Consider conditions for which a mercury-in-glass

Chapter , Problem 7.7

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Consider conditions for which a mercury-in-glass thermometer of 4-mm diameter is inserted to a length L through the wall of a duct in which air at 77 C is flowing. If the stem of the thermometer at the duct wall is at the wall temperature Tw 15 C, conduction heat transfer through the glass causes the bulb temperature to be lower than that of the airstream. (a) Develop a relationship for the immersion error, Ti T(L) T, as a function of air velocity, thermometer diameter, and insertion length L. (b) To what length L must the thermometer be inserted if the immersion error is not to exceed 0.25 C when the air velocity is 10 m/s? (c) Using the insertion length determined in part (b), calculate and plot the immersion error as a function of air velocity for the range 2 to 20 m/s. (d) For a given insertion length, will the immersion error increase or decrease if the diameter of the thermometer is increased? Is the immersion error more sensitive to the diameter or air velocity?