eml 4304l thermal fluids lab thermal conduction experiment # 3
DESCRIPTION
EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3. Mechanical Engineering Department FAMU/FSU College of Engineering. Outline. Purpose of the lab Fundamental Equations Unit 3 and Unit 4 Analysis Unit 1 and Unit 2 Analysis Error Analysis. PURPOSE. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/1.jpg)
EML 4304L Thermal Fluids Lab Thermal Conduction
Experiment # 3
EML 4304L Thermal Fluids Lab Thermal Conduction
Experiment # 3
Mechanical Engineering Department FAMU/FSU College of Engineering
![Page 2: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/2.jpg)
Outline
•Purpose of the lab•Fundamental Equations•Unit 3 and Unit 4 Analysis•Unit 1 and Unit 2 Analysis•Error Analysis
![Page 3: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/3.jpg)
PURPOSE
• Conduct a series of thermal conduction experiments which examines the effects on heat transfer with varying cross-sectional area and distance. – Using this thermal conduction information derive
Fourier’s law of thermal conduction.
• Analyze the temperature variance in a series of metal rods that are in physical contact. – From this information determine thermal resistance
and contact resistance.
![Page 4: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/4.jpg)
Heat flowfor units 3 and 4
Q conduction=-k A dT / dx
Q coolant=m Cp dT / t
![Page 5: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/5.jpg)
Heat flowfor units 1 and 2
![Page 6: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/6.jpg)
Fundamental
Equations
![Page 7: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/7.jpg)
Rate of heat flow at the heat sinkmw = mass of cooling water displaced in time t (kg)
Cp = Specific heat of water at constant pressure (kJ/kg °C)
T = (Tout - Tin) of cooling water (°C)
t = time required to displace a volume Vw of water (s)
This equation is used to determine the amount of energy that is being absorbed by the coolant. Once this is determined for each unit, it is assumed to be the constant rate of conduction through each material.
t
TCmq pw
![Page 8: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/8.jpg)
Qcond = KA(ΔT/Δx)
Rate of heat conduction
K = thermal conductivity constant (W/m °C)
A = cross-sectional area (m2)
T = temperature difference across the material (°C)
x = distance between temperature readings (m)
Used to determine rate of heat conduction through a body based on material properties, area, temperature difference, and length of material.
![Page 9: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/9.jpg)
Fourier’s law of heat conduction
-K = thermal conductivity constant (W/m °C)
A = cross-sectional area (m2)
dT = differential element for temperature (°C)
dx = differential element for distance (m)
Qcond = -KA dT/dx
Used to determine rate of heat conduction through a body based on material properties, area, and temperature/distance gradient.
![Page 10: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/10.jpg)
• Q=KA ΔT/Δx Q=-KA dT/dx
• dT/dx = temperature gradient
x
T
dT/dx
![Page 11: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/11.jpg)
Conservation of EnergyQin = Q out
Q conduction = Q coolant
Calculations
This equation assumes there is no heat loss through the system boundary. Though each unit is insulated, there will still be some heat loss.
TCmdx
dTAk p
![Page 12: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/12.jpg)
Thermal Contact Resistance
Rt,c = Thermal contact resistance (ºC/W)
T = Temperature change (ºC)
q = Heat flux (W)
RT
qt c,
Calculates thermal contact resistance for a given temperature discontinuity and a known power input.
![Page 13: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/13.jpg)
Heat Conduction for Units 3 and 4
![Page 14: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/14.jpg)
Thermocouple Placement for Units 3 and 4
![Page 15: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/15.jpg)
UNIT #3Q=KA*ΔT/Δx
Diameter is a function of x:
D(x)=D0+mx
D(x)=1”+(x/(11+1/16))
![Page 16: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/16.jpg)
Unit #3
Area can also be written as a function of x:
A = (/4) d2
A(x) = (/4) d(x)2
Q=KA*dT/dx
![Page 17: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/17.jpg)
Unit #3
Q = -k A T/x = -k A(x) T/x
Q k A x( )dT
dx
Q x1
A x( )
d k T1
d
![Page 18: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/18.jpg)
Unit #3
Once k is solved for, the temperature can be found for any distance, x.
T x( ) T 0Q
kx
1
A x( )
d
0
)(1
TT
dxxA
Qk
![Page 19: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/19.jpg)
UNIT #4
x2 x1
QinQout
Q=KA*ΔT/Δx
K = coeff. of therm. conductivity NOTE: K is unknown and must be determined
![Page 20: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/20.jpg)
Thermal Contact Resistance
Determination Units #1 and #2
![Page 21: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/21.jpg)
Thermal contact resistance(Rc) is a discontinuity in the temperature gradients between two materials in contact. The value is determined by projecting the temperature gradients, calculating the temperature difference, and dividing the temperature difference by the power that is transmitted through the materials.
Factors affecting thermal contact resistance: 1 - Surface Roughness2 - Type of materials in contact3 - Temperature materials are at4 - Pressure applied to materials5 - Type of fluid trapped at interface
![Page 22: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/22.jpg)
elements are enclosed in the insulating jacket. Figure1 illustrates the schematics of the apparatus. The dimensions of the tapered rod are indicated in Fig. 2.elements are enclosed in the insulating jacket. Figure1 illustrates the schematics of the apparatus. The dimensions of the tapered rod are indicated in Fig. 2.elements are enclosed in the insulating jacket. Figure1 illustrates the schematics of the apparatus. The dimensions of the tapered rod are indicated in Fig. 2.
![Page 23: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/23.jpg)
Units #1 and #2
Cu (Al)
Contact Resistance
T1T10
x1x2
Stainless Steel
Steel (Mg)
![Page 24: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/24.jpg)
Thermocouple placement for units 1 and 2
![Page 25: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/25.jpg)
Ideal Thermal Conduction
T1
T2
T3
T4
Material 1 Material 2
T2 = T3
![Page 26: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/26.jpg)
Actual Thermal Conduction
T1T2
T3
T4
Material 1 Material 2
T2 = T3
Temperature profile due to thermal contact resistance
![Page 27: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/27.jpg)
Material 1 Material 2
T2
T3Projected Slope T3
Projected Slope T2
ΔTTemperature profile due to thermal contact resistance
![Page 28: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/28.jpg)
Temperature vs Distance
Temperature(ºF)
Distance(inches)
Material 1
Material 2
Material 3
Discontinuities where ΔT must be determined
![Page 29: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/29.jpg)
Thermal Contact Resistance Calculation
Rt,c = ΔT/Q
Qwtr=mwCp(ΔT)
Q = Qwtr
ΔT (determined by projection of slope and measuring difference in temperatures)
![Page 30: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/30.jpg)
Errors
• Time
Flow rate
Steady State• Heat Losses
Not perfectly insulated• Unit #4 Thermocouples #3 and #5
Inconsistent readings
![Page 31: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/31.jpg)
![Page 32: EML 4304L Thermal Fluids Lab Thermal Conduction Experiment # 3](https://reader036.vdocument.in/reader036/viewer/2022081506/56814930550346895db66e59/html5/thumbnails/32.jpg)
Heat flowfor units 3 and 4