A thermometer well 22 cm in diameter and 0.5 mm thick is made of steel (k = 27 W/m.K) and it is to be used to measure the temperature of steam flowing through a pipe. Calculate the minimum length of...

A thermometer well 22 cm in diameter and 0.5 mm thick is made of steel (k = 27 W/m.K) and it is to be used to measure the temperature of steam flowing through a pipe. Calculate the minimum length of well so that the error is less than 0.5% of the difference between pipe well and the fluid temperature. Take steam temperature as 250°C and h = 98 W/ m².K.