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# Thermal Conductivity Assignment

Added on - 21 Apr 2020

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Methodology on thermal conductivity measurement1METHODOLOGY ONTHERMAL CONDUCTIVITY MESUREMENTBy NameCourseInstructorInstitutionLocationDate
Methodology on thermal conductivity measurement2METHODOLOGYThe thermal conductivity is the ability of a material to be able to transmit heat energy andthis is always measured in watts per square meter for a given surface area where themeasurement is conducted[CITATION Don15 \l 1033 ]. A temperature gradient of 1 K per unitthickness of the material is always taken as 1 meter. The heat conduction is best defined by theFourier’s law of conduction. For unidirectional heat flow, the law states that the local heat flux ina uniform substance is directly proportional to the negative temperature gradient. For the smallheat shield like the one in this design can be seen in the following diagram;Fig 1: showing the temperature variations heat shield having sensor.(Thomass, T., 2015)The design will be based on steady-state thermal conductivity test techniques from ASTM(American Society for Testing and Materials). This ASTM society has made two important testmethods, these include D 5470 and E1 225 for the measurement of the thermal conductivityλ[ CITATION Fis12 \l 1033 ]. These two are further explained below;ASTM E1225This is a test employed for obtaining λ through steady-state method, it is basicallyemployed for the composite shield whose conductivity is in the range of 0.2 < λ< 200 (Wmλ) over
Methodology on thermal conductivity measurement3a temperature of between 90K to 1300K[ CITATION Ban14 \l 1033 ]. The diagram below shows thetest apparatus;Fig 2: Showing the test Apparatus for the ASTM E 1225(Thomass, T., 2015)Those meter bar X are defined as a piece of reference material (that is their thermalconductivity λ are known) are employed to measure the heat flux through an imposedtemperature range[ CITATION Bri11 \l 1033 ]. During the selection of meter bar materials, theASTM E 1225 standard proposes that the thermal conductance of the meter barsλmlmbe alike tothe thermal conductance of the sampleλsls. There ratioklis very vital since the assumption ismade that the heat flux throughout the apparatus is uniform, hence we can say that
Methodology on thermal conductivity measurement4λm(dTdx)m=λs(dTdx)s. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(iii)Where λl is the corresponding thermal conductivity in meter bar per sample anddTdxis thecorresponding temperature gradient[CITATION Sta15 \l 1033 ]. Through having alike thermalconductance withboth sample and meter bars, there is the possibility of a similar drop intemperature in the sample and meter bars.To obtain the value of thermal conductivity λ, some multiple calculations are conducted.These calculations are based on the temperature measured at each meter bar and the heat flux permeter bar. The formulas below can be employed to determine the heat flux in different positions.q =λm (T2T1Z2Z1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(iv)Where q is heat flux,λm is the thermal conductivity of the metal bar, T1 is the lower temperature(temperature at Z1), T2is the higher temperature (temperature at Z2). Z1 is the distance from thepoint z1 to the end of the composite heat shield (where heat is being shielded) and Z2is thedistance from point Z2to the end of the composite heat shield (where the heat is being shielded)[ CITATION Den11 \l 1033 ]. The above equation (iv) is employed to help obtain heat flux q, and inthe design specifications, the lowest temperature is given as 4000C while the highest temperatureis given as 6000C. But the temperature in this design is used in their absolute value hence,T1= 273+ 400 = 673KT6= 273+600= 873 K  