1. Background

This Combustion File consists of a compilation of experimental data from a variety of sources on the [GLOSS]emissivity[/GLOSS] of metals used in high temperature applications.  The data is cast in the form of temperature dependent correlation equations that can be used for modelling purposes.  Correlations for other materials may be found in four other linked Combustion Files:

·          CF148 – firebrick and refractories

·          CF149 – carbons and coal ash

·          CF223 – glasses and ceramics

·          CF224 – coatings, paints, paper, porcelain and water

 

Background information on the definition and general aspects of the surface emissivity of materials may be found in CF146. Information on the effects of surface roughness is presented in CF 150.

Users of this combustion file should note:

• The data are tabulated in HTML form lower on this page.
• The same data, prepared for calculation, are presented in individual Microsoft Excel Worksheets, all contained within a Workbook.
• The Excel Worksheets also contains two columns allowing the user to calculate surface emissivity directly by inputting a temperature value
• This workbook can be down-loaded by the reader and saved to a local hard disk.
• To achieve this click on the “xls” icon on the left hand side of the banner above. The file will be retrieved from the server, and with up-to-date versions of the browser, will appear in a separate window, from which it may be saved to the user’s hard disk.
• With the exception of the temperature input cells for the calculator, the data in these worksheets are protected – thus the reader cannot change the worksheet without knowledge of the protection password.
• However the reader can copy and paste the data into his/her own project work book as required – at this point the accuracy and integrity of the data becomes the responsibility of the reader.
• To overview the data available – see text and tables below.
• All credits and sources, and where necessary, instructions/advice for data use, are presented in this html file. These are not necessarily reproduced in the Excel Work Sheets.  

2. The correlation equation

Section 3 lists the emissivity, e_0(T), of a wide range of metals as a function of temperature.  These are expressed as least squares polynomials fitted to data from the references listed under Sources below. They are correlated by the expression:

 

e_0(T) = a +10^-5bT + 10^-8cT² +10^-10dT³                                        (1)

 

where T is the absolute temperature (K)

and a, b, c, d are fitted coefficients.

 

 Omitted entries for the coefficients should be taken as zero.  Extrapolation beyond the quoted temperature range should be undertaken with caution especially for strongly non-linear relationships where the c and d coefficients are non-zero.  The s.d. column contains the standard deviation of the individual emissivity measurements about the fitted line, but this is only included where a reasonable estimate is obtainable. 

3. Emissivity data and correlation coefficients

Material	e0(T)					T range	Ref.	e range
	a	b	c	d	s.d.	K
Aluminium
polished	0.0263	5.01			0.013	300 – 900	1	0.04-0.07
oxidised	0.0463	5.01				450 – 900	1	0.07-0.09
lightly oxidised	0.11	21				473 – 873	1	0.11-0.19
Brass
polished	0.03					473	2	0.03
natural, unoxidised	0.035					298	2	0.04
oxidised @ 600°C	0.6					573 – 873	2	0.6
Copper
polished	0.021	1.98			0.005	300 – 1200	1	0.03-0.05
oxide, red heat 30 min	0.06	15.4				400 – 1050	1	0.12-0.22
oxidised at 1000 K		80				600 – 1000	1	0.48-0.8
thick oxide	0.72	20				400 – 1000	1	0.8-0.92
Gold	0.0432	-8.88	7.15		0.001	600 – 1000	1	0.02-0.026
Iron/steel , Polished		18.2				100 – 1050	1	0.24-0.61
iron oxide, red heat 30 min	0.173	68.6	-25.6		0.03	100 – 1050	1	0.24-0.61
molten	0.35					1810 – 1860	3	0.35
heavily oxidised	0.72	20				400 – 1000	1	0.8-0.92

Material

e_0(T)

T range

Ref.

e range

 

a

b

c

d

s.d.

K

 

 

Stainless steels

 

 

 

 

 

 

 

 

  N-155, oxidation

  retarded

0.0144

17.0

 

 

0.024

    100 – 1500

1

0.031-0.27

  N-155, lightly oxidised

-0.0372

27.8

 

 

0.05

   450 – 1300

1

0.09-0.32

  oxidised at high Temp.

0.42

30

 

 

 

   600 – 1400

1

0.60-0.84

  heavily oxidised

0.72

20

 

 

 

   400 – 1000

1

0.8-0.92

Molybdenum, polished

0.0288

12.7

 

 

0.003

    100 – 1800

1

0.04-0.26

                      oxidised

0.82

 

 

 

 

   600 – 800

1

0.82

Nickel, polished

0.0140

12.9

 

 

0.02

    100 – 1500

1

0.005-0.21

            oxidised

 

60

 

 

 

   400 – 1000

1

0.24-0.6

Nichrome, clean

0.65

 

 

 

 

323

2

0.65

                 oxidised

0.71

16

 

 

 

   773 – 1273

2

0.83-0.91

Palladium, polished

-0.03

11.7

 

 

0.01

   400 – 1550

1

0.03-0.16

Platinum, polished

0.008

10.8

 

 

0.014

    100 – 1500

1

0.02-0.17

Silver, electrolytic

0.0119

1.90

 

 

0.005

   400 – 1200

1

0.02-0.035

Titanium (lightly oxidised)

0.2

61

 

 

 

   673 – 1023

 

0.6-00.82

Tin, polished

0.00846

10.8

 

 

 

   300 – 500

1

0.041-0.06

Tungsten, polished

-0.003

10.5

 

 

0.03

   550 – 2800

1

0.03-0.26

Zinc, polished

0.04

50

 

 

 

   473 – 573

2

0.04-0.05

         unoxidised

0.05

 

 

 

 

573

2

0.05

Acknowledgements

This work was funded in part by the UK Heat Transfer and Fluid Flow Service (HTFS) and part supported by the UK EPSRC. The information contained within this file was first published in the Journal of the Institute of Energy. 74, No 500 September 2001 (pp 91 – 99). The permission of the UK Institute of Energy to reproduce it here is gratefully acknowledged.

Sources

1.        TOULOUKIAN, Y.S. and DE WITT, D.P, Thermal radiative properties: Metallic elements and alloys, 1970, Vol. 7. TOULOUKIAN, Y.S. and DE WITT, D.P. Thermal radiative properties.  Nonmetallic solids, 1971, Vol. 8; in Thermophysical Properties of Matter, TPRC Data Series (edited by Touloukian, Y.S. and Ho, C.Y.) Plenum Press, New York.

2.       Handbook of Chemistry and Physics (60th Edition), CRC Press, Boca Raton, Florida, 1981.

3.       RATANAPUPECH, P. and BAUTISTA, R.G. Normal spectral emissivities of liquid iron, liquid nickel and liquid iron-nickel alloys.  High Temperature Science, 1981, 14(4) 269-283.