebilme kabiliyetinden ötürü oldukça yaygındır. Hareket halinde veya durgun katı yakıt parçacıklarının tek tek yüzey sıcaklıklarının ölçülüp, pirometrik yarıçaplarının (sabit yayınırlık ve küresel şekil kabulü) hesaplanması amacıyla pirometre cihazının kurulumu gerçekleştirilmiştir.Reaksiyon halindeki katı yakıt parçacığının yüzeyinden neşredilen ışınım, bir optik düzenek (lensler, optik fiber, ve filtreler) yardımı ile algılanıp filtrelenir. Dürbün prensibi ile çalışan bir optik prob aracılığı ile sinyal optik probun öbür ucuna sabitlenen optik fiber girişine odaklanır. Daha sonra optik fiber, ana ve referans olmak üzere iki kanala ayrılır. Referans kanalında sinyal, lensler yardımı ile kızılötesi dalgaboyunda çalışan foto algılayıcıya iletilir. Ana kanala ulaşan sinyalin ise bir kısmı görünen (kırmızı) dalgaboyunu hissetme yetisi olan foto algılayıcıya yansıtılırken sinyalin geri kalanı yine kızılötesi bir foto algılayıcıya yansıtılmadan iletilir. Foto algılayıcılara varmadan sinyaller filtre elemanları ile belli ve dar dalgaboylarında filtrelenir. Filtreleme sonrasında ışınım değerleri silikon foto algılayıcılarda algılanır ve elektrik sinyalleri üretilir. Bu elektrik sinyalleri çok küçük büyüklüklerde olduklarından, üretilen bu elektrik sinyalleri ölçüm kolaylığı için kuvvetlendirilir. Kuvvetlendirilen bu sinyaller analog formdan, dijital formda çevrilerek bilgisayara aktarılır. Bilgisayarda ise ölçümler Lab-view 9.0 programında geliştirilen yazılım yardımı ile sonuçlar kayıt edilir ve elde edilen veriler amaca yönelik olarak işlenir.Kurulumu tamamlandıktan sonra, uygulamaya konmadan önce pirometre cihazının kalibre edilmesi gerekmektedir. Bu sebepten pirometre cihazı siyah cisim ısı kaynağına karşı 800-1200°C arasında kalibre edilmiştir. Bu işlem 50°C artmak koşuluyla her sıcaklıkta beşer kere tekrarlanıp, kabul edilir küçüklükte sapmalarla elde edilen ortalama veriler sıcaklık tespitinde kullanılmıştır. Siyah cisim ısı kaynağı limitli sıcaklıklarda referans değerler sağladığından 1200°C üstü sıcaklıklar için kalibrasyon eğrisi Wien yasası kullanılarak ekstrapole edilmiştir. Yüksek sıcaklıklarda daha kesin veriler elde etmek adına ticari metodlar incelenmiştir. Bu tip uygulamalarda en sık kullanılan, önceden kalibre edilmiş tungsten filament lambasının üretimi durduruluğu için yeni bir yöntem geliştirme yoluna gidilmiştir.Siyah cisim kapasitesinin yetmediği yüksek sıcaklarda daha doğru sonuçlar almak adına ince bir tungsten levhanın elektriksel ısıtılmasına dayalı yeni bir yöntem geliştirilmiştir. Bu yöntemde enstitü dahilinde mevcut ve kullanıma hazır olan kapalı bir elektrot sisteminden yararlanılmıştır. Elektrotlar arasına yerleştirilen ince tungsten levha elektrik ile ısıtılıp yüzeyinin yüksek sıcaklıklara çıkması sağlanmıştır. İstenmeyen reaksiyonların önüne geçmek için sistem, deneyler esnasında bir inert gaz olan Argon gazı ile doldurulmuştur. Bir diğer yandan da C tipi termokapıl ile levhanın alt tarafından yüzey sıcaklığına bağlı olarak voltaj değerleri okunup, okunan bu değerlerin sıcaklık olarak karşılıkları C tipi termokapıla ait referans tablosundan elde edilmiştir. Sinyal iletim kayıplarını önlemek için de kompensazyon kablosu kullanılmıştır.Yeni geliştirilen bu yöntemin sonuçları ile siyah cisim kalibrasyon çizgileri aynı trende sahip olmalarına rağmen birbirleri ile yeterli tutarlık göstermemiştir. Bu duruma sebep olarak görüş açısı, yayınırlık katsayısı gibi faktörlerin yanında Argon gazının yarattığı soğutma etkisi ve en önemli olarak eski ve zayıf thermokapıl bağlantıları düşünülmüştür. Ayrıca uzun deney zamanlarında tungsten buharlaşması meydana gelmiştir. Bu durum levhanın kesitinin daralmasına ve aynı koşullarda farklı sonuçlar alınmasına yol açmıştır. Bu problem tungsten levhanın belirli zaman aralıklarında değiştirilmesi ile ortadan kaldırılabilmiştir. Zaman kısıtlaması olduğundan siyah cisim kalibrasyonundan ve Wien yasası ile yürütülen ektrapolasyondan elde edilen değerler ile deneyler gerçekleştirerek cihazın uygulanabilirliği, verdiği sonuçların güvenilirliği ve tutarlılığının test edilmesi amaçlanmıştır. Yeni geliştirilen metod hala geçerli bir yöntemdir. Gerekli iyileştirmeler yapılarak yöntemin daha da geliştirilmesi ve yüksek sıcaklıklarda kalibrasyon uygulamalarında kullanılması mümkündür.Deneyler enstitüye ait sürüklemeli akış yanma reaktöründe gerçekleştirilmiştir. Set sıcaklığı her zaman 1100°C olarak ayarlanmış olup yakıt olarak Caliro tipi saman taneleri kullanılmıştır. Reaktör üzerinde mevcut özel gözlem pencerelerinden pirometre ile yanmakta olan taneler izlenmiştir. Pirometrenin, taneleri rahatlıkla tanıyabilmesi için reaktör penceresinin karşının soğuk arka plan olmasına dikkat edilmiştir. Gözlenen ve yanan katı yakıt tanelerinden alınan sinyaller bilgisayar programında değerlendirilmiştir. Alınan sinyal değerleri yardımı ile, önceden elde edilen kalibrasyon eğrileri üzerinde iteratif yöntemler uygulayarak katı yakıt tanelerinin yüzey sıcaklıkları ölçülmüş, daha sonra bu ölçülen yüzey sıcaklıkları uygun denklemlerde yerine konarak tam küresel çaplı tanecik ve sabit yayınırlık kabulu ile tanelerin pirometrik boyutları hesaplanmıştır. Her foto algılayıcıya ait sinyal grafiklerinde, yanmakta olan tanenin gözlenmesi anında meydana gelen tepe noktaların zaman düzleminde yerlerini temel alan kriterler yardımı ile hatalı ölçümlerin olabildiğince aza indirgenmesi hedeflenmiştir.Pirometre cihazı ile hava/yakıt oranı, gözlem penceresi yüksekliği, reaktör filtresinin temizliği, katı yakıta sülfür ve Kaolin ilavesi gibi etkenlerin, tanelerin yüzey sıcaklıkları ve pirometrik çapları üzerindeki etkileri incelenmiştir. Hava yakıt oranı, reaktörün optimum değerine yaklaştıkça tanelerin ortalama sıcaklık dağılımında artış görünürken ortalama pirometrik çap değerleri azalmakta ve bu durum yanma işleminin iyileştiğini göstermektedir. Ayrıca farklı tarihlerde ama aynı koşullarda yapılan deney sonuçları pirometre cihazının tutarlı ve tekrarlanabilir sonuçlar sağladığını kanıtlamıştır. Gözlem penceresinin yüksekliğinin değiştirilmesi yanma işleminin farklı aşamaları hakkında fikir verirken, reaktör filtresinin temizlenmesi ile tespit edilen yanan tane sayısında artış meydana gelmiştir. Katı saman yakıtına sülfür eklenmesi önemli değişiklere yol açmazken, Kaolin ilavesi sonucu tespit edilen tanecik sayısı iki katına çıkmış, ortalama pirometrik çap büyük ölçüde azalmış ve ortalama yüzey sıcaklığı artmıştır. Bu durum pirometrenin Kaolin tanelerini de saman tanesi olarak tespit etmesi ile açıklanabilmektedir. Yapılan deneyler pirometre cihazının uygulanabilir olduğunu göstermiş ve ayrıca reaktör çalışma koşullarının daha uygun biçimde düzenlenmesine de fayda sağlamıştır.Bu proje, bazı ek çalışmalarla desteklenebilir ve geliştirilebilir. Yanma sonu gazları ve yanma öncesi saman taneciklerinin laboratuvar analizleri, sonuçların değerlendirilmesi büyük fayda sağlayacaktır. Ayrıca analog-dijital dönüştürücünün 1500-1600°C üstünde doyuma ulaşması daha yüksek sıcaklıklarda ölçüm yapılmasını mümkün kılamamaktadır. Bu sorun, foto algılayıcıların öncül sinyal büyütme oranları küçültülerek giderilebilir. Bu durumda kalibrasyon işlemi en baştan tekrarlanmalıdır. Yeni geliştirilen kalibrasyon metodu daha iyi sistem elemanları kullanılarak yüksek sıcaklıklarda güvenilir ve net veriler sağlayabilir. Pirometre, uzun deney saatleri sonucunda ısınmakta ve bu da foto algılayıcıların hassasiyetini etkileyip yanlış sonuçlar elde edilmesine yol açmaktadır. Bu etki de bir fan soğutma sistemi ilavesi ile kolaylıkla giderilebilir.Sonuç olarak pirometre kurulumu yapılmış ve siyah cisim ısı kaynağında kalibrasyonu gerçekleştirilmiştir. Daha sonra yüksek sıcaklıklarda, elde edilmiş olan kalibrasyon değerleri ekstrapole edilmiştir. Kalibre edilmiş pirometre başarılı bir şekilde uygulamaya konarak ölçümler alınmış ve bu ölçümler sonucu yanma işlemi hakkında değerli sonuçlar elde edilmiştir. Biyokütle yakıtlarının yanma kinetikleri hakkında aydınlatıcı veriler sağlamıştır. Ayrıca reaktör çalışması hakkında yardımcı bilgi sağlanarak (örn. düzensiz yakıt besleme) cihazın uygulanabilirliği kontrol edilmiştir. Bu projenin genel amacı pirometre kalibrasyonuna ek olarak cihazın güvenilirliğinin ve ölçüm sonuçlarının tekrar gerçekleştirilebilirliğinin test edilmesi olmuştur. The 2-color pyrometer is an optical measurement instrument which enables non-contact temperature detection using the ratio of monochromatic radiation signals from the object at two different wavelengths determined as visible and infrared. A built in-house instrument has been set up to obtain the surface temperature of the individual fuel particles and then calculate the pyrometric diameter (fixed emissivity, perfect spheres). The emitted radiation from the surface of reacting fuel particle is collected and filtered by an optic system (lenses, optic fibers and bandpass filters). The radiation is then detected and quantified using silicon photodiodes in main and reference channels. The electric signals are eventually amplified and sent to a computer for evaluation and post-processing after getting converted into digital form. By running iterative routines, one can determine the surface temperature of a particle with respect to calibration results obtained in advance. Then the size of a particle can be computed based on the measured surface temperature with spherical particle assumption. Thus, calibration of the instrument is required. The pyrometer was calibrated against a black body radiator and calibration curve were extrapolated for higher temperature levels (>1200°C). To increase the level of precision at elevated temperature levels, a self-design method enforcing electrical heating of a thin tungsten sheet in Argon purge was developed. As the results were not satisfying enough to acceps as valid calibration, extrapolation curves have been hence chosen to perform the measurement campaign in an entrained flow combustion reactor with various combustion conditions such as air-fuel ratio, optical port level, filter cleaning, sulfur and Kaolin addition into Caliro type straw. The instrument has been successfully tested during this campaign delivering precious information about the reacting particles and combustion kinetics being able to provide additional information about the status of the reactor (e.g. non-constant mass feeding) served the purpose of checking the applicability of the pyrometer. Aim of this work was, further to the calibration, to test and prove the reliability of the instrument and the reproducibility of the results. 111

In this paper, a large-scale computational analysis has been undertaken of tubular radiators with fin arrays in which the temperature of the fluid varies along the radiator length. The presence of an optimum fin outer diameter for a given pipe diameter, which is independent of other thermophysical parameters, has been brought out. A set of useful correlations, which will enable the designer to quickly evaluate the performance of the system, is developed for different fin profiles. A design methodology assuming an infinite fluid side heat transfer coefficient has been presented. Comparisons have been made for validating the present calculations.

The combined surface radiation and free convection problem are numerically investigated at low or moderate temperature levels for cavities with A in the range of 2-20. The correlations for heat convection and heat radiation across the cavity is given, which showed that correlation for radiation is superior to the parallel plate formula. The temperature profiles are obtained by solving flow equations which accounted the effect of turbulence. However it needs to be emphasized that the calculations are not valid in three dimensional, only if depth of cavity is very large compared to spacing, two dimensional approximation is reasonable.