Thermometric well is used to measure the temperature of gas flowing through a pipeline. A small tube called thermometric well is welded radially into the pipeline. The well is partially filled with some liquid and the thermometer is immersed into this liquid. When the temperature of the gas flowing through the pipeline is higher than the ambient temperature, the heat flows from the hot gases towards the tube walls along the well.
This may cause temperature at the bottom of well to become colder than the gas flowing around. Obviously the temperature indicated by the thermometer will not be the true temperature of the gas. The error in the temperature measurement is estimated with the help of the theory of extended surfaces.
The protective tube (well) can be considered as a hollow fin (internal diameter d, thickness δ and length l), and the temperature distribution obtained by using the relation applicable to a fin with tip insulated-
where t0 is the temperature of the pipe wall, f is the temperature of hot gas or air flowing through the pipeline, and t is the temperature at any distance v measured from pipe wall along the thermometric well.
If x = i then,
where tl is the temperature recorded by the thermometer at the bottom of the well.
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The perimeter of the protective well P = π(d + 2δ) = πd, and its cross-sectional area Ac = πdδ. Therefore,
Apparently, diameter of the well does not have any effect on temperature measurement by the thermometer.
The error can be minimized by:
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(i) Lagging the tube so that conduction of heat along its length is arrested.
(ii) Increasing the value of parameter ml
For a rectangular fin m = √2h/kδ. An increase in m can be affected by using a thinner tube of low thermal conductivity or by increasing the convection coefficient through finning the manometric well. The operative length I is increased by inclining the pocket and setting its projection beyond the pipe axis.
The need to locate the protective tube oblique (inclined) would arise if the desired length is more than the diameter of pipeline. The diameter of tube does not have any effect on increasing the accuracy of temperature measurement.
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Example:
Measurements of temperature of gas flowing through a pipe has been made by mercury-in- glass thermometer dipped into an oil-filled steel tube (protective well) welded radially to the pipe line. The thermometer indicates a temperature at the end of the steel tube which is lower than the gas temperature due to transfer of heat by conduction along the protective well.
How large is the measurement error if the thermometer reads t1 = 85°C and the temperature at the base of the protective well (pipe wall) is t0 = 40°C. The protective tube is 125 mm long and has 1.5 mm thick wall. It may be presumed that the thermal conductivity of the tube material is 56 W/mK and the local coefficient of heat transfer from gas to the protective tube is 23.5 W/m2K.
Solution:
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The temperature distribution along the length of the pocket is given by-
Where t1 is the temperature at the bottom of the pocket, ta is the temperature of gas flowing and t0 is the temperature of the pipe wall.
