In order to achieve uniform distribution of heat flux over an isothermal heated target surface, a numerical algorithm is developed to obtain an optimized array of four laminar impinging slot jets. Root mean square deviation of the local Nusselt distribution from the desired Nusselt number is considered as the objective function. Jets' widths, jet-to-jet and jet-to-surface spacings, and the overall flow rate are chosen as design variables. Conjugate gradients method along with backtracking line search is applied to optimize the objective function calculated by numerical simulation for three different cases of Nu = 7, 9, and 11. For each of these desired Nusselt numbers, an almost uniform distribution of local Nusselt number with percent of root mean square error less than 2.5% is achieved in fewer than 12 iterations. An experimental study using a Mach–Zehnder interferometer (MZI) has been performed. The measured distribution of local Nusselt number is in good agreement with numerical results in all three optimal configurations.
Issue Section:
Research Papers
Topics:
Design,
Heat flux,
Jets,
Flow (Dynamics),
Algorithms,
Heat transfer,
Errors,
Interferometers,
Optimization
References
1.
Roetzel
, W.
, and Newman
, M.
, 1975
, “Uniform Heat Flux in a Paper Drying Drum With a Non-Cylindrical Condensation Surface Operating Under Rimming Conditions
,” Int. J. Heat Mass Transfer
, 18
(4
), pp. 553
–557
.10.1016/0017-9310(75)90296-32.
Sparrow
, E. M.
, and Carlson
, C. K.
, 1987
, “Experimental Investigation of Heat Flux Uniformity at Thin, Electrically Heated Metallic Foils
,” Int. J. Heat Mass Transfer
, 30
(3
), pp. 601
–604
.10.1016/0017-9310(87)90274-23.
Birla
, S. L.
, Wang
, S.
, Tang
, J.
, and Hallman
, G.
, 2004
, “Improving Heating Uniformity of Fresh Fruit in Radio Frequency Treatments for Pest Control
,” Postharvest Biol. Technol.
, 33
(2
), pp. 205
–217
.10.1016/j.postharvbio.2004.02.0104.
Rafidi
, N.
, and Blasiak
, W.
, 2006
, “Heat Transfer Characteristics of HiTAC Heating Furnace Using Regenerative Burners
,” Appl. Therm. Eng.
, 26
(16
), pp. 2027
–2034
.10.1016/j.applthermaleng.2005.12.0165.
Zareifard
, M. R.
, Marcotte
, M.
, and Dostie
, M.
, 2006
, “A Method for Balancing Heat Fluxes Validated for a Newly Designed Pilot Plant Oven
,” J. Food Eng.
, 76
(3
), pp. 303
–312
.10.1016/j.jfoodeng.2005.05.0376.
Chander
, S.
, and Ray
, A.
, 2007
, “Heat Transfer Characteristics of Three Interacting Methane Air Flame Jets Impinging on a Flat Surface
,” Int. J. Heat Mass Transfer
,” 50
(3–4
), pp. 640
–653
.10.1016/j.ijheatmasstransfer.2006.07.0117.
Martin
, H.
, 1977
, “Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces
,” Adv. Heat Transfer
, 13
, pp. 1
–60
.10.1016/S0065-2717(08)70221-18.
Zuckerman
, N.
, and Lior
, N.
, 2006
, “Jet Impingement Heat Transfer: Physics, Correlations, and Numerical Modeling
,” Adv. Heat Transfer
, 39
, pp. 565
–631
.10.1016/S0065-2717(06)39006-59.
Gardon
, R.
, and Akfirat
, J. C.
, 1966
, “Heat Transfer Characteristics of Impinging Two-Dimensional Air Jets
,” ASME J. Heat Transfer
, 88
(1
), pp. 101
–107
.10.1115/1.369144910.
Huber
, A. M.
, and Viskanta
, R.
, 1994
, “Effect of Jet-Jet Spacing on Convective Heat Transfer to Confined, Impinging Arrays of Axisymmetric Air Jet
,” Int. J. Heat Mass Transfer
, 37
(18
), pp. 2859
–2869
.10.1016/0017-9310(94)90340-911.
Wadsworth
, D. C.
, and Mudawar
, I.
, 1990
, “Cooling of a Multichip Electronic Module by Means of Confined Two-Dimensional Jets of Dielectric Liquid
,” ASME J. Heat Transfer
, 112
(4
), pp. 891
–898
.10.1115/1.291049612.
Wang
, L.
, Sundén
, B.
, Borg
, A.
, and Abrahamsson
, H.
, 2011
, “Control of Jet Impingement Heat Transfer in Crossflow by Using a Rib
,” Int. J. Heat Mass Transfer
, 54
(19–20
), pp. 4157
–4166
.10.1016/j.ijheatmasstransfer.2011.06.00413.
Na-Pompet
, K.
, and Boonsupthip
, W.
, 2011
, “Effect of a Narrow Channel on Heat Transfer Enhancement of a Slot-Jet Impingement System
,” J. Food Eng.
, 103
(4
), pp. 366
–376
.10.1016/j.jfoodeng.2010.11.00614.
San
, J. Y.
, and Chen
, J. J.
, 2014
, “Effects of Jet-to-Jet Spacing and Jet Height on Heat Transfer Characteristics of an Impinging Jet Array
,” Int. J. Heat Mass Transfer
, 71
, pp. 8
–17
.10.1016/j.ijheatmasstransfer.2013.11.07915.
Xing
, Y.
, and Weigand
, B.
, 2013
, “Optimum Jet-to-Plate Spacing of Inline Impingement Heat Transfer for Different Crossflow Schemes
,” ASME J. Heat Transfer
, 135
(7
), p. 072201
.10.1115/1.402356216.
Versteeg
, H. K.
, and Malalasekera
, W.
, 2007
, An Introduction to Computational Fluid Dynamics—The Finite Volume Method
, Pearson
, London
.17.
Patankar
, S. V.
, 1980
, Numerical Heat Transfer and Fluid Flow
, McGraw-Hill
, New York
.18.
Alifanov
, O. M.
, 1994
, Inverse Heat Transfer Problems
, Springer-Verlag, Berlin
, Chap. 6.19.
Woodburry
, K. A.
, 2003
, Inverse Engineering Handbook
, CRC Press
, Boca Raton, FL
, Chap. 3.20.
Hestenes
, M. R.
, and Stiefel
, E.
, 1952
, “Methods of Conjugate Gradients for Solving Linear Equations
,” J. Res. Natl. Bur. Stand.
, 49
(6
), pp. 409
–436
.10.6028/jres.049.04421.
Fletcher
, R.
, and Reeves
, C. M.
, 1964
, “Function Minimization by Conjugate Gradients
,” Comput. J.
, 7
(2
), pp. 149
–154
.10.1093/comjnl/7.2.14922.
Nocedal
, J.
, and Wright
, S. J.
, 1999
, Numerical Optimization
, Springer
, New York
, Chap. 3.23.
Hauf
, W.
, and Grigull
, U.
, 1970
, “Optical Methods in Heat Transfer
,” Adv. Heat Transfer
, 6
, pp. 133
–366
.10.1016/S0065-2717(08)70151-524.
Eckert
, E. R. G.
, and Soehngen
, E. E.
, 1984
, “Studies on Heat Transfer in Laminar Free Convection With the Mach–Zehnder Interferometer
,” AF USAF Air Materiel Command, Wright-Paterson Air Force Base, OH, Technical Report No. 5747.25.
Eckert
, E. R. G.
, and Goldstein
, R. J.
, 1976
, Measurements in Heat Transfer
, McGraw-Hill, New York
, pp. 241
–293
.26.
Kline
, S. J.
, and McClintock
, F. A.
, 1953
, “Describing Experimental Uncertainties in Single Sample Experiment
,” ASME J. Mech. Eng.
, 75
(1
), pp. 3
–8
.27.
Flack
, R. D.
, 1978
, “Mach–Zehnder Interferometer Errors Resulting From Test Section Misalignment
,” Appl. Opt.
, 17
(7
), pp. 985
–987
.10.1364/AO.17.000985Copyright © 2015 by ASME
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