1. ME 322: Instrumentation Lecture 25 March 25, 2014 Professor Miles Greiner Thermocouple response to sinusoidally varying temperature, radiation and conduction errors

2. Announcements/Reminders This week: Lab 8 Discretely Sampled Signals – How is the lab going? – Next Week: Transient Temperature Measurements HW 9 is due Monday Midterm II, Wednesday, April 1, 2015 – Review Monday Trying to schedule an extra-credit opportunity – LabVIEW Computer-Based Measurements – NI field engineer will walk through the LabVIEW development environment – Time TBA – 1% of grade extra credit for actively attending

3. TC Response to Sinusoidally-Varying Environment Temperature For example, a TC in an engine cylinder or exhaust “Eventually” the TC will have – The same average temperature and unsteady frequency as the environment temperature – However, its unsteady amplitude will be less than the environment temperature’s. – TC temperature peak will be delayed by time t D T ENV T TC T tDtD

4. Heat Transfer from Environment to TC Q = hA(T E –T) Environment Temp T E (t) T D=2r Heat Transfer to TC

5. Solution

6. Particular Solution =0 For all times

7. Result

8. Compare to Environment Temperature T tDtD

9. Example A car engine runs at f = 1000 rpm. A type J thermocouple with D = 0.1 mm is placed in one of its cylinders. How high must the convection coefficient be so that the amplitude of the thermocouple temperature variations is 90% as large as the environment temperature variations? If the combustion gases may be assumed to have the properties of air at 600 ° C, what is the required Nusselt number? ID: Steady or Unsteady?

10. Material Properties

11. Common Temperature Measurement Errors Even for steady temperatures Lead wires act like a fin, cooling the surface compared to the case when the sensor is not there The temperature of a sensor on a post will be between the fluid and duct surface temperature

12. High Temperature (combustion) Gas Measurements Radiation heat transfer is important and can cause errors TC temperature changes until convection heat transfer to sensor equals radiation heat transfer from sensor – Q = Ah(T gas – T S ) = A  (T S 4 -T W 4 )  = Stefan-Boltzmann constant = 5.67x10 -8 W/m 2 K 4  Sensor emissivity (surface property ≤ 1) T[K] = T[C] + 273.15 Measurement Error = T gas – T S = (  /h)(T S 4 -T W 4 ) Q Conv =Ah(T gas – T S ) TSTS Q Rad =A  (T S 4 -T W 4 ) T gas TWTW Sensor h, T S, A, 

13. Problem 9.39 (p. 335) Calculate the actual temperature of exhaust gas from a diesel engine in a pipe, if the measuring thermocouple reads 500 ° C and the exhaust pipe is 350 ° C. The emissivity of the thermocouple is 0.7 and the convection heat-transfer coefficient of the flow over the thermocouple is 200 W/m 2 -C. ID: Steady or Unsteady? What if there is uncertainty in emissivity?

15. Conduction through Support (Fin Configuration) T∞T∞ h x L A, P, k T0T0 TSTS

16. Example A 1-cm-long, 1-mm-diameter stainless steel support (k = 20 W/mK) is mounted inside a pipe whose temperature is 200 ° C. The heat transfer coefficient between gas in the pipe and the support is 100 W/m 2 K, and a sensor at the end of the support reads 350 ° C. What is the gas temperature? Assume  sensor = 0 Steady or unsteady Radiation or Conduction errors

17. Solution