MECH 322 Instrumentation

Sinan Ozcan: I believe, I performed 50% of the work.Soma : I believe, I performed 50% of the work.

Transient Thermocouple Response in Boiling Water, Air and Room-

Temperature Water

Performed: 04/10/04

ABSTRACT• The goal of this lab demonstrates errors that can occur

when measuring time-dependent temperature • A computer data acquisition system and signal

conditioner were used to measure the temperature of a thermocouple as it was plunged into boiling water, air, and room temperature water.

• The thermocouple approached the environment temperature more quickly in the water environments than in air

• 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.

• Numerically differentiating the measured thermocouple temperature is not an accurate method for determining the initial heat transfer rate to it from boiling water.

Fig. 1 Sensed Temperature versus Type-J Thermocouple Output Voltage

• The third order polynomial appears to accurately represent the data. • The Relation between signal conditioner output VOUT and the thermocouple

voltage VTC is VTC = (VOUT /G) + VZERO, where VZERO = -4.632 mV and G = 0.105143 V/mV

• These relations are used to interpret the voltage measured by the data acquisition system in terms of the temperature of the thermocouple bead.

TTC = 0.0105VTC3 - 0.2179VTC

2 + 19.839VTC - 0.0002

0

20

40

60

80

100

120

0 1 2 3 4 5 6

Thermocouple Voltage VTC [mV]

Th

erm

oco

up

le T

em

pe

ratu

re T

TC [

0C

]

Figure 2 VI Front Panel

Figure 3 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.

• Thermocouple material properties are based on the average values of Iron and Constantan (A.J. Wheeler and A.R. Gangi, Introduction to Engineering Experimentation, 2nd Ed., Pearson Education Inc., 2004, page 431)

• The approximate time for a temperature front to reach the thermocouple center is tT = D2c/4k

Table 1 Thermocouple PropertiesEffective

Diameter D Density ρThermal

Conductivity kSpecific Heat c

Initial Transient Time tT

[in] [kg/m3] [W/mK] [J/kgK] [sec]0.053 8400 44.5 416 0.036

• The slope exhibits a continuous variation (not a step change) when it is placed in the boiling water at time t = 1.55 sec.

• The measured temperature slope may respond slowly at first because the TC interior temperature does not change immediately after it is placed in the hot environment.

• The thermocouple reaches its final temperature at around t = 1.9 sec

• The dimensionless temperature error is = (T-TF)/(TI-TF)

Fig. 4 Thermocouple temperature versus Time in Boiling Water

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3

Time, t [sec]

Te

mp

era

ture

, T

[C

]

Ti = 19.0oC

TF = 90.9oC

Fig. 5 Dimensionless Temperature Error versus Time in Boiling Water

• The dimensionless temperature error decays exponentially during the time period t = 1.764 to 1.826 sec with time constant b = -0.282 1/sec.

• The effective heat transfer coef. is determined from h = -cDb/6

= 5.396E+20e-2.822E+01t

0.001

0.01

0.1

1

1.5 1.6 1.7 1.8 1.9 2 2.1 2.2t [sec]

tB = 1.764 sectE = 1.826 sec

h = 2.2x104 W/m2K

Fig. 6 Dimensionless Temperature Error versus Time t for Room Temperature Air and Water

• The initial and final TC temperatures were Ti = 91.1°C and TF = 19.7°C.

• The dimensionless temperature error decays exponentially during the time periods t = 1.143 to 1.521 sec (in air) and t = 1.883 to 1.970 sec (in water).

= 2.4779e-0.9649t

= 3.441E+16e-2.116E+01t

0.001

0.01

0.1

1

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5

Time, t [sec]

Dim

ensi

on

less

Tem

per

atu

re E

rro

r,

tB = 1.143 sectE = 1.521 sec

h = 742 W/m2K

tB = 1.883 sectE = 1.970 sec

h = 1.6x104 W/m2K

TC in air

TC in water

Table 2 Effective Mean Heat Transfer Coefficients

• The dimensional heat transfer coefficients are higher in the water than in air due to its 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 characterizes the temperature differences within the thermocouple divided by the difference between the thermocouple surface temperature and its surroundings

• The thermocouple is not a uniform temperature body in the water environments

Environment h kFluid NuD Bi Lumped

[W/m2K] [W/mK] hD/kFluid hD/kTC Bi < 0.1?

Boiling Water 21708 0.680 43.0 0.66 noRoom Temperature Air 742 0.026 38.1 0.02 yes

Room Temperature Water 16277 0.600 36.5 0.49 no

Fig. 7 The Heat Transfer Rate to TC in Boiling Water versus Time

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

• The heat transfer is significant between t = 1.55 and 1.9 sec• The heat transfer rate to the TC actually peaks at t = 1.55 sec when it is first placed in the

boiling water, and then decrease. • The measured heat transfer appears to increase for 0.13 sec before decreasing because the

slope of the curve in Fig. 4 increases at a finite rate when the TC is placed in boiling water. This delay is 4 times larger than the initial transient time tT = 0.036 sec. This difference may be because the TC is not a lumped body (Bi > 0.1)

-0.5

0

0.5

1

1.5

2

2.5

1.5 1.6 1.7 1.8 1.9 2

Time, t [sec]

Hea

t T

ran

sfe

r R

ate,

Q [

W]

Dt = 0.001 secDt = 0.01 secDt = 0.1 sec

Extra Figures (not part of report)

Summary of 2006 Data

• Air has consistently lowest h• h increases with D?

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

Fig. 6 Thermocouple Temperature versus Time for Room Temperature Air and Water

• There are two periods of significant temperature change when the TC is first place in the air and water.

0

10

20

30

40

50

60

70

80

90

100

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5

t [sec]

T [

C]

Thermocouple in Air

Thermocouple in Room Temperature

Water

TI = 91.1oC

TF = 19.7oC

0

5000

10000

15000

20000

25000

30000

35000

1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85

Time, t [sec]

He

at

Tra

ns

fer

Co

eff

icie

nt,

h [

W/m

K]

• Calculated from h = (cD/6)[(dT/dt)/(TF – T)] = Q/[D2(TF – T)]

• It appears to increase after then thermocouple is plunged into the boiling water at t = 1.55 sec. This may be because the heat transfer rate Q is calculated based on the slope of the temperature versus time data, and this is not an accurate method.

• (horizontal line calculated from curve fit in Fig. 5) appears to accurately represent the mean value of the time dependent heat transfer coefficient for the time period t = 1.764 to 1.826 sec.

Fig. 9 Heat Transfer Coefficient versus Time for Boiling Water

h

h