A probe of overall length L = 200 mm and diameter D = 12.5 mm is inserted through a duct wall such that a portion of its length, referred to as the immersion length L i , is in contact with the water stream whose temperature, T8,i , is to be determined. The convection coefficients over the immersion and ambient-exposed lengths are hi = 1100 W/m2 · K and ho = 10 W/m. K. respectively. The probe has a thermal conductivity of 177 W/m · K and is in poor thermal contact with the duct wall.

(a) Derive an expression for evaluating the measurement error, ?Terr = Ttip - T8,i, which is the difference between the tip temperature, T lip , and the water temperature, T8.i'

(b) With the water and ambient air temperatures at 80 and 20°C, respectively, calculate the measurement error, 6.Tem as a function of immersion length for the conditions L/L = 0.225,0.425, and 0.625.

(c) Compute and plot the effects of probe thermal conductivity and water velocity (hi) on the measurement error.