MECH 322 Instrumentation

Lab 9 Transient Thermocouple Response in Water and Air

Performed: 03/23/07

Group 0Miles Greiner

Lab Instructors:Mithun Gudipati, Venkata Venigalla

ABSTRACT• The goal of this lab is to measure the heat transfer

coefficient for a thermocouple in three different environments.

• A computer data acquisition system and signal conditioner are used to measure the temperature of a thermocouple as it is placed in boiling water, air, and room temperature water.

• Effective mean heat transfer coefficients were determined for time periods when the measured temperature decayed exponentially to the environment temperature. The heat transfer for the water environments were significantly higher than for air.

Figure 1 VI Front Panel

Figure 2 VI Block Diagram

Formula--------------------This Express VI is configured as follows:Formula: Vout/0.105143 -4.632

Formula2--------------------This Express VI is configured as follows:Formula: 1.049E-02*X1**3 - 2.179E-01*X1**2 + 1.984E+01*X1 - 1.890E-04

Convert from Dynamic DataConvert from Dynamic DataConverts the dynamic data type to numeric, Boolean, waveform, and array data types for use with other VIs and functions.

• The diameter uncertainty is estimated to be 10% of its value.

• Thermocouple material properties values are the average of Iron and Constantan values. The uncertainty is half the difference between these values. The values were taken from [A.J. Wheeler and A.R. Gangi, Introduction to Engineering Experimentation, 2nd Ed., Pearson Education Inc., 2004, page 431]

• The time for the effect of a temperature change at the thermocouple surface to cause a significant change at its center is tT = D2c/kTC. Its likely uncertainty is calculated from the uncertainty in the input values.

Table 1 Thermocouple PropertiesEffective

Diameter D [in]

Density ρ [kg/m3]

Thermal Conductivity kTC [W/mK]

Specific Heat c [J/kgK]

Initial Transient

Time tT [sec]

Value 0.059 8400 45 416 0.183s Uncertainty 0.006 530 24 31 0.10

• The times on the chart indicate when the thermocouple was first placed in the boiling water, air and room temperature water.

• The boiling water and room temperatures were TB = 95.2°C and TR = 19.7°C.

• The thermocouple reaches the fluid temperature in the water baths but not in air• The slope exhibits a continuous variation (not a step change) at each transition. • The measured temperature slope may respond slowly at first because the TC interior

temperature does not change immediately after it is placed in the new environment.

Fig. 3 Thermocouple temperature versus Time

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8

Time, t [sec]

Te

mp

era

ture

, T

[oC

]

tB = 0.78 sIn Boiling Water

tA = 3.36 sIn Air

tR = 5.78 sIn Room Temperature Water

Fig. 4 Dimensionless Temperature Error versus Time in Boiling Water

• The dimensionless temperature error decreases with time and exhibits random variation when it is less than < 0.05

• The versus t curve is nearly straight on a log-linear scale during time t = 1.14 to 1.27 s.

– The exponential decay constant during that time is b = -13.65 1/s.

For t = 1.14 to 1.27 s = 1.867E+06e-1.365E+01t

0.01

0.1

1

0.8 0.9 1 1.1 1.2 1.3 1.4

Time, t [sec]

BO

IL =

(T

B-T

(t))

/(T

B-T

R)

Fig. 5 Dimensionless Temperature Error versus Time t for Room Temperature Air and Water

• The dimensionless temperature error decays exponentially during two time periods:– In air: t = 3.83 to 5.74 s with decay constant b = -0.3697 1/s, and – In room temperature water: t = 5.86 to 6.00s with decay constant b = -7.856 1/s.

In AirFor t = 3.83 to 5.74 sec

= 2.8268e-0.3697t

In Room Temp WaterFor t = 5.86 to 6.00 sec

= 2E+19e-7.856t

0.01

0.1

1

3 3.5 4 4.5 5 5.5 6 6.5 7

Time t [sec]

Ro

om

Table 2 Effective Mean Heat Transfer Coefficients

• The effective heat transfer coefficient is h = -cDb/6. Its uncertainty is 22% of its value, and is determined assuming the uncertainty in b is very small.

• The dimensional heat transfer coefficients are orders of magnitude higher in water than air due to water’s higher thermal conductivity

• The Nusselt numbers NuD (dimensionless heat transfer coefficient) in the three different environments are more nearly equal than the dimensional heat transfer coefficients, h.

• The Biot Bi number indicates the thermocouple does not have a uniform temperature in the water environments

Environment b [1/s]

h

[W/m2C]

Wh

[W/m2C]kFluid

[W/mC]NuD

hD/kFluid

Bi hD/kTC

Lumped (Bi < 0.1?)

Boiling Water -13.7 11873 2643 0.680 26 0.398 noAir -0.37 322 72 0.026 18 0.011 yes

Room Temperature Water -7.86 6833 1521 0.600 17 0.229 no

Extra-CreditFig. 6 The Heat Transfer Rate to TC in Boiling Water versus Time

• Calculated based on Q = (cD3/6)(dT/dt), with four finite difference time steps tD = 0.001, 0.01, 0.05 and 0.1 s. tD = 0.01 to 0.05 sec are the best compromise between noise and responsiveness

• The heat transfer is significant between t = 0.95 and 1.3 sec• The measured heat transfer appears to increase for 0.15 sec before

decreasing. This delay is roughly the same as the initial transient time tT = 0.18 sec.

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0.6 0.8 1 1.2 1.4 1.6

Time t [sec]

Hea

t T

ran

sfer

Q [

W]

Dt = 0.001 secDt = 0.01 secDt = 0.1 secDt = 0.05 sec

Extra Figure (not part of report) Summary of 2006 Data

• Air has consistently lowest h• h increases as D decreases?

100

1000

10000

100000

0 0.0005 0.001 0.0015 0.002 0.0025 0.003

TC Diameter, D [m]

Hea

t T

ran

s. C

oef

h [

W/m

2 K]

BoilingAir Water