IMPACT COLLEGE OF ENGINEERING AND APPLIED SCIENCES
SAHAKARA NAGAR SOUTH, BENGALURU - 560092
DEPARTMENT OF MECHANICAL ENGINEERING
HEAT TRANSFER LAB
DETERMINATION OF STEFAN BOLTZMANN CONSTANT
OBJECTIVE: To determine the value of Stefan Boltzmann constant for radiation
heat transfer.
PRINCIPLE: The energy exchange between a small black body located at the center
q 1-2
of a hemispherical surface is given by q1-2 = A ( T14 – T24 ) or =
A( T14 - T24 )
Where A is the surface area of the small body.
The method consists of maintaining the hemispherical surface to a desired
constant high temperature by supplying preheated water at a temperature close to
boiling point on the outside of the hemispherical dome. A small copper disc coated
with lamp black is introduced at the center of the hemisphere and the rate of
temperature rise of the disc is determined graphically. Then by equating the rate of
radiation energy exchange between the hemispherical surface and the disc to the rate
of energy absorption by the disc, the Stefan Boltzmann constant is evaluated.
APPARATUS: The fig shows the cross-sectional view of the apparatus.
Saleha Nadeem B.E., M. Tech (Thermal) Asst. prof., Dept. of ME, ICEAS.
IMPACT COLLEGE OF ENGINEERING AND APPLIED SCIENCES
SAHAKARA NAGAR SOUTH, BENGALURU - 560092
DEPARTMENT OF MECHANICAL ENGINEERING
REF NO DESCRIPTION
1 WATER INLET
2 WATER OUTLET
3 WATER CIRCULATION
4 SPECIMEN-
5 ________ROD
6 _______ ___mm Dia.
7 WATER JACKET
8 COPPER BOWL ___mm Dia.
PROCEDURE:
a) Fill the water in the upper tank.
b) Switch on the immersion heater and heat the water upto 90o C.
c) Remove the disc before pouring the water into the tank.
d) Switch off the heater and open the valve to allow the water into the lower tank.
e) Allow it to reach steady state.
f) Note down the thermocouple temperatures T1, T2, T3, & T4.
g) Insert the disc and immediately note the temperature T4 at every five seconds
interval from zero seconds.
dT
h) Draw the graph of temperature vs time and find
dt
m.C p . ( dT / dt )
i) Calculate ` ’ using the equation : = 4 4
A ( Ths - Ts )
Where Cp = Specific heat of surface in kJ / kg oK
DATA SHEET
SPECIFICATIONS:
Specimen material : _______
Size of the disc : __ mm, ___ mm thickness
Base plate : ____ mm,___ mm thickness (_____)
Heater : 1.5 kW Capacity, immersion type
Copper Bowl : _____ mm
Digital temperature indicator : 0 – 199.9 oC
Saleha Nadeem B.E., M. Tech (Thermal) Asst. prof., Dept. of ME, ICEAS.
IMPACT COLLEGE OF ENGINEERING AND APPLIED SCIENCES
SAHAKARA NAGAR SOUTH, BENGALURU - 560092
DEPARTMENT OF MECHANICAL ENGINEERING
Thermocouples used : 5 numbers, on hemisphere
Stop watch : Digital type
Overhead tank : SS, approximately 1-liter capacity
Water Jacket : 230 mm, SS
Mass of Specimen, m : 5 gm.
T1, T2, T3, are Surface Temperatures, T4, Specimen temperature before
insertion
T5, Heater Temperature.
TABULATION OF READINGS
TRIAL THERMOCOUPLE READINGS ( OC )
NO.
T1 T2 T3 T4 T5
Variation Of Temperature V/S Time Of The Specimen
TRIAL 1 TRIAL 2
TEM
TEMP TEMP TEMP TIM TIM
TIME TIME P
( OC) ( OC) ( OC) E E
( C)
O
0 0
SPECIMEN CALCULATION:
d 2
Area of the disc, A1 = = m2.
4
Mass of the disc, m = 5 10-3 kg.
Saleha Nadeem B.E., M. Tech (Thermal) Asst. prof., Dept. of ME, ICEAS.
IMPACT COLLEGE OF ENGINEERING AND APPLIED SCIENCES
SAHAKARA NAGAR SOUTH, BENGALURU - 560092
DEPARTMENT OF MECHANICAL ENGINEERING
Specific heat of the disc material (____), CPs = 385 J/Kg K.
T1 + T2 + T3
Temperature of the hemispherical surface = Ths = = oC or K.
3
Average temperature of the disc before insertion, T4 = ts = C.
o
Ts = ts + 273 = K.
dT
Rate of temperature rise of the disc, = ( From graph )
dt
dT
Rate of energy absorption by the disc, mCP x = W.
dt
Rate of radiation energy exchange between the disc and the enclosure,
= A1F12(Ths4 – Ts4) W.
Where is the Stefan Boltzmann constant, F12 = 1 for a small body in a large
enclosure.
Equating Rate of radiation energy exchange to rate of energy absorption by the
disc, we
dT
Get, A1F12 ( Ths4 – Ts4 ) = mCPs
dt
dT
mC P
Stefan Boltzmann constant = dt
4
A1 ( Ths - Ts4 )
=………………….W/m2K4
GRAPH :
Temp v/s Time
RESULT:
The value of the Stefan Boltzmann’s constant is _____________ W/m K4
and the theoretical value is ________________ W/m-K4
Saleha Nadeem B.E., M. Tech (Thermal) Asst. prof., Dept. of ME, ICEAS.
