Measurement of heat transfer distribution is frequently required in engineering. However, some heat transfer techniques are not able to measure accurately on two-dimensional curved surfaces. In this field, periodic-transient measurement methods are advantageous. This paper describes the development of a periodic-transient technique for high-resolution heat transfer measurement and its application to multiple air-jet cooling of a concave solar receiver window. In contrast to other measurement techniques, the periodic-transient technique requires neither homogenous heating nor quantitative measurement of surface or fluid temperatures. The heat transfer coefficient is determined by periodically heating the substrate and evaluating the phase shift between the heat flux penetrating the substrate and the resulting temperature response. Equations for a hollow-sphere and flat-plate substrates are derived. The curved window surface is periodically heated by a simple device with standard light bulbs. A procedure for taking the transient heating characteristic into consideration is described. The distribution of surface temperature fluctuation is measured nonintrusively by thermography. For the sample application of air-jet cooling, a detailed uncertainty estimation is presented. The relative measurement uncertainty of the local, convective heat transfer coefficient ranges from 2.4% to +14.1% for h=10W(m2K) and from 2.3% to +9.7% for h=200W(m2K). The uncertainty of the spatially averaged heat transfer coefficient lies between +2.0% and +9.8% for hm=10W(m2K) and between +0.7% and +6.7% for hm=200W(m2K). The periodic-transient method described complements established techniques for high-resolution heat transfer measurements on two-dimensional curved surfaces.

1.
Childs
,
P. R. N.
,
Greenwood
,
J. R.
, and
Long
,
C. A.
, 1999, “
Heat Flux Measurement Techniques
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
213
(
7
), pp.
655
677
.
2.
Diller
,
T. E.
, 1993, “
Advances in Heat Flux Measurements
,”
Advances in Heat Transfer
,
Academic
,
New York
, Vol.
23
, pp.
279
368
.
3.
Moffat
,
R. J.
, 1988, “
Experimental Methods in Heat Transfer
,”
Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics
,
R. K.
Shah
,
E. N.
Ganić
, and
K. T.
Yang
, eds.,
Elsevier
,
New York
, pp.
13
31
.
4.
Scott
,
C. J.
, 1976, “
Transient Experimental Techniques for Surface Heat Flux Rates
,”
Measurements in Heat Transfer
,
2nd ed.
,
E. R. G.
Eckert
and
R. J.
Goldstein
, eds.,
Hemisphere
,
Washington, DC
, pp.
375
396
.
5.
Lee
,
D. H.
,
Chung
,
Y. S.
, and
Kim
,
D. S.
, 1997, “
Turbulent Flow and Heat Transfer Measurements on a Curved Surface With a Fully Developed Round Impinging Jet
,”
Int. J. Heat Fluid Flow
0142-727X,
18
, pp.
160
169
.
6.
Sargent
,
S. R.
,
Hedlund
,
C. R.
, and
Ligrani
,
P. M.
, 1998, “
An Infrared Thermography Imaging System for Convective Heat Transfer Measurements in Complex Flows
,”
Meas. Sci. Technol.
0957-0233,
9
, pp.
1974
1981
.
7.
Hofmann
,
H.
,
Martin
,
H.
, and
Kind
,
M.
, 2003, “
Experimental Setup for Heat Transfer Measurements in Pulsating Impinging Jet Flow
,”
Proceedings of the International Symposium on Transient Convective Heat and Mass Transfer in Single and Two-Phase Flow
,
Cesme, Turkey
, Aug. 17–22.
8.
Hofmann
,
H.
, 2005, “
Wärmeübergang beim pulsierenden Prallstrahl
,” Ph.D. thesis, Universität Karlsruhe (TH), Universitätsverlag Karlsruhe.
9.
Baehr
,
H. D.
, and
Stephan
,
K.
, 1996, “
Wärme- und Stoffübertragung
,”
2nd ed.
,
Springer-Verlag
,
Berlin
.
10.
Ångström
,
A. J.
, 1861, “
Neue Methode, das Wärmeleitungsvermögen der Körper zu bestimmen
,”
Ann. Phys. Chem.
0003-3804,
114
(
12
), pp.
513
530
.
11.
Baughn
,
J. W.
,
Anderson
,
M. R.
,
Mayhew
,
J. E.
, and
Butler
,
R. J.
, 1997, “
A Periodic Transient Method Using Liquid Crystals for the Measurement of Local Heat Transfer Coefficients
,”
Proceedings of the ASME Heat Transfer Division
, ASME, New York, HTD-Vol.
353
, pp.
73
80
.
12.
Kosky
,
P. G.
,
Maylotte
,
D. H.
, and
Gallo
,
J. P.
, 1999, “
Ångström Methods Applied to Simultaneous Measurements of Thermal Diffusivity and Heat Transfer Coefficents: Part, 1, Theory
,”
Int. Commun. Heat Mass Transfer
0735-1933,
26
(
8
), pp.
1051
1059
.
13.
Kosky
,
P. G.
,
Maylotte
,
D. H.
, and
Gallo
,
J. P.
, 1999, “
Ångström Methods Applied to Simultaneous Measurements of Thermal Diffusivity and Heat Transfer Coefficents: Part, 2, Experimental
,”
Int. Commun. Heat Mass Transfer
0735-1933,
26
(
8
), pp.
1061
1068
.
14.
Roetzel
,
W.
,
Prinzen
,
S.
, and
Wandelt
,
M.
, 1993, “
Temperature Oscillation Technique for Determination of Local Convective Heat Transfer Coefficients Without Fluid Temperature Measurement
,”
Chem. Eng. Technol.
0930-7516,
16
, pp.
89
93
.
15.
Prinzen
,
S.
, 1991, “
Experimentelle Bestimmung örtlicher Wärmeübergangskoeffizienten mittels Temperaturschwingungen der Wand
,” Fortschritt-Berichte, VDI, Reihe, 19, Nr. 51.
16.
Carlomagno
,
G. M.
, and
De Lucca
,
L
, 1989, “
Infrared Thermograpy in Heat Transfer
,”
Handbook of Flow Visualization
,
W. J.
Yang
, ed.,
Hemisphere
,
Washington, DC
, pp.
531
553
.
17.
Anderson
,
M. R.
, and
Baughn
,
J. W.
, 2005, “
Liquid Crystal Thermography: Illumination Spectral Effects. Part 1-Experiments
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
127
(
5
), pp.
581
587
.
18.
Anderson
,
M. R.
, and
Baughn
,
J. W.
, 2005, “
Thermochromic Liquid Crystal Thermography: Illumination Spectral Effects. Part 2-Theory
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
127
(
5
), pp.
588
597
.
19.
Campbell
,
R. P.
, and
Molezzi
,
M. J.
, 1996, “
Applications of Advanced Liquid Crystal Video Thermography to Turbine Cooling Passage Heat Transfer Measurement
,” GE Research & Development Center, Technical Information Series No. 96CRD036.
20.
Moffat
,
R. J.
, 1990, “
Experimental Heat Transfer
,”
Heat Transfer
,
G.
Hestroni
, ed.,
Hemisphere
,
Washington, DC
, Vol.
1
, pp.
187
205
.
21.
Fiebig
,
M.
, and
Schulz
,
K.
, 1999, “
Ammonia Absorption Method and Liquid Crystal Thermography for Accurate Local Mass and Heat Transfer Measurements
,”
Applied Optical Measurements
,
M.
Lehner
and
D.
Mewes
, eds.,
Springer-Verlag
,
Berlin
, pp.
19
33
.
22.
Kottke
,
V.
, and
Schmidt
,
K.-G
, 1985, “
Measuring Techniques for Determination of Local Mass and Heat Transfer in Industrial Scale
,”
Measurement Techniques in Heat and Mass Transfer
,
R. I.
Soloukhin
and
N. H.
Afgan
, eds.,
Hemisphere
,
Washington, DC
, pp.
325
335
.
23.
Schlünder
,
E. U.
, and
Gnielinsky
,
V.
, 1967, “
Wärme- und Stoffübertragung zwischen Gut und aufprallendem Düsenstrahl
,”
Chem.-Ing.-Tech.
0009-286X,
39
(
9/10
), pp.
578
584
.
24.
Goldstein
,
R. J.
, and
Cho
,
H. H.
, 1995, “
A Review of Mass Transfer Measurements Using Naphthalene Sublimation
,”
Exp. Therm. Fluid Sci.
0894-1777,
10
, pp.
416
434
.
25.
Röger
,
M.
,
Buck
,
R.
, and
Müller-Steinhagen
,
H.
, 2005, “
Numerical and Experimental Investigation of a Multiple Air Jet Cooling System for Application in a Solar Thermal Receiver
,”
ASME J. Heat Transfer
0022-1481,
127
(
8
), pp.
863
876
.
26.
Röger
,
M.
,
Pfänder
,
M.
, and
Buck
,
R.
, 2006, “
Multiple Air-Jet Window Cooling for High-Temperature Pressurized Volumetric Receivers: Testing, Evaluation, and Modeling
,”
ASME J. Sol. Energy Eng.
0199-6231,
128
(
3
), pp.
265
274
.
27.
Röger
,
M.
, 2006, “
Verfahren und Vorrichtung zur ortsaufgelösten Bestimmung des Wärmeübergangskoeffizienten an einem Messgegenstand
,” German Patent No. 102004026520.
28.
Mandelis
,
A.
, 2001,
Diffusion-Wave Fields: Mathematical Methods and Green’s functions
,
Springer
,
New York
.
29.
Mandelis
,
A.
, 2000, “
Diffusion Waves and their Uses
,”
Phys. Today
0031-9228,
53
(
8
),
29
34
.
30.
Tautz
,
H.
, 1971,
Wärmeleitung und Temperaturausgleich
,
Chemie
,
Weinheim/Bergstr
.
31.
Doetsch
,
G.
, 1970,
Einführung in Theorie und Anwendung der Laplace-Transformation
,
2nd ed.
,
Birkhäuser
,
Basel, Stuttgart
.
32.
Heraeus Quarzschmelze
, 1985,
Quarzglas und Quarzgut
,
Heraeus Quarzschmelze GmbH
,
Hanau, Germany
.
33.
Omega
, 2003, Omega Engineering, Inc. Calibration Report No. HFS-4.
34.
Omega
, 2001, User’s Guide Thin Film Heat Flux Sensor HFS-1, HFS-2, HFS-3, HFS-4, Omega Engineering, Inc., Stamford, USA.
35.
3M
, 1998, 3M 467MP, 467MPF, 468MP Klebstoff-Filme ohne Träger, Product information 08/98, 3M Deutschland GmbH, Neuss.
36.
Goratec
, Manual Thermgraphy Camera TVS-2000 Series (in German), GORATEC Technology GmbH & Co KG, Erding, Germany.
37.
Schlichting
,
H.
, and
Gersten
,
K.
, 1997,
Grenzschicht-Theorie
,
9th ed.
,
Springer-Verlag
,
Berlin
.
38.
Herwig
,
H.
, 1985, “
Asymptotische Theorie zur Erfassung des Einflusses variabler Stoffwerte auf Impuls- und Wärmeübertragung
,” Fortschritt-Berichte VDI, Reihe, 7, Nr. 93.
39.
Röger
,
M.
, and
Uhlig
,
R.
, 2005, “
Cooling Device for Curved Window Subjected to Radiation, Solar Receiver and Process for Cooling a Curved Window
,” European Patent No. EP 1598608 A2.
40.
Röger
,
M.
, 2005, “
Fensterkühlung für solare Hochtemperatur-Receiver
,” Fortschritt-Berichte VDI, Reihe 6, Nr. 534.
This content is only available via PDF.
You do not currently have access to this content.