Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology, Pune
Stefan Boltzmann constant
5
Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology, Pune
Name: Roll No: Div: Batch:
Sem: AY:
Date of conduction: Date of submission:
EXPERIMENT NO. 6
TITLE: To find Stefan Boltzmann constant for radiation HT.
AIM: To find value of Stefan Boltzmann constant for radiation heat transfer.
Apparatus/Instrumentation: Ammeter, Voltmeter, Dimmer stat, digital Temperature Indicator
Experimental setup.
INTRODUCTION:
Stefan Boltzmann law states that the thermal radiation heat flux or emissive power of black
surface is proportional to fourth power of its absolute temperature of surface and given by,
q 4 W
=σ T 2
A m
The constant of proportionality is σ called as Stefan Boltzmann constant and has value of
−8 W
σ =5.67 ×10 2 4
m K
Stefan Boltzmann law can be derived by integrating Planks law over entire spectrum of
wave length.
Where, Eb is emissive power of black surface.
Ebλ is monochromatic emissive power of black surface.
σ is Stefan Boltzmann constant.
T is absolute temperature (in K).
Element toward enclosure Q1=F 1−s σ T 14 A 1 , also Enclosure toward element Qs ¿ F s−1 σ T 4s A s ,
A1
Applying reciprocity theorem, F 1−2 A1 = F 2−1 A2 Therefore, F 2−1 = × F1−2
A2
Department of Mechanical Engineering Heat Transfer Lab
Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology, Pune
We know, F 1−s = 1 for current condition.
Therefore, Rate of heat exchange between enclosure and element give is by,
Qs −1 ¿ F 1−s σ (T ¿¿ s 4−T 41 ) A 1 ¿ ….. (a)
dT
Q=mC p @ t = 0 …. (b) Rate of heat exchange at t = 0
dt
Divide (b) by (a) we get,
dT
mC p ×
dt
σ= ¿
A × ( T s −T 1 ¿
4 4
EXPERIMENTAL ANALYSIS
A. Experimental set-up:
It consists of hemisphere steel which is placed inside container. The container has hole
through which small copper disc can be located at the centre of hemisphere. 5 thermocouples are
located on hemisphere steel, while a thermocouple is fitted on copper disc.
A temperature controller is provided for controlling temperature of water by controlling
heater. A dimmer stat is provided to change voltage heater as per requirement.
B. Description of components:
1. Water tank: It is made up of SS material. A copper hemisphere placed inside this
tank.
2. Heater: This is clamp type heater which is surrounded by aluminum. One end of this
bar is heated with heating coil so that this heat is transferred from one end to other by
conduction. This heater is inserted in tank.
3. Sensor: K type sensor is used for measuring temperature of copper hemisphere at
different points, while one sensor is used to measure temperature of water.
4. Temperature indicator: 8 Channel (0 - 400 ºC)
Department of Mechanical Engineering Heat Transfer Lab
Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology, Pune
5. Temperature controller: Used to control temperature of water using thermocouple
switches of heater when temperature is above specified temperature(100ºC)
C. Procedure:
1. Fill the tank with water up to level mark till overflow starts.
2. Fix enclosure properly on top of tank with horizontal surface immersed above 70 ºC.
3. Set the thermostat above 70 ºC.
4. Give supply to heater coil from mains.
5. Check for leakage of current and make proper earthing.
6. Wait till temperature of water reaches between values on thermostat at 90 ºC.
7. Put off heater supply.
8. Record test disc temperature before its introduction in its position on cover.
9. Introduce disc in the position with thermocouples leads connected to temperature.
Indicator and record time in seconds when temperature indicator changes temperature.
10. After completion of readings switch off main supply.
Technical Specifications:
1. Temperature indicator (0 - 400 ºC)
2. Heater (0 - 500W)
3. Copper hemisphere disc: 200mm
4. Outer Jacket: 250mm
5. Base plate: 300mm
6. Test disc: 30mm thk
7. Material of disc: copper
8. Mass of disc 30gm(0.030 Kg)
9. Water tank: 250 mm X 225 mm, SS material
Observation Table:
Sr.no T1 ºC. T2 ºC. T3ºC. T4 ºC. T5 ºC. Tavg ºC. T6 ºC Time
Test plate (sec)
1
2
3
4
CALCULATIONS:
Use equations explained above in experiment theory to calculate Stefan Boltzmann constant.
1. Stefan Boltzmann constant by practical calculations,
Department of Mechanical Engineering Heat Transfer Lab
Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology, Pune
dT
m×C p ×
dt
σ=
A × ( T s −T 6 )
4 4
Where,
m = mass of test disc = 30gm
C p= 0.381 KJ/Kg K
2. Surface temperature (T s)
T 1+T 2 +T 3 +T 4 +T 5
T s=
5
T6 = Disc temperature before introduced
GRAPH:
Show variation of temperature of test disc (T6) across time (sec)
CONCLUSION WITH SUPPORTIVE JUSTIFICATION:
The experimental value of Stefan Boltzmann constant is_____________
Experimental set-up:
Department of Mechanical Engineering Heat Transfer Lab
Bansilal Ramnath Agarwal Charitable Trust’s
Vishwakarma Institute of Technology, Pune
Figure (a), Schematic of Experimental Set-Up.
Department of Mechanical Engineering Heat Transfer Lab
