58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.), these should not be ncluded n your report. - To study the transent coolng of a heated object n room temperature. - To determne the apparent heat transfer coeffcent assumng a lumped capactance heat transfer model. EQUIPMENT Name Model S/N Thermstor Standard Calbrator DAQ Fve Specmens Test Stand Thermocouples Pyrometer Tempbook or DBK19 Computer The thermal system response and effectve heat transfer coeffcent experment requred the use of several peces of equpment. Heat transfer s measured on an alumnum cube, an alumnum rod, a polshed brass rod and a blackened brass rod. An Oven s used to heat the objects to slghtly less than 200º Celsus. Fve thermocouples are used to measure the temperature of each of the objects and ambent temperature. A Pyrometer s used to measure the heat transfer. A thermstor and calbrator are used to calbrate the thermocouples. A test stand holds each of the objects whle they cooled at room temperature. Also, a NI data acquston system s used to gather the data for the LabVIEW software applcaton. REQUIRED READING See reference [1], [2] and ths wrte-up for theory and data reducton. PRELAB QUESTIONS 1- What s heat transfer coeffcent? 2- What s Lumped Capactance method? 3- What s dmensonless temperature n ths experment and why we use ths parameter? 4- What s the Tme Constant n ths experment? 5- What s the valdty of the Lumped Capactance Method?
58:080 Expermental Engneerng 2 PROCEDURE a. (Note: step b. s to be executed n conjuncton wth ths step) Calbrate at least sx TCs, and usng the technques you have learned n ths class to determne ther accuracy relatve to a local standard. You wll not need to use an ce pont cell here. Also, you wll not need to use the reference juncton TC. Gven the tme you have n one lab perod, determne the number of calbraton ponts you wll use (calbrator settngs), startng from about 20 C hgher that room temperature to the maxmum temperature your standard can read (probably about 130 C). Calbrate at least sx TCs; one for each of the fve bodes, and one for the ambent temperature. You may want to calbrate one or two more TC n case one fals durng the experment. Determne the types of TCs you wll use, the channels on the data acquston system you wll use, and the software setup (LabVIEW). You should set up a statstc module to gve you random readng varatons durng the calbraton. b. Calbrate an nfrared pyrometer sensor, startng from about 50 C to 150 C n ncrements of 25 C. The pyrometer calbrator (black-body calbrator) wll be shared between groups f more than one workstaton s runnng of ths lab. Share the calbrator by puttng t on an extenson cord and passng t back and forth between the two groups. If you need help, the TA wll help you setup the pyrometer and you wll need a power supply for t. Connect 12 V DC to the red (+) and black (-) power wres, and the sgnal s read from the whte (-) and blue (+) wres. The sgnal wll be read usng a voltage nput channel on the data acquston system. Determne repeatablty error usng one temperature settng on the pyrometer calbrator for the pyrometer. c. Measure each specmen's mass, area, etc. You can use the accuracy nformaton you determned n Lab 1 n your uncertanty calculatons for mcrometers or calpers used here. d. Increase specmen's temperature as hgh as possble (maybe 200 C max) usng the oven and use a thermocouple to measure the temperature of the specmen and the ambent ar. e. Remove the specmen from the oven usng tongs or oven mts and start recordng the temperature hstory of the specmen and the ambent ar when the specmen s postoned on the stand. Record the temperature of the surface of the cube usng the pyrometer. f. Three dfferent cases are to be studed: 1. Polshed and blackened Brass cylnders. 2. Alumnum and Brass cylnders. 3. Alumnum cylnder and cube (same surface area). g. Dscuss your observatons of each object you use n the experment, for example, on the decay of (dmensonless) temperature and the tme constants of the decay. Compare (plot) the nternal wth the surface temperature of the body measured wth the pyrometer. What does ths tell you about the lumped thermal capactance assumpton?
58:080 Expermental Engneerng 3 h. See pages 60-61 of the lecture notes on the course webste for the theoretcal development of ths dynamc system and the equatons you wll need for the analyss. Based on an approprate physcal model, obtan from the data an "apparent" heat transfer coeffcent for each object, and compare the "apparent" heat transfer coeffcents wth the values calculated from theoretcal consderatons; dscuss the results as approprate. Determne the apparent heat transfer coeffcent by fndng the tme constant through a curve ft of the data as shown n example 3.5 n your text. Compare ths wth the tme constant found from the Temperature-Tme plot.. Dscuss uncertanty of measurements (uncertanty for the tme constant s statstcally found va the curve ft used n h. above). Also see the wrte-up that follows. Analyss Temperature Response Determnaton of Apparent Heat Transfer Coeffcent Three dfferent cases are to be studed for comparson: 1. Polshed and blackened Brass cylnders. 2. Alumnum and Brass cylnders. 3. Alumnum cylnder and cube (same surface area). 1. Dscuss your observatons of each object you use n the experment, for example, on the decay of (dmensonless) temperature and the tme constants of the decay. The dmensonless temperature s gven n equaton (1), where T s s the body, T s the ntal and T s the room temperature, respectvely. See example plot below. T ( T T ) (1) Fgure 1 Dmensonless Temperature Decay- Polshed Brass Cylnder
ln(dmensonless Temperature) 58:080 Expermental Engneerng 4 Compare (plot) the nternal wth the surface temperature of the body measured wth the pyrometer. What does ths tell you about the lumped thermal capactance assumpton? Ths should be straghtforward. 2. Based on an approprate physcal model, obtan from the data an "apparent" heat transfer coeffcent for each object, and compare the "apparent" heat transfer coeffcents wth the values calculated from theoretcal consderatons; dscuss the results as approprate. A lumped thermal capactance heat transfer model (body at unform temperature) wth a constant Newtonan heat transfer coeffcent leads to a frst-order system equaton defned by the error fracton Γ n terms of temperatures, that decays exponentally wth tme accordng to a tme constant τ ( t) T ( t) e T T t / Note: ths error fracton s our dmensonless temperature. In ths case the heat transfer coeffcent s apparent snce t wll nclude convecton and radaton, and wll not be perfectly constant. (2) 3. Determne the apparent heat transfer coeffcent by fndng the tme constant through a curve ft of the data as shown n example 3.5 n your text. Compare ths wth the tme constant found from the Temperature-Tme plot. Usng the equaton above, takng the natural log of both sdes, one can put the temperature versus tme data nto a form such that lnear regresson can be used to determne the tme constant and ts uncertanty (standard error of the slope). ( t) T ln( ( t)) ln( ) T T t (3) 0-0.5 Determnaton of Tme Constant (Polshed Brass Cylnder) 0 500 1000 1500 2000-1 -1.5-2 y = -0.0015x - 0.0713-2.5-3 Tme (s) Fgure 2 Determnaton of Tme Constant- Polshed Brass Cylnder
58:080 Expermental Engneerng 5 An example plot and curve ft for the data shown earler s gven here. The tme constant from the curve ft s 662 seconds. From the raw data (Temperature vs. Tme plot) t s much less. Dscuss any observatons about ths and ts possble causes. The apparent heat transfer coeffcent h s found from the tme constant τ, mass of specmen m, the specmen specfc heat c v and the surface area of the specmen A s : mc ha v s (4) 4. If requested, determne and dscuss the uncertanty of the measurements (hnt: uncertanty for the tme constant s statstcally found va the curve ft used above, propagate the error to the results usng uncertantes for mass of specmen m, and the surface area of the specmen A s. You can neglect the uncertanty for the specmen specfc heat c v.). To determne the uncertanty n h you must use error propagaton to that result usng the equaton for h. It s assumed you wll perform smlar calbraton and uncertanty calculatons for the thermocouples as requred n the Lab 2 workstatons. You wll be graded on whether you perform these uncertanty calculatons correctly and how thorough you perform them. REFERENCES 1. Fglola, Rchard S., and Donald E. Beasley. Theory and Desgn for Mechancal Measurements 5 th ed., Wley Inc., 2011. 2. Theodore L. Bergman, Frank P. Incropera, Adrenne S. Lavne, Davd P. DeWtt. Fundamentals of Heat and Mass Transfer, 6 th ed., Wley Inc., 2007, Chapter 5, Sectons 5.1-5.3.