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Temperature Measurement of Fluids Low Velocity Gas Contact sensors Assume that a gas, with a temperature, T., flows in a tube with a flow-velocity below about 20 m/s, as shown in Figure 17.1(a) . In the tube there is a sheathed sensor, whose sensitive part, at temperature, TT , is placed in the sheath bottom. This case corresponds to a thermocouple with the measuring junction welded into the sheath bottom . Also let the temperature ofthe internal surface ofthe tube wall be TW , while the length to diameter ratio of the sensor sheath is assumed to be so large that. | Temperature Measurement Second Edition L. Michalski K. Eckersdorf J. Kucharski J. McGhee Copyright 2001 John Wiley Sons Ltd ISBNs 0-471-86779-9 Hardback 0-470-84613-5 Electronic 17 Temperature Measurement of Fluids 17.1 Low Velocity Gas 17.1.1 Contact sensors Assume that a gas with a temperature flows in a tube with a flow-velocity below about 20 m s as shown in Figure 17.1 a . In the tube there is a sheathed sensor whose sensitive part at temperature Tt is placed in the sheath bottom. This case corresponds to a thermocouple with the measuring junction welded into the sheath bottom. Also let the temperature of the internal surface of the tube wall be Tw while the length to diameter ratio of the sensor sheath is assumed to be so large that heat transfer through the sheath bottom can be neglected. It is further assumed that the gas temperature Tg is higher than the temperature of the tube wall 7W. Consider a cylindrical sheath element of length dx placed at a distance x from the sheath end as represented in Figure 17.1 b . In the thermal steadystate it is apparent that the heat balance must take account of all conduction convection and radiation effects. a ARRANGEMENT W SHEATH ELEMENT D 1 TUBE GAS SENSOR -r StNSUK T SHEATH d k HEAT FLUX k - CONVECTION r - RADIATION - CONDUCTION Figure 17.1 Gas temperature measurement in a tube by a sheathed sensor 362 TEMPERATURE MEASUREMENT OF FLUIDS The convection heat flux from the gas to an element of length dx is dd k ak Ddx Tg - Tx 17.1 where ak is the convective heat transfer coefficient Tg is the gas temperature and Tx is the sheath temperature at a distance x from its end. Assuming that the gas transmissivity equals unity the heat flux dissipated from this element by radiation to the tube wall is given by d r ETCofl dr î tx y 100 J 17.2 where et is the emissivity of the sheath surface Co is the radiation constant of a black body and 7W is the temperature of the tube wall and the other symbols are as in equation 17.1 . .