Errors associated with interferometric measurement of convective heat transfer coefficients

J. M. Mehta; W. Z. Black

doi:10.1364/AO.16.001720

Applied Optics
Vol. 16,
Issue 6,
pp. 1720-1726
(1977)
•https://doi.org/10.1364/AO.16.001720

Errors associated with interferometric measurement of convective heat transfer coefficients

J. M. Mehta and W. Z. Black

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J. M. Mehta and W. Z. Black, "Errors associated with interferometric measurement of convective heat transfer coefficients," Appl. Opt. 16, 1720-1726 (1977)

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Abstract

Errors caused by refraction and end effects in interferometric systems are studied analytically. Both errors are estimated for Mach-Zehnder and differential interferometers when these instruments were used to measure convective heat transfer coefficients in air and water. Both errors were found to be larger for the Mach-Zehnder interferometer than for the differential interferometer. This result suggests that the differential interferometer is potentially a more suitable and accurate device than the Mach-Zehnder interferometer, if one wishes to measure heat transfer coefficients. Convective heat transfer coefficients measured with a differential interferometer are presented. The experimental study used a specially designed test section, which was inserted into the interferometer. The test involved heat dissipated from a vertical plate by free convection to water. The measured results were found to compare satisfactorily with published results at Rayleigh numbers less than 10⁴. At higher Rayleigh numbers, refraction caused sufficient bending of the light rays that a zone of no information next to the heated surface resulted in significant errors.

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		$ϕ = \frac{T_{s} - T_{a}}{T_{s}}$

L/δ	α	0.05	0.10	0.20
	0.00	0.209	0.126	0.087
	0.25	0.0525	0.0316	0.0215
10	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.150	−0.0633	−0.0433
	0.667	−0.221	−0.126	−0.0858
	1.00	−0.420	−0.253	−0.168
	0.00	0.0525	0.0316	0.0215
	0.25	0.0131	0.00795	0.00535
5	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.0262	−0.0158	−0.0107
	0.667	−0.0525	−0.0316	−0.0214
	1.00	−0.105	−0.0632	−0.0426
	0.00	0.00841	0.0056	0.0034
	0.25	0.0021	0.00126	0.00085
2	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.0042	0.00253	0.00171
	0.667	−0.0084	0.00506	0.00342
	1.00	−0.0168	0.01012	0.00689

		$ϕ = \frac{T_{s} - T_{a}}{T_{s}}$

L/δ	α	0.05	0.10	0.20
	0.00	1.10	2.204	4.08
	0.25	0.282	0.715	1.634
10	0.333	0.0042	0.0048	1.2303
	0.50	−0.560	−0.130	−1.236
	0.667	−1.134	−2.75	−3.913
	1.00	−2.301	−5.310	−28.04
	0.00	0.292	0.699	1.299
	0.25	0.071	0.179	0.373
5	0.333	0.0232	0.0218	0.0234
	0.50	−0.141	−0.355	−0.710
	0.667	−0.284	−0.716	−1.45
	1.00	−0.571	−1.14	−2.845
	0.00	0.045	0.114	0.237
	0.25	0.013	0.028	0.0597
2	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.023	−0.057	−0.119
	0.667	−0.095	−0.115	−0.238
	1.00	−0.091	−0.230	−0.478

		$ϕ = \frac{T_{s} - T_{a}}{T_{s}}$

L/δ	α	0.05	0.10	0.20
	0.00	0.244	0.185	0.331
	0.25	0.0613	0.0415	0.083
10	0.333	≃0.000	≃0.000	≃0.000
	0.50	−0.122	−0.093	−0.166
	0.667	−0.245	−0.186	−0.332
	1.00	−0.491	−0.373	−0.647
	0.00	0.0613	0.0465	0.383
	0.25	0.0153	0.0116	0.002
5	0.333	≃0.00	≃0.00	≃0.ν
	0.50	−0.0306	−0.0232	−0.041
	0.667	−0.0613	−0.0415	−0.083
	1.00	−0.122	−0.0393	−0.166
	0.00	0.00981	0.00745	0.0132
	0.25	0.00245	0.00186	0.0033
2	0.333	≃0.00	≃0.00	≃0.ν
	0.50	−0.0049	−0.0037	−0.0066
	0.667	−0.0093	−0.00745	−0.0132
	1.00	−0.0196	−0.0149	−0.0265

		$ϕ = \frac{T_{s} - T_{a}}{T_{s}}$

L/δ	α	0.05	0.10	0.20
	0.00	1.280	5.41	19.32
	0.25	0.336	1.430	5.034
10	0.333	0.040	0.0486	0.
	0.50	−0.648	−2.81	−10.09
	0.667	−1.310	−5.78	−22.72
	1.00	−2.667	−12.07	−48.94
	0.00	0.326	1.430	5.62
	0.25	0.082	0.363	1.45
5	0.333	≃0.00	0.0030	0.025
	0.50	−0.164	−0.724	−2.871
	0.667	−0.328	−1.460	−5.83
	1.00	−0.66	−2.95	−11.92
	0.00	0.052	0.233	0.931
	0.25	0.013	0.058	0.234
2	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.026	−0.116	−0.467
	0.667	−0.052	−0.233	−0.936
	1.00	−0.105	−0.468	−1.

		$ϕ = \frac{T_{s} - T_{a}}{T_{s}}$

L/δ	α	0.05	0.10	0.20
	0.00	0.209	0.126	0.087
	0.25	0.0525	0.0316	0.0215
10	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.150	−0.0633	−0.0433
	0.667	−0.221	−0.126	−0.0858
	1.00	−0.420	−0.253	−0.168
	0.00	0.0525	0.0316	0.0215
	0.25	0.0131	0.00795	0.00535
5	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.0262	−0.0158	−0.0107
	0.667	−0.0525	−0.0316	−0.0214
	1.00	−0.105	−0.0632	−0.0426
	0.00	0.00841	0.0056	0.0034
	0.25	0.0021	0.00126	0.00085
2	0.333	≃0.00	≃0.00	≃0.00
	0.50	−0.0042	0.00253	0.00171
	0.667	−0.0084	0.00506	0.00342
	1.00	−0.0168	0.01012	0.00689

Abstract

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Figures (11)

Tables (4)

Equations (18)

Applied Optics