Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method

Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are r...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Applied sciences Ročník 12; číslo 5; s. 2738
Hlavní autori: Rincon-Tabares, Juan-Sebastian, Velasquez-Gonzalez, Juan C., Ramirez-Tamayo, Daniel, Montoya, Arturo, Millwater, Harry, Restrepo, David
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.03.2022
Predmet:
ISSN:2076-3417, 2076-3417
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are required to predict the thermal response. Numerical tools are even more relevant when the number of parameters influencing the model is large, and it is necessary to isolate the most influential variables. In this regard, sensitivity analysis can be conducted to increase the process understanding and identify those variables. Here, we combine the complex-variable differentiation theory with the finite element formulation for transient heat transfer, allowing one to compute efficient and accurate first-order sensitivities. Although this approach takes advantage of complex algebra to calculate sensitivities, the method is implemented with real-variable solvers, facilitating the application within commercial software. We present this new methodology in a numerical example using the commercial software Abaqus. The calculation of sensitivities for the temperature and heat flux with respect to temperature-dependent material properties, boundary conditions, geometric parameters, and time are demonstrated. To highlight, the new sensitivity method showed step-size independence, mesh perturbation independence, and reduced computational time contrasting traditional sensitivity analysis methods such as finite differentiation.
AbstractList Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the materials and environmental conditions. If these factors change with time and temperature, the process becomes nonlinear and numerical methods are required to predict the thermal response. Numerical tools are even more relevant when the number of parameters influencing the model is large, and it is necessary to isolate the most influential variables. In this regard, sensitivity analysis can be conducted to increase the process understanding and identify those variables. Here, we combine the complex-variable differentiation theory with the finite element formulation for transient heat transfer, allowing one to compute efficient and accurate first-order sensitivities. Although this approach takes advantage of complex algebra to calculate sensitivities, the method is implemented with real-variable solvers, facilitating the application within commercial software. We present this new methodology in a numerical example using the commercial software Abaqus. The calculation of sensitivities for the temperature and heat flux with respect to temperature-dependent material properties, boundary conditions, geometric parameters, and time are demonstrated. To highlight, the new sensitivity method showed step-size independence, mesh perturbation independence, and reduced computational time contrasting traditional sensitivity analysis methods such as finite differentiation.
Author Velasquez-Gonzalez, Juan C.
Rincon-Tabares, Juan-Sebastian
Millwater, Harry
Restrepo, David
Montoya, Arturo
Ramirez-Tamayo, Daniel
Author_xml – sequence: 1
  givenname: Juan-Sebastian
  orcidid: 0000-0001-6798-4532
  surname: Rincon-Tabares
  fullname: Rincon-Tabares, Juan-Sebastian
– sequence: 2
  givenname: Juan C.
  orcidid: 0000-0003-2442-437X
  surname: Velasquez-Gonzalez
  fullname: Velasquez-Gonzalez, Juan C.
– sequence: 3
  givenname: Daniel
  surname: Ramirez-Tamayo
  fullname: Ramirez-Tamayo, Daniel
– sequence: 4
  givenname: Arturo
  surname: Montoya
  fullname: Montoya, Arturo
– sequence: 5
  givenname: Harry
  orcidid: 0000-0001-7097-9283
  surname: Millwater
  fullname: Millwater, Harry
– sequence: 6
  givenname: David
  orcidid: 0000-0001-5462-5434
  surname: Restrepo
  fullname: Restrepo, David
BookMark eNptkd9LHDEQx0OxULU-9R8I9LGs5sdusvsoh1ZBaaFnX8MkmfNy7G22SRTvv2_0ShFxXmaY72e-AzNH5GCKExLyhbNTKQd2BvPMBeuElv0HciiYVo1suT54VX8iJzlvWI2By56zQ-J_4ZRDCY-h7Oj5BOMuh0xXMdFlgqrgVOhyjWkLI_2Zoh1xm-ldDtM9LWuki7idR3xqfkMKUEV6GaZQkF5U7nn0Fss6-s_k4wrGjCf_8jG5u7xYLq6amx_frxfnN42Tqi2Nt0q2_Uo5a7UbNGhpnReMW95ZISWwvtXM6U5yj722oAbtnFdWo9QOBcpjcr339RE2Zk5hC2lnIgTz0ojp3kAqwY1odPVTvIWub7GVQoPqAHqvHNrBD0JUr697rznFPw-Yi9nEh1QPlI1QUnd9x7q2Ut_2lEsx54Sr_1s5M89fMa--Umn-hnahQAlxKgnC-O7MXwL3ke8
CitedBy_id crossref_primary_10_2514_1_J062834
crossref_primary_10_3390_electronics13193827
crossref_primary_10_3390_s23010453
crossref_primary_10_1115_1_4069175
crossref_primary_10_1016_j_actaastro_2025_04_053
crossref_primary_10_1016_j_finel_2025_104461
Cites_doi 10.1016/j.jqsrt.2011.01.029
10.1007/978-94-007-2739-7_897
10.3390/app9071445
10.1080/08916152.2018.1431738
10.1016/j.engfracmech.2016.04.002
10.3390/app11020647
10.3390/cryst9060321
10.3390/jmmp2030063
10.3390/app11104708
10.1016/j.ijmecsci.2017.08.035
10.1016/j.measurement.2020.108440
10.1016/j.ijheatmasstransfer.2016.04.058
10.3390/cryst9110605
10.1002/nme.5280
10.1016/j.ijpvp.2019.05.004
10.1080/10407790.2017.1420325
10.3390/cryst11101182
10.2514/1.J057231
10.1007/s40192-020-00169-1
10.1080/10407790.2019.1580047
10.1016/j.engfracmech.2021.107638
10.1016/j.applthermaleng.2021.117276
10.2514/6.2011-886
10.3390/app9030455
10.3390/app9040754
10.2514/6.2013-1580
10.1016/j.ijthermalsci.2017.02.003
10.1002/srin.202000465
10.1016/j.ijthermalsci.2012.02.024
10.2514/1.T4323
10.1016/j.measurement.2018.06.057
10.1371/journal.pone.0250583
10.3390/cryst11080977
10.3390/cryst10060532
10.1016/j.engfracmech.2018.09.023
10.1137/0704019
10.1080/10407782.2013.846594
10.3390/cryst11080888
10.1201/9780203749784
10.1002/2014WR016527
10.2514/6.2009-2711
10.2514/1.J053282
10.1007/978-3-030-11530-2
10.1016/j.engfracmech.2013.07.012
10.1080/01495739.2016.1264871
10.3390/cryst12010074
10.1016/j.applthermaleng.2016.08.116
10.2514/1.J052184
10.1016/j.ijheatmasstransfer.2016.02.085
10.3390/cryst8040143
10.2351/1.4726445
10.1016/j.ijthermalsci.2019.06.002
10.1016/j.est.2021.102507
10.1061/(ASCE)EM.1943-7889.0000837
10.1137/S003614459631241X
10.1016/j.icheatmasstransfer.2021.105478
10.19053/01211129.v27.n47.2018.7749
10.1016/j.ijfatigue.2019.05.036
10.1016/j.ijheatmasstransfer.2013.01.056
10.3390/cryst11040385
10.1016/j.finel.2011.05.003
10.1016/j.ijfatigue.2012.01.016
10.1016/j.applthermaleng.2016.11.098
10.1016/j.ijheatmasstransfer.2020.120765
10.1007/978-3-642-19777-2_1
10.1002/nme.5988
10.1016/j.applthermaleng.2019.113902
10.1016/j.ijheatmasstransfer.2006.03.001
10.1002/nme.5141
10.1016/j.enganabound.2005.03.001
10.3390/jmmp1010003
10.3390/cryst11040322
10.1016/j.engstruct.2017.04.014
10.3390/app8122567
10.1002/nme.6657
10.1115/1.4042353
10.1002/widm.1305
10.1016/j.ijheatmasstransfer.2004.01.023
10.1016/j.engfracmech.2012.02.006
ContentType Journal Article
Copyright 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
ABUWG
AFKRA
AZQEC
BENPR
CCPQU
DWQXO
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
DOA
DOI 10.3390/app12052738
DatabaseName CrossRef
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
ProQuest One
ProQuest Central Korea
ProQuest Central Premium
ProQuest One Academic (New)
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
DOAJ Open Access Full Text
DatabaseTitle CrossRef
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
DatabaseTitleList Publicly Available Content Database
CrossRef

Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: PIMPY
  name: ProQuest Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Sciences (General)
EISSN 2076-3417
ExternalDocumentID oai_doaj_org_article_733a614a584e4327a65aa8d6ceb9d922
10_3390_app12052738
GroupedDBID .4S
2XV
5VS
7XC
8CJ
8FE
8FG
8FH
AADQD
AAFWJ
AAYXX
ADBBV
ADMLS
AFFHD
AFKRA
AFPKN
AFZYC
ALMA_UNASSIGNED_HOLDINGS
APEBS
ARCSS
BCNDV
BENPR
CCPQU
CITATION
CZ9
D1I
D1J
D1K
GROUPED_DOAJ
IAO
IGS
ITC
K6-
K6V
KC.
KQ8
L6V
LK5
LK8
M7R
MODMG
M~E
OK1
P62
PHGZM
PHGZT
PIMPY
PROAC
TUS
ABUWG
AZQEC
DWQXO
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
ID FETCH-LOGICAL-c364t-db6348f6cbb7c97a73bcd201b15b233a08470c7531de87ba697ccd6b7e37ce2e3
IEDL.DBID BENPR
ISICitedReferencesCount 11
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000768966100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2076-3417
IngestDate Mon Dec 08 04:16:21 EST 2025
Mon Jun 30 07:28:20 EDT 2025
Sat Nov 29 07:16:36 EST 2025
Tue Nov 18 20:54:08 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 5
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c364t-db6348f6cbb7c97a73bcd201b15b233a08470c7531de87ba697ccd6b7e37ce2e3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-7097-9283
0000-0001-6798-4532
0000-0003-2442-437X
0000-0001-5462-5434
OpenAccessLink https://www.proquest.com/docview/2637585054?pq-origsite=%requestingapplication%
PQID 2637585054
PQPubID 2032433
ParticipantIDs doaj_primary_oai_doaj_org_article_733a614a584e4327a65aa8d6ceb9d922
proquest_journals_2637585054
crossref_primary_10_3390_app12052738
crossref_citationtrail_10_3390_app12052738
PublicationCentury 2000
PublicationDate 2022-03-01
PublicationDateYYYYMMDD 2022-03-01
PublicationDate_xml – month: 03
  year: 2022
  text: 2022-03-01
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Applied sciences
PublicationYear 2022
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References Cui (ref_58) 2011; 112
Jantos (ref_18) 2019; 117
Lane (ref_49) 2020; 9
Navarro (ref_81) 2022; 89
Squire (ref_56) 1998; 40
Morville (ref_84) 2012; 24
ref_14
Montoya (ref_87) 2018; 202
ref_11
ref_55
Shevchuk (ref_30) 2006; 49
Daouas (ref_63) 2018; 73
Indinger (ref_31) 2004; 47
(ref_34) 2018; 27
Montoya (ref_79) 2017; 40
ref_19
Razavi (ref_44) 2015; 51
ref_17
Alam (ref_23) 2018; 128
Kant (ref_4) 2021; 38
Cui (ref_15) 2016; 106
Du (ref_46) 2017; 113
(ref_37) 2019; 159
Thi (ref_10) 2017; 143
Wang (ref_47) 2019; 144
ref_25
Ellahi (ref_50) 2016; 109
ref_68
ref_22
ref_21
ref_62
Soulami (ref_73) 2021; 247
Cui (ref_67) 2015; 29
Stieven (ref_7) 2021; 166
Voorhees (ref_69) 2012; 40
ref_29
ref_28
Levin (ref_35) 2013; 61
ref_26
Zhang (ref_27) 2014; 65
Garza (ref_80) 2015; 53
Wagner (ref_72) 2019; 127
Sinha (ref_36) 2017; 4
Kotrbacek (ref_6) 2021; 92
Margossian (ref_54) 2019; 9
Cui (ref_65) 2012; 58
ref_78
ref_33
ref_32
Millwater (ref_71) 2016; 162
Baydin (ref_52) 2015; 18
Pourmehran (ref_38) 2015; 130
Pierre (ref_20) 2017; 116
Righetti (ref_12) 2021; 196
Huan (ref_5) 2021; 168
Martins (ref_51) 2013; 51
ref_39
Montoya (ref_76) 2015; 132–133
Fielder (ref_77) 2019; 173
Millwater (ref_61) 2013; 109
Wagner (ref_70) 2012; 86
Voorhees (ref_60) 2011; 47
Zhou (ref_64) 2016; 100
Lyness (ref_57) 1967; 4
ref_83
ref_82
Cui (ref_66) 2016; 97
Manjhi (ref_24) 2018; 31
Fielder (ref_75) 2017; 133
Montoya (ref_86) 2018; 56
ref_45
ref_89
ref_88
ref_43
ref_42
Pamin (ref_16) 2017; 109
ref_41
Jayapragasam (ref_53) 2018; 74
ref_85
ref_40
ref_1
ref_3
Gao (ref_59) 2005; 29
ref_2
Alhusseny (ref_13) 2021; 127
Montoya (ref_74) 2015; 141
ref_48
Parry (ref_90) 2016; 12
ref_9
ref_8
References_xml – volume: 112
  start-page: 1336
  year: 2011
  ident: ref_58
  article-title: A new inverse approach for the equivalent gray radiative property of a non-Gray medium using a modified zonal method and the complex-Variable-differentiation method
  publication-title: J. Quant. Spectrosc. Radiat. Transf.
  doi: 10.1016/j.jqsrt.2011.01.029
– volume: 12
  start-page: 1
  year: 2016
  ident: ref_90
  article-title: Understanding the effect of laser scan strategy on residual stress in selective laser melting through thermo-Mechanical simulation
  publication-title: Addit. Manuf.
– ident: ref_32
– ident: ref_82
  doi: 10.1007/978-94-007-2739-7_897
– ident: ref_33
  doi: 10.3390/app9071445
– volume: 31
  start-page: 405
  year: 2018
  ident: ref_24
  article-title: Stagnation point transient heat flux measurement analysis from coaxial thermocouples
  publication-title: Exp. Heat Transf.
  doi: 10.1080/08916152.2018.1431738
– volume: 162
  start-page: 95
  year: 2016
  ident: ref_71
  article-title: A virtual crack extension method to compute energy release rates using a complex variable finite element method
  publication-title: Eng. Fract. Mech.
  doi: 10.1016/j.engfracmech.2016.04.002
– ident: ref_21
  doi: 10.3390/app11020647
– volume: 130
  start-page: 1
  year: 2015
  ident: ref_38
  article-title: Statistical optimization of microchannel heat sink (mchs) geometry cooled by different nanofluids using RSM analysis
  publication-title: Eur. Phys. J. Plus
– ident: ref_2
  doi: 10.3390/cryst9060321
– ident: ref_48
  doi: 10.3390/jmmp2030063
– ident: ref_78
  doi: 10.3390/app11104708
– volume: 133
  start-page: 112
  year: 2017
  ident: ref_75
  article-title: Residual stress sensitivity analysis using a complex variable finite element method
  publication-title: Int. J. Mech. Sci.
  doi: 10.1016/j.ijmecsci.2017.08.035
– volume: 168
  start-page: 108440
  year: 2021
  ident: ref_5
  article-title: A theoretical investigation of modelling the temperature measurement in oil pipelines with edge devices
  publication-title: Meas. J. Int. Meas. Confed.
  doi: 10.1016/j.measurement.2020.108440
– volume: 100
  start-page: 1
  year: 2016
  ident: ref_64
  article-title: Algorithms for the estimation of transient surface heat flux during ultra-Fast surface cooling
  publication-title: Int. J. Heat Mass Transf.
  doi: 10.1016/j.ijheatmasstransfer.2016.04.058
– ident: ref_43
  doi: 10.3390/cryst9110605
– volume: 109
  start-page: 102
  year: 2017
  ident: ref_16
  article-title: Local and non-Local thermomechanical modeling of elastic-Plastic materials undergoing large strains
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.5280
– volume: 173
  start-page: 101
  year: 2019
  ident: ref_77
  article-title: Efficient estimate of residual stress variance using complex variable finite element methods
  publication-title: Int. J. Press. Vessel. Pip.
  doi: 10.1016/j.ijpvp.2019.05.004
– ident: ref_88
– volume: 89
  start-page: 1
  year: 2022
  ident: ref_81
  article-title: Arbitrary-Order sensitivity analysis in phononic metamaterials using the multicomplex taylor series expansion method coupled with bloch’s theorem
  publication-title: J. Appl. Mech.
– volume: 73
  start-page: 106
  year: 2018
  ident: ref_63
  article-title: An Alternative sensitivity method for a two-Dimensional inverse heat conduction-radiation problem based on transient hot-Wire measurements
  publication-title: Numer. Heat Transf. Part B Fundam.
  doi: 10.1080/10407790.2017.1420325
– ident: ref_11
  doi: 10.3390/cryst11101182
– volume: 56
  start-page: 4632
  year: 2018
  ident: ref_86
  article-title: Complex-Variable finite-Element method for mixed mode fracture and interface cracks
  publication-title: AIAA J.
  doi: 10.2514/1.J057231
– volume: 9
  start-page: 16
  year: 2020
  ident: ref_49
  article-title: Measurements of melt pool geometry and cooling rates of individual laser traces on IN625 bare plates
  publication-title: Integr. Mater. Manuf. Innov.
  doi: 10.1007/s40192-020-00169-1
– volume: 74
  start-page: 729
  year: 2018
  ident: ref_53
  article-title: Computing sensitivity coefficients by using complex differentiation: Application to heat conduction problem
  publication-title: Numer. Heat Transf. Part B Fundam.
  doi: 10.1080/10407790.2019.1580047
– volume: 247
  start-page: 107638
  year: 2021
  ident: ref_73
  article-title: A complex-Variable cohesive finite element subroutine to enable efficient determination of interfacial cohesive material parameters
  publication-title: Eng. Fract. Mech.
  doi: 10.1016/j.engfracmech.2021.107638
– volume: 196
  start-page: 117276
  year: 2021
  ident: ref_12
  article-title: On the design of phase change materials based thermal management systems for electronics cooling
  publication-title: Appl. Therm. Eng.
  doi: 10.1016/j.applthermaleng.2021.117276
– ident: ref_89
  doi: 10.2514/6.2011-886
– ident: ref_9
  doi: 10.3390/app9030455
– ident: ref_26
  doi: 10.3390/app9040754
– ident: ref_55
  doi: 10.2514/6.2013-1580
– volume: 116
  start-page: 63
  year: 2017
  ident: ref_20
  article-title: Transient pulsed technique to characterize the radiative and conductive properties of bio aerogels
  publication-title: Int. J. Therm. Sci.
  doi: 10.1016/j.ijthermalsci.2017.02.003
– ident: ref_83
– volume: 4
  start-page: 70
  year: 2017
  ident: ref_36
  article-title: Computational analysis of heat sink or extended surface
  publication-title: Int. Res. J. Eng. Technol.
– volume: 92
  start-page: 2000465
  year: 2021
  ident: ref_6
  article-title: Heat transfer correlations for secondary cooling in continuous casting
  publication-title: Steel Res. Int.
  doi: 10.1002/srin.202000465
– volume: 58
  start-page: 113
  year: 2012
  ident: ref_65
  article-title: A new approach for the estimation of temperature-Dependent thermal properties by solving transient inverse heat conduction problems
  publication-title: Int. J. Therm. Sci.
  doi: 10.1016/j.ijthermalsci.2012.02.024
– volume: 29
  start-page: 253
  year: 2015
  ident: ref_67
  article-title: Robust Inverse approach for two-Dimensional transient nonlinear heat conduction problems
  publication-title: J. Thermophys. Heat Transf.
  doi: 10.2514/1.T4323
– volume: 18
  start-page: 1
  year: 2015
  ident: ref_52
  article-title: Automatic differentiation in machine learning: A survey
  publication-title: J. Mach. Learn. Res.
– volume: 128
  start-page: 352
  year: 2018
  ident: ref_23
  article-title: Stagnation point transient heat flux measurement analysis from coaxial thermocouples
  publication-title: Meas. J. Int. Meas. Confed.
  doi: 10.1016/j.measurement.2018.06.057
– ident: ref_3
  doi: 10.1371/journal.pone.0250583
– ident: ref_25
  doi: 10.3390/cryst11080977
– ident: ref_40
  doi: 10.3390/cryst10060532
– volume: 202
  start-page: 242
  year: 2018
  ident: ref_87
  article-title: A complex-Variable virtual crack extension finite element method for elastic-Plastic fracture mechanics
  publication-title: Eng. Fract. Mech.
  doi: 10.1016/j.engfracmech.2018.09.023
– volume: 4
  start-page: 202
  year: 1967
  ident: ref_57
  article-title: Numerical differentiation of analytic functions
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0704019
– volume: 65
  start-page: 627
  year: 2014
  ident: ref_27
  article-title: Experimental and numerical study of transient electronic chip cooling by liquid flow in microchannel heat sinks
  publication-title: Numer. Heat Transf. Part A Appl.
  doi: 10.1080/10407782.2013.846594
– ident: ref_41
  doi: 10.3390/cryst11080888
– ident: ref_45
  doi: 10.1201/9780203749784
– volume: 51
  start-page: 3070
  year: 2015
  ident: ref_44
  article-title: What do we mean by sensitivity analysis? The need for comprehensive characterization of “global” Sensitivity in earth and environmental systems models
  publication-title: Water Resour. Res.
  doi: 10.1002/2014WR016527
– ident: ref_68
  doi: 10.2514/6.2009-2711
– volume: 53
  start-page: 1188
  year: 2015
  ident: ref_80
  article-title: Multicomplex newmark-Beta time integration method for sensitivity analysis in structural dynamics
  publication-title: AIAA J.
  doi: 10.2514/1.J053282
– ident: ref_1
  doi: 10.1007/978-3-030-11530-2
– volume: 109
  start-page: 302
  year: 2013
  ident: ref_61
  article-title: Improved WCTSE method for the generation of 2D weight functions through implementation into a commercial finite element code
  publication-title: Eng. Fract. Mech.
  doi: 10.1016/j.engfracmech.2013.07.012
– volume: 40
  start-page: 302
  year: 2017
  ident: ref_79
  article-title: Sensitivity analysis in thermoelastic problems using the complex finite element method
  publication-title: J. Therm. Stress.
  doi: 10.1080/01495739.2016.1264871
– ident: ref_42
  doi: 10.3390/cryst12010074
– volume: 109
  start-page: 761
  year: 2016
  ident: ref_50
  article-title: Enhancement of heat transfer and heat exchanger effectiveness in a double pipe heat exchanger filled with porous media: Numerical simulation and sensitivity analysis of turbulent fluid flow
  publication-title: Appl. Therm. Eng.
  doi: 10.1016/j.applthermaleng.2016.08.116
– volume: 51
  start-page: 2582
  year: 2013
  ident: ref_51
  article-title: Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models
  publication-title: Am. Inst. Aeronaut. Astronaut.
  doi: 10.2514/1.J052184
– volume: 97
  start-page: 908
  year: 2016
  ident: ref_66
  article-title: A modified levenberg-Marquardt algorithm for simultaneous estimation of multi-Parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems
  publication-title: Int. J. Heat Mass Transf.
  doi: 10.1016/j.ijheatmasstransfer.2016.02.085
– ident: ref_14
  doi: 10.3390/cryst8040143
– volume: 24
  start-page: 032008
  year: 2012
  ident: ref_84
  article-title: 2D longitudinal modeling of heat transfer and fluid flow during multilayered direct laser metal deposition process
  publication-title: J. Laser Appl.
  doi: 10.2351/1.4726445
– volume: 144
  start-page: 147
  year: 2019
  ident: ref_47
  article-title: Non-Probabilistic interval process model and method for uncertainty analysis of transient heat transfer problem
  publication-title: Int. J. Therm. Sci.
  doi: 10.1016/j.ijthermalsci.2019.06.002
– volume: 38
  start-page: 102507
  year: 2021
  ident: ref_4
  article-title: Heat transfer and energy storage performances of phase change materials encapsulated in honeycomb cells
  publication-title: J. Energy Storage
  doi: 10.1016/j.est.2021.102507
– volume: 141
  start-page: 04014118
  year: 2015
  ident: ref_74
  article-title: Finite-Element sensitivity for plasticity using complex variable methods
  publication-title: J. Eng. Mech.
  doi: 10.1061/(ASCE)EM.1943-7889.0000837
– volume: 40
  start-page: 110
  year: 1998
  ident: ref_56
  article-title: Using complex variables to estimate derivatives of real functions
  publication-title: SIAM Rev.
  doi: 10.1137/S003614459631241X
– volume: 127
  start-page: 105478
  year: 2021
  ident: ref_13
  article-title: Dissipating the heat generated in high-Performance electronics using graphitic foam heat-Sinks cooled with a dielectric liquid
  publication-title: Int. Commun. Heat Mass Transf.
  doi: 10.1016/j.icheatmasstransfer.2021.105478
– volume: 27
  start-page: 31
  year: 2018
  ident: ref_34
  article-title: Thermal transfer analysis of tubes with extended surface with fractal design
  publication-title: Rev. Fac. Ing.
  doi: 10.19053/01211129.v27.n47.2018.7749
– volume: 127
  start-page: 229
  year: 2019
  ident: ref_72
  article-title: A finite element-Based adaptive energy response function method for 2D curvilinear progressive fracture
  publication-title: Int. J. Fatigue
  doi: 10.1016/j.ijfatigue.2019.05.036
– volume: 61
  start-page: 638
  year: 2013
  ident: ref_35
  article-title: Numerical optimization af a PCM-Based heat sink with internal fins
  publication-title: Int. J. Heat Mass Transf.
  doi: 10.1016/j.ijheatmasstransfer.2013.01.056
– ident: ref_22
  doi: 10.3390/cryst11040385
– volume: 47
  start-page: 1146
  year: 2011
  ident: ref_60
  article-title: Complex variable methods for shape sensitivity of finite element models
  publication-title: Finite Elem. Anal. Des.
  doi: 10.1016/j.finel.2011.05.003
– volume: 40
  start-page: 61
  year: 2012
  ident: ref_69
  article-title: Fatigue sensitivity analysis using complex variable methods
  publication-title: Int. J. Fatigue
  doi: 10.1016/j.ijfatigue.2012.01.016
– volume: 113
  start-page: 867
  year: 2017
  ident: ref_46
  article-title: Numerical simulation and parameter sensitivity analysis of coupled heat transfer by PCCS containment wall
  publication-title: Appl. Therm. Eng.
  doi: 10.1016/j.applthermaleng.2016.11.098
– volume: 166
  start-page: 120765
  year: 2021
  ident: ref_7
  article-title: Interfacial heat transfer coefficient in unidirectional permanent mold casting: Modeling and inverse estimation
  publication-title: Int. J. Heat Mass Transf.
  doi: 10.1016/j.ijheatmasstransfer.2020.120765
– ident: ref_29
– ident: ref_28
  doi: 10.1007/978-3-642-19777-2_1
– volume: 117
  start-page: 991
  year: 2019
  ident: ref_18
  article-title: An accurate and fast regularization approach to thermodynamic topology optimization
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.5988
– volume: 159
  start-page: 113902
  year: 2019
  ident: ref_37
  article-title: Study of gasketed-Plate heat exchanger performance based on energy efficiency indexes
  publication-title: Appl. Therm. Eng.
  doi: 10.1016/j.applthermaleng.2019.113902
– volume: 49
  start-page: 3530
  year: 2006
  ident: ref_30
  article-title: Unsteady conjugate laminar heat transfer of a rotating non-Uniformly heated disk: Application to the transient experimental technique
  publication-title: Int. J. Heat Mass Transf.
  doi: 10.1016/j.ijheatmasstransfer.2006.03.001
– volume: 106
  start-page: 953
  year: 2016
  ident: ref_15
  article-title: Time-Step constraints in transient coupled finite element analysis
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.5141
– volume: 29
  start-page: 788
  year: 2005
  ident: ref_59
  article-title: A new inverse analysis approach for multi-region heat conduction bem using complex-Variable-Differentiation method
  publication-title: Eng. Anal. Bound. Elem.
  doi: 10.1016/j.enganabound.2005.03.001
– ident: ref_85
  doi: 10.3390/jmmp1010003
– ident: ref_8
  doi: 10.3390/cryst11040322
– volume: 143
  start-page: 11
  year: 2017
  ident: ref_10
  article-title: Finite element analysis of heat transfer through timber elements exposed to fire
  publication-title: Eng. Struct.
  doi: 10.1016/j.engstruct.2017.04.014
– ident: ref_17
  doi: 10.3390/app8122567
– ident: ref_39
  doi: 10.1002/nme.6657
– ident: ref_19
– ident: ref_62
  doi: 10.1115/1.4042353
– volume: 132–133
  start-page: 27
  year: 2015
  ident: ref_76
  article-title: Complex finite element sensitivity method for creep analysis
  publication-title: Int. J. Press. Vessel. Pip.
– volume: 9
  start-page: e1305
  year: 2019
  ident: ref_54
  article-title: A review of automatic differentiation and its efficient implementation
  publication-title: Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
  doi: 10.1002/widm.1305
– volume: 47
  start-page: 3577
  year: 2004
  ident: ref_31
  article-title: Transient laminar conjugate heat transfer of a rotating disk: Theory and numerical simulations
  publication-title: Int. J. Heat Mass Transf.
  doi: 10.1016/j.ijheatmasstransfer.2004.01.023
– volume: 86
  start-page: 23
  year: 2012
  ident: ref_70
  article-title: 2D weight function development using a complex taylor series expansion method
  publication-title: Eng. Fract. Mech.
  doi: 10.1016/j.engfracmech.2012.02.006
SSID ssj0000913810
Score 2.287637
Snippet Solving transient heat transfer equations is required to understand the evolution of temperature and heat flux. This physics is highly dependent on the...
SourceID doaj
proquest
crossref
SourceType Open Website
Aggregation Database
Enrichment Source
Index Database
StartPage 2738
SubjectTerms Algorithms
Approximation
Boundary conditions
complex-variable differentiation
Cooling
Design optimization
finite differences
Finite element analysis
finite elements
heat conduction
Heat transfer
Methods
Partial differential equations
Sensitivity analysis
transient conduction
SummonAdditionalLinks – databaseName: DOAJ Open Access Full Text
  dbid: DOA
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEB5EPOhBbFWsVsmhBxUWd5M2j6NKixdLwQe9LXkVCqVKW8Wf7yTZlgUFL16XgV0mk_nmY2e-AehI45yUPM8QqpGgeMUzGWLZaGQjE0NpMdFx2YQYDuV4rEa1VV-hJyzJAyfH3QjGNEKIRqD0XUaF5j2tpePWG-UUjdk3F6pGpmIOVkWQrkoDeQx5ffgfXNC8lyZRahAUlfp_JOKILoMD2K_KQnKbPqcBW37ehL2aWGATGtU1XJLLSiv66hDcU2hATxsgyFpghGAhSiIIhWFHgpGA2XdGRml3zJLENgGClR8J2WDmv7JXZMxhhooMpqEGJf3UVE4e437pI3gZ9J_vH7JqcUJmGe-uMmc468oJt8YIq4QWzFiHSG-KnqHozxwhKbdIVArnpTCaK2Gt40Z4Jqynnh3D9vxt7k-AINvwklvHDNaJWPxp9KpVhfG574kJ5y24XvuytJWqeFhuMSuRXQTHlzXHt6CzMX5PYhq_m92FQ9mYBAXs-ADjoqziovwrLlrQXh9pWV3LZUk5C_wIy9TT_3jHGezSMA0RW9LasL1afPhz2LGfq-lycREj8hsqROVx
  priority: 102
  providerName: Directory of Open Access Journals
Title Sensitivity Analysis for Transient Thermal Problems Using the Complex-Variable Finite Element Method
URI https://www.proquest.com/docview/2637585054
https://doaj.org/article/733a614a584e4327a65aa8d6ceb9d922
Volume 12
WOSCitedRecordID wos000768966100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 2076-3417
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913810
  issn: 2076-3417
  databaseCode: DOA
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2076-3417
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913810
  issn: 2076-3417
  databaseCode: M~E
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 2076-3417
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913810
  issn: 2076-3417
  databaseCode: BENPR
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Publicly Available Content Database
  customDbUrl:
  eissn: 2076-3417
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000913810
  issn: 2076-3417
  databaseCode: PIMPY
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LTxsxEB6V0AMc2vKompYiHzi0SCt27cT2nqpSJWoPRKsWEJxWfgUhRQlkA-rP74zXSSOBeulxd33wasYz34xnvgE40tZ7rWWeoavGACWUMtOky9ZgNDK2nBdjE4dNqNFIX12VVUq4NamscmkTo6H2M0c58hMuBUFbRBhf7u4zmhpFt6tphMYGbBJTGe_A5ulgVP1cZVmI9VIXeduYJzC-p3vhguf9tiNlzRVFxv4nBjl6meHr_93fG3iV8CX72irEDrwI013YXmMd3IWddJ4b9imRTn_eA_-LKtnbURJsyVTCENGy6M2oa5KhSqEZn7CqHULTsFhvwBBCMjIrk_A7u8TQm5qx2PCWwCwbtNXp7CwOqt6Hi-Hg_Nv3LE1gyJyQvUXmrRQ9PZbOWuVKZZSwziNksEXfciFMjr4tdxjxFD5oZY0slXNeWhWEcoEH8RY609k0vAOGYUvQ0nlhEXAiijQoFlcWNuShr8ZSduF4KYzaJXpympIxqTFMIcnVa5LrwtFq8V3LyvH8slOS6moJUWnHF7P5TZ1OZq3wPxCjGERioSe4Mrg3o710wZa-5LwLB0uB1-l8N_Vfab__9-cPsMWpYSJWrR1AZzF_CB_hpXtc3Dbzw6SuhzETgE_Vj7Pq-g9qMvfD
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9NAEB2VFAl6AFpaESiwhyIBkoW96-yuDwhRSNSqbRRBQb2Z_QqqFCUlTvn4U_xGZtZ2iATi1gNXe2V57bczb3Zn5gHsaeu91jJN0FVjgBIKmWjCsjUYjYwt59nYRLEJNRzqs7NitAY_21oYSqtsbWI01H7maI_8BZeCqC0yjFcXXxJSjaLT1VZCo4bFUfjxDUO26uXhW_y_Tzgf9E_fHCSNqkDihMwXibdS5HosnbXKFcooYZ1HN2iznuVCmBTtdeqQxWc-aGWNLJRzXloVhHKBB4HPvQbruchz3oH1_f5w9G65q0NdNnWW1oWAQhQpnUNnPO3VFTArri8qBPzhAKJXG9z-377HHbjV8Gf2ugb8JqyF6RZsrHRV3ILNxl5V7GnTVPvZXfDvKVO_lspgbScWhoydRW9NVaEMlwy6qQkb1SI7FYv5FAwpMiOzOQnfk48GFyzeZINzIuusX2ffs5MoxL0NH65k7jvQmc6m4R4wDMuCls4Li4QaWbJBGLgisyENPTWWsgvP259fuqb9OqmATEoMwwgp5QpSurC3HHxRdx35-7B9QtFyCLUKjxdm889lY3lKhfNADmaQaYZccGXw3Yz20gVb-ILzLuy2ACsb-1WVv9F1_9-3H8ONg9OT4_L4cHj0AG5yKg6JGXq70FnML8NDuO6-Ls6r-aNmqTD4dNVo_AVMMVNq
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEB6VtELlAG2haqCleygSIFm1d5Pd9QGhliaiKo0iXurN7MtVpSgpcejjr_HrmF2vQyQQtx64eleW1_525hvvzHwAe1JbKyVPE3TVGKC4nCfSY1krjEZKTWlWqiA2IQYDeXaWD5fgZ1ML49MqG5sYDLWdGP-PfJ9y5qktMoz9MqZFDI_6by-_J15Byp-0NnIaNURO3O01hm_Vm-Mj_NYvKO33Pr97n0SFgcQw3pklVnPWkSU3WguTCyWYNhZdos66mjKmUrTdqUFGn1knhVY8F8ZYroVjwjjqGN73HiwL9PqdFiwf9gbDj_M_PL7jpszSuiiQsTz1Z9IZTbt1NcyCGwxqAX84g-Dh-o_-53ezBg8jryYH9UZYhyU33oAHC90WN2A92rGKvIzNtl89BvvJZ_DXEhqk6dBCkMmT4MV9tSjBrYTua0SGtfhORUKeBUHqTLw5Hbmb5KvCjYyDpH_hSTzp1Vn55DQIdD-BL3ey9k1ojSdjtwUEwzUnubFMI9FG9qwQEibPtEtdV5Sct-F1A4TCxLbsXh1kVGB45lFTLKCmDXvzyZd1N5K_Tzv0iJpP8S3Ew4XJ9LyIFqkQuA7kZgoZqOswKhQ-m5KWG6dzm1Pahu0GbEW0a1XxG2lP_z28C_cRgsWH48HJM1ilvmYkJO5tQ2s2_eF2YMVczS6q6fO4awh8u2sw_gJlV1w2
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Sensitivity+Analysis+for+Transient+Thermal+Problems+Using+the+Complex-Variable+Finite+Element+Method&rft.jtitle=Applied+sciences&rft.au=Juan-Sebastian+Rincon-Tabares&rft.au=Velasquez-Gonzalez%2C+Juan+C&rft.au=Ramirez-Tamayo%2C+Daniel&rft.au=Montoya%2C+Arturo&rft.date=2022-03-01&rft.pub=MDPI+AG&rft.eissn=2076-3417&rft.volume=12&rft.issue=5&rft.spage=2738&rft_id=info:doi/10.3390%2Fapp12052738&rft.externalDBID=HAS_PDF_LINK
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2076-3417&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2076-3417&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2076-3417&client=summon