Question

1. (40 pts) A spherical thermocouple (TC) is inserted into a duct to measure temperature of flowing air. The duct and TC were initially cold (27°C) and are exposed to sudden flow of hot air (77°C) at 3 m/s. a) (15 pts) What is the convective heat transfer coefficient on the TC surface? b) (15 pts) How long does it take for the TC to read the gas temperature (i.e. the temperature difference to reach 2% of the initial temperature difference)? c) (10 pts) If you want to decrease this time, comment on how beneficial would changing the diameter of the TC be? (would it increase proportionally?) TC: d=1.0 mm, k = 100 W/mK, Co = 385 J/kgk, p=8920 kg/m2 BONUS (2.5 pts): What else besides changing of the TC diameter could you do to decrease the response time?

Please help with the following problem and show work thank you

Answer 1

Calculate convective heat transfer coefficient. h = 12.12 – 1.16v+11.64/v = 12.12–1.16(3)+11.6/(3) = 28.732 W/m²K Calculate the required time to obtain given temperature ratio. T-T T.-T. 6hr 6ht In 7, T-T T-T ap pc D 1=-(02)(TI)- (8920) (385)(0.001) 6(28.732) In (0.02) = 77.93 sec Write the equation for time required.

t=- PC, D 6h T-T T:-T to D Fort → decrease =D decrease Write the equation for time required. pc, D 6h In T-T T:-T 900 to- h Fort decrease h → increase hot air velocity → increase