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Introduction to Finite Element Concepts

by: Timmothy Windler

Introduction to Finite Element Concepts CEE 6900

Timmothy Windler
GPA 3.77

Faisal Hossain

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Faisal Hossain
Class Notes
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This 12 page Class Notes was uploaded by Timmothy Windler on Wednesday October 21, 2015. The Class Notes belongs to CEE 6900 at Tennessee Tech University taught by Faisal Hossain in Fall. Since its upload, it has received 15 views. For similar materials see /class/225707/cee-6900-tennessee-tech-university in Civil and Environmental Engineering (CEE) at Tennessee Tech University.

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Date Created: 10/21/15
Lime 8 Thermal Infrared Thermal Imaging mam1e Thermal Imaging Sensors A Review of Thermal Laws A simple Slab Model Atmospheric windows Visible Reflective Infrared Thermal Infrared 04 07 07 3 3 14 r Fliotographic Infrared Mid Infrared 13 3 3 x 5 J V 02 Absorption Transmission 01 03 04 K 06 i8391HHxli5 2 6 8 1012 15 3d Wavelength in Micrometers am Thermal Infrared Thermal Infrared energy is emitted form all objects that have a temperature greater than absolute zero Humans sense thermal energy primarily through the sense of touch Our eyes are not sensitive to the re ective infrared 07 3 microns or thermal infrared energy 3 14 microns Engineers have developed detectors that are sensitive to thermal infrared radiation These thermal infrared sensors allow humans to sense a previously invisible world as they monitor the thermal characteristics of the landscape Thermal Imaging J Thermal Infrared 3 Lune 15 um Detector Electronics Image r Lens Data J Thermal sensors measure the thermal properties of targets J The detectors are cooled to temperatures glam close to absolute zero in order to limit their own thermal emissions History of Thermal IR RS J Most important development the development of the detector element by nations at war during World War II J Early detectors were lead salt photodetectors now we have very fast detectors consisting of mercurydoped germanium Ge2Hg Indium antimonide lnSb and others J In 1968 the government declassi ed thermal infrared remote sensing systems that did not exceed a certain spatial resolution and temperature sensitivity History of Thermal IR RS V 1960 US Television JR Operational Satellite TIROS V 1978 Heat Capacity Mapping Mission HCCM 600 m resolution V 1978 Nimbus 7 V 1980 Thermal Infrared Multispectral Scanner TllVIS V 1982 1984 Landsat Thematic Mapper 4 and 5 2 bands V T oday GOES spatial resolution of 8 km every 30 minutes V Today NOAAAVHRR 1 km once a day V Today ASTER 90 m 5 spectral bands TIR Principles V An analyst cannot interpret a thermal infrared image as if it were an aerial photograph or a normal image produced by a multispectral scanner V Rather the image analyst must think thermally Diurnal Properties of TIR b 10ch age local sunnse sunset 2 E E Q E 0 a Vege E 5 quot water 5 5 water thermal E crossover so si om39e z39 0 metal objects 7 v l l 0 2 am 4 arn 6 am 8 arm 12 4 pm 8 pm 0 midnight noon mldmght 4 1 Day LI Thermal Imaging GOES TIR image 105 125 pm 10 Thermal Imaging NOTE Lighter color represents higher temperature GOES TIR image 105 125 pm Nightime Thermal Infrared Imagery of an Airport Thermal Imaging Features Imagery is available both day and night Atmospheric scattering is minimal compared to visible radiation Absorption by atmospheric gases normally restricts thermal sensing to two specific regions 3 7 Sum and 814um The spatial resolution of thermal sensors is usually fairly coarse relative to the spatial resolution possible in the visible and reflected 39 rare Used in many applications such as distinguishing low and high level clouds heat loss monitoring forest fire mapping sea surface temperature etc Planck39s Formula Blackbody Spectral Emittance 2hc2 hC B T 7 Where x 7 A may MT c speed of light 300x102g ms 1 h Planck s constant 663x103934 Is k Boltzmann s constant 138x10393 1K1 You don39t have to remember this formula Planck39s Law 5000 K Spectral curves Ior blackbady radIanIs lncreasIng Iqu 4 2x10 6 25xira axure ixur7 5x10397 1x105 15x10 Wavelength ml mm mama WWW IN MI WWW 15 Wien39s Displacement Law The Wavelength With the highest level of emitted radiation 201 for an object of temperature T can be calculated as 1m 2 K T Where k 2898 urnK I In I H I II I W E 10 1 E 10 w E 10 E 39 r xr ID do 10 39 9 4 39 I I I I o m 1 10 um Waverengzn um Know this formula 16 StefanBoltzmann Law Blackbody The amount of EM radiation emitted from a body in Wm 2 can be calculated as 4 E 2 0T Where T is the temperature in K o is a constant Spectrally integrate the Planck distribution to determine total irradiance from blackbody Know this formula Emlsswlty The world is not composed of radiating blackbodiesi Rather itis composed of selectively radiating bodies such as rocks soil and water that emit only a fraction of the energy emitted from a blackbody at the same temperature Emissivizy is the ratio between the radiant ux exiting a real world selective radiating body I r and a blackbody at the same temperature 3 1m a Em A 113 EltBgt Radiate energy for different objects compared with a blackbody at the same temperature blackbody 350K 5 0 a 098 Radiant Energy W cm392 um39l x 103 LA 0 I 0 5 10 15 Wavelength tun 70 1 o XlOquot 6 0 Granite 60 Dunite 1 I 3 K 50 40 30 20 10 Radiant Energy W m392 pm l x 103 Radiant Energy W cm392 um39 I l 0 I I l 0 5 1 0 1 5 20 25 O 5 10 1 5 20 25 Wavelength um Wavelength um 19 Emissivity T w0 rocks lying next to one another on the ground could have the same true kinetic surface temperature but have di erent apparent temperatures when sensed by a thermal radiometer simply because their emissivities are different The emissivity of an object may be in uenced by a number factors including color darker colored objects are usually better absorbers and emitters ie they have a higher emissivity than lighter colored objects which tend to re ect more of the incident energy surface roughness the greater the surface roughness of an object relative to the size of the incident wavelength the greater the surface area of the object and potential for absorption and re emission of energy 20 lO Emissivity moisture content the more moisture an object contains the greater its ability to absorb energy and become a good emitter Wet soil particles have a high emissivity similar to water compaction the degree of soil compaction can effect emissivity eldafview the emissivity of a single leaf measured with a very high resolution thermal radiometer will have a different emissivity than an entire tree crown viewed using a coarse spatial resolution radiometer wavelength the emissivity of an object is generally considered to be wavelength dependent Viewing angle 2l V I u u I Table 89 from 8 7 14 1111 E m Material Emissivity s asphalt shingle dry 097 asphalt shingle wet 100 cedarshake shingle dry 095 cedarshake shingle wet 099 tarstone 097 aluminum sheet 009 copper oxidized 078 iron sheetrusted 069 tin tinplated sheet irnu 007 brick redcommon 093 paint average of 16 colors 094 sand 090 wood planed oak 090 frost crystals 098 22 Emissivity 0 The Russian physicist Kirchoff found that in the infrared portion of the spectrum the spectral emissivity of an object generally equals its spectral absorptance ie 0938 This is often phrased as good absorbers are good emitters and good re ectors are poor emitters Also most realworld materials are usually opaque to thermal radiation meaning that no radiant flux exits from the other side of the terrain element Therefore we may assume transmittance 10 Substituting emissivity for absorptance and removing transmittance from the equation yields lzpz l az Emissivity This simple relationship describes why objects appear as they do on thermal infrared imagery Because the terrain does not lose any incident energy to transmittance all of the energy leaving the object must be accounted for by the inverse relationship between reflectance and emissivity If re ectivity increases then emissivity must decrease If emissivity increases then re ectivity must decrease For example water absorbs almost all incident energy and reflects very little Therefore water is a very good emitter and has a high emissivity close to 1 Conversely a sheet metal roof reflects most of the incident energy absorbs very little yielding an emissivity much less than 1 Therefore metal objects such as cars aircraft and metal roofs almost always look very cold dark on thermal infrared imagery 7 they are poor emitters


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