HEAT TRANFER BY RADIATION 1
OVERVIEW download HeatRadiation1.xls
A body having a surface temperature, T , in degrees kelvin radiates energy according to
H=seAT^{4} watts.
A is the exposed area of the body. e is the emissivity of the body. Its value lies between 0 and 1. s is the StefanBoltzmann constant = 5.67E08 W/(m^{2 o}K^{4}). It is a “Universal Constant. When the surrounding of the body are at temperature T_{0} , the net radiation is
H=seA(T^{4}T_{0}^{4}) .
When the body is hotter than the surrounding, T >T_{0}^{ }, then the body radiates energy away. When T <T_{0}^{ }, the body absorbs energy.
Emissivity
When the emissivity e = 0, the body is called a perfect or ideal reflector. It sends all the radiation back to the surrounding without interaction. When e = 1, the body is called an perfect absorber, of a black body. The body aborbs all the radiation that it receives and reradiates it in all direction.
USING THIS SPREADSHEET
This spreadsheet calculates the heat , H (watts) transferred by radiaton between two bodies at different teperatures, one at the higher temperature T_{H }(K), the other at the lower temperature T_{L}(K). The formula
H=seA(T_{H}^{4}T_{L}^{4})
describes the situation. The body temperature can be either T_{H }or_{ }T_{L}^{ }.
You can only change the values in the yellow cells .
To start, in cell C6 the emissivity has been set to 1 . In cell C7 the area set to 1 (m^{2}). In cell C8 TL has been set to 273 K.
The first situation is ROW 12. You have entered the value 70 in A12 for 70^{o}F . Cell B12 shows that temperature as 2.94E+02 K (294.11 K). Cell C12 calculate H as 1.09E+02 W (109 watts radiated for every m^{2 }– see cell C7). Cells F12 and G12 show the values of T_{H}^{4}^{ }and T_{L}^{4 }, respectively. Finally, cell H12 shows the formula with all numbers. This is the energy you would radiate for each m^{2} of exposed skin if your skin temperature we 70^{o}F when the surroundings are 32^{o}F = 0^{o}C = 273 K.
The second situation starts at ROW 16 . This part produces a table and graph. Cell B16 has the increment value of 100. That is the temperaature T_{H} will increase by 100 K in each increment. From ROW 18 down, the values are COLUMNS B,C, G, G and H are as described in the first situation, above.
Sample of the Spreadsheet

A 
B 
C 
D 
E 
F 
G 
H 
1 
HEAT TRANSFERRED BY RADIATION BETWEEN A BODY AT HIGH TEMP T_{H} TO A BODY AT LOW TEMP T_{L}. 

2 








3 
YOU CAN ONLY CHANGE VALUES IN YELLOW CELLS 

4 








5 
StefanBoltzmann Constant 
s 
5.67E08 
W/(m^{2 o}K^{4}) A Universal Constant 


6 
emissivity 
e 
1 
Dimensionless. Can have any value from 0 to 1. 

7 
Area 
A 
1 
m^{2 }Can have any value you want. 


8 
Low Temp 
T_{L }Low Temp 
273 
^{o}K Can have any value from >= 0. 


9 








10 

T_{H }High Temp 
H=seA(T_{H}^{4}T_{L}^{4}) 


T_{H}^{4} 
T_{L}^{4} 
FORMULA with VALUES 
11 
^{o}F 
^{o}K 
Watts 


^{o}K^{4} 
^{o}K^{4} 
H=seA(T_{h}^{4}T_{L}^{4}) 
12 
70 
2.94E+02 
1.09E+02 


7.482E+09 
5.555E+09 
H = 0.00000005669*1*1*(294.111111111111^4  A^4) 
13 
ABOVE YOU CAN SET ANY VALUE IN ^{o}F . IT IS CONVERTED TO ^{o}K AND H IS CALCULATED 

14 








15 
BELOW IS FOR A CONTINUOUS RANGE OF VALUES BETWEEN T_{L} AND T_{H} IN INCREMENTS OF DK 

16 
DK Temp Increments 
100 
^{o}K 





17 

T_{H} 
H 


T_{H}^{4} 
T_{L}^{4} 
FORMULA with VALUES 
18 

273 
0.00E+00 


5.6E+9 
5.6E+9 
H = 0.00000005669*1*1*(273^4  A^4) 
19 

373 
7.82E+02 


19.4E+9 
5.6E+9 
H = 0.00000005669*1*1*(373^4  A^4) 
20 

473 
2.52E+03 


50.1E+9 
5.6E+9 
H = 0.00000005669*1*1*(473^4  A^4) 
21 

573 
5.80E+03 


107.8E+9 
5.6E+9 
H = 0.00000005669*1*1*(573^4  A^4) 
22 

673 
1.13E+04 


205.1E+9 
5.6E+9 
H = 0.00000005669*1*1*(673^4  A^4) 
© Hulan E. Jack Jr. 2002