Study of the Effective Thermal Emittance of Cylindrical Cavities*

James Vollmer

doi:10.1364/JOSA.47.000926

Journal of the Optical Society of America
Vol. 47,
Issue 10,
pp. 926-932
(1957)
•https://doi.org/10.1364/JOSA.47.000926

Study of the Effective Thermal Emittance of Cylindrical Cavities

James Vollmer

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James Vollmer, "Study of the Effective Thermal Emittance of Cylindrical Cavities*," J. Opt. Soc. Am. 47, 926-932 (1957)

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Abstract

An equation is derived which relates the effective emittance of a cylindrical cavity to the emittance of the construction material, the ratio of the length to the radius of the cylinder, and the distance separating the cylinder and the receiver. This equation was checked by measuring the effective emittance of shallow cylinders of two different lengths, at four axial distances, and with three filter systems. The use of filters in combination with a construction material whose spectral emittance varies sharply is equivalent to varying the emittance of the construction material. In all cases considered, the experimental result and the value predicted are in agreement within the experimental limits.

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x	Measured ∊(x)	Predicted ∊(x)	% deviation of predicted from measured ∊(x)
2.988	0.905	0.899	−0.7
2.632	0.913	0.910	−0.3
2.017	0.876	0.883	+0.8
1.286	0.803	0.827	+3.0
0.6379	0.765	0.747	−2.3

Filter	d+x₀	6.005	8.980	12.97	16.96
Pyrex	Measured	0.459	0.456	0.464	0.466
Pyrex	1 band calc	0.472	0.486	0.500	0.504

Silica	Measured	0.530	0.531	0.541	0.549
	1 band calc	0.557	0.573	0.586	0.592
	2 band calc	0.546			0.582

Fluorite	Measured		0.731	0.727	0.726
	1 band calc		0.845	0.857	0.862
	3 band calc				0.766

Total	Measured			0.754	0.754
	1 band calc			0.871	0.876
	4 band calc			0.789	0.785

Filter	d+x₀	6.005	8.980	12.97	16.96
Pyrex	Measured	0.537	0.540	0.561	0.569
Pyrex	1 band calc	0.544	0.568	0.587	0.598

Silica	Measured	0.602	0.605	0.629	0.641
	1 band calc	0.624	0.649	0.669	0.680
	2 band calc	0.615			0.669

Fluorite	Measured		0.770	0.785	0.780
	1 band calc		0.886	0.893	0.902
	3 band calc				0.818

Total	Measured			0.806	0.803
	1 band calc			0.903	0.912
	4 band calc			0.825	0.833

l	d	$\frac{{r_{2}}^{2} + d^{2}}{{r_{2}}^{2}}$	−c₁	−ν₁	x₀
2.988	5.968	37.08	0.08984	0.3943	0.0370
2.988	8.952	81.66	0.03398	0.2844	0.0280
2.988	12.93	169.2	0.01312	0.2069	0.0390
2.988	16.91	288.7	0.006369	0.1625	0.0500
3.966	5.968	37.08	0.07662	0.3720	0.0370
3.966	8.952	81.66	0.03008	0.2724	0.0300
3.966	12.93	169.2	0.01198	0.2004	0.0390
3.966	16.91	288.7	0.005915	0.1584	0.0500

l	Band	∊	+α	−A	−B	∊B
2.988	P	0.0941	0.3068	0.6531	0.1887	0.5279
	S	0.1279	0.3576	0.6187	0.1444	0.6186
	F	0.3703	0.6085	0.3904	0.0289	0.8867
	∞	0.3961	0.6294	0.3698	0.0246	0.8990
	P−S	0.1605	0.4006	0.5847	0.1135	0.6847
	S−F	0.6037	0.7769	0.2229	0.0062	0.9597
	F−∞	0.6246	0.7903	0.2097	0.0053	0.9635
3.966	P	0.0941	0.3068	0.6706	0.1435	0.6411
	S	0.1279	0.3576	0.6305	0.1036	0.7262
	F	0.3703	0.6085	0.3911	0.1600	0.9374
	∞	0.3961	0.6294	0.3704	0.0133	0.9453
	P−S	0.1605	0.4006
	S−F	0.6037	0.7769
	F−∞	0.6246	0.7903

d+x₀	Band	t^W	T_c^c°K	t^c	E₁	E₀	Reflectance
6.005	P	0.000	1101	0.2169	2.633	0.046	1.0245
6.005	S	0.000	1101	0.4413	5.945	0.032	1.0245
8.980	P	0.000	1097	0.2151	1.173	0.007	1.0344
8.980	S	0.000	1097	0.4391	2.745	0.002	1.0344
8.980	F	0.1800	1097	0.8980	7.478	0.071	1.0344
12.97	P	0.000	1100	0.2162	0.581	0.002	1.0286
12.97	S	0.000	1100	0.4405	1.368	0.012	1.0286
12.97	F	0.1800	1100	0.8985	3.757	0.080	1.0286
12.97	∞	1.000	1100	1.000	4.404	0.211	1.0286
16.96	P	0.000	1104	0.2183	0.355	0.005	1.022
16.96	S	0.000	1104	0.4430	0.832	0.004	1.022
16.96	F	0.1800	1104	0.8992	2.264	0.068	1.022
16.96	∞	1.000	1104	1.000	2.669	0.156	1.022

Abstract

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Figures (3)

Tables (7)

Equations (13)

Journal of the Optical Society of America