HEAT TRANFER BY RADIATION 1

OVERVIEW download HeatRadiation1.xls

A body having a surface temperature, T , in degrees kelvin radiates energy according to


H=seAT4 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 Stefan-Boltzmann constant = 5.67E-08 W/(m2 oK4). It is a “Universal Constant. When the surrounding of the body are at temperature T0 , the net radiation is


H=seA(T4-T04) .


When the body is hotter than the surrounding, T >T0 , then the body radiates energy away. When T <T0 , 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 re-radiates 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 TH (K), the other at the lower temperature TL(K). The formula


H=seA(TH4-TL4)


describes the situation. The body temperature can be either TH or TL .


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 (m2). 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 70oF . 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 m2 – see cell C7). Cells F12 and G12 show the values of TH4 and TL4 , respectively. Finally, cell H12 shows the formula with all numbers. This is the energy you would radiate for each m2 of exposed skin if your skin temperature we 70oF when the surroundings are 32oF = 0oC = 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 TH 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 TH TO A BODY AT LOW TEMP TL.

2








3

YOU CAN ONLY CHANGE VALUES IN YELLOW CELLS

4









5

Stefan-Boltzmann Constant

s

5.67E-08

W/(m2 oK4) A Universal Constant


6

emissivity

e

1

Dimensionless. Can have any value from 0 to 1.

7

Area

A

1

m2 Can have any value you want.


8

Low Temp

TL Low Temp

273

oK Can have any value from >= 0.


9









10


TH High Temp

H=seA(TH4-TL4)



TH4

TL4

FORMULA with VALUES

11

oF

oK

Watts



oK4

oK4

H=seA(Th4-TL4)

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 oF . IT IS CONVERTED TO oK AND H IS CALCULATED

14









15

BELOW IS FOR A CONTINUOUS RANGE OF VALUES BETWEEN TL AND TH IN INCREMENTS OF DK

16

DK Temp Increments

100

oK






17


TH

H



TH4

TL4

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