# Thermometric Error Analysis

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5. 3. 4 Typical application and thermometric error
Consider a typical application such as the measurement of surface temperature by a surface mounted thermocouple as shown in Figure 5.9 (a).
Figure 5. 9 : (a) Surface mounted thermocouple in Example 5. 1 (b) Thermal resistance network model
Heat loss from the thermocouple is modeled as shown above by discussion leading to Equation 5.3. Thermocouple attached to the surface of a massive solid whose temperature we would like to measure. Excepting where the thermocouple has been attached the rest of the surface of the solid is assumed to be perfectly insulated. Since the thermocouple conducts away some heat from the solid there is a depression of temperature of the solid where the thermocouple
Then Equation 5.26 is rewritten as
Where θ=T-T_ref and m_(ef f)=√((h_f+h_R )P/(k_w A)) is the effective fin parameter. Equation 5.27 is the familiar fin equation whose solution is well known. Assuming insulated boundary condition at the sensor location, the indicated sensor temperature is given by

The thermometric error is thus given by
Following points may be made in summary The longer the depth of immersion L smaller the thermometric error Lower the thermal conductivity of the well material the smaller the thermometric error Smaller the emmissivity of the well and hence the h_R smaller the thermometric error Larger the fluid velocity and hence the h smaller the thermometric error

Example 5.5
Air at a temperature of 100 °C is flowing in a tube of diameter 10 cm at an average velocity of 0.5 m⁄s. The tube walls are at a temperature of 90 °C. A thermometer well of outer diameter 4mm and wall thickness O.5 mm made of stainless steel is immersed to a depth of 5cm, perpendicular to the tube axis. The steel tube is dirty because of usage and has a surface emissivity of 0.2. What will be the temperature indicated by a thermocouple that is attached to the bottom of the thermometer well? What is the consequence of ignoring

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