Transient Temperature Fields in Growing Bodies Subject to Discrete and Continuous Growth Regimes

The heat transfer problems for growing bodies is the is the subject of present research. Temperature distributions in growing bodies that appear during discrete and continuous growth are studied. The investigation is based on analytical and semianalytical solutions. Analytical solutions are of the f...

Full description

Saved in:
Bibliographic Details
Published inProcedia IUTAM Vol. 23; pp. 120 - 129
Main Authors Lychev, S., Manzhirov, A., Shatalov, M., Fedotov, I.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2017
Subjects
analytical solution
continuous growth
discrete growth
eigenfunctions
Galerkin method
Growing bodies
heat transfer
semianalytical solution
eigenfunctions
continuous growth
discrete growth
semianalytical solution
analytical solution
Galerkin method
heat transfer
Growing bodies
Online AccessGet full text

Cover

Abstract The heat transfer problems for growing bodies is the is the subject of present research. Temperature distributions in growing bodies that appear during discrete and continuous growth are studied. The investigation is based on analytical and semianalytical solutions. Analytical solutions are of the form of spectral expansions. The applicability of the analytical solutions is limited to a narrow class for laws of evolution of growth boundaries. Semianalytical solutions have a wider range of applications. The calculation and analysis of temperature fields in the ball under the condition of central symmetry are provided. An analysis of the temperature behavior on the growth boundary shows that, depending on the accretion rate, the boundary can be considered as an isothermal boundary (for high values of the accretion rate) or a boundary with variable effective temperature determined in the process of solving the problem.
AbstractList The heat transfer problems for growing bodies is the is the subject of present research. Temperature distributions in growing bodies that appear during discrete and continuous growth are studied. The investigation is based on analytical and semianalytical solutions. Analytical solutions are of the form of spectral expansions. The applicability of the analytical solutions is limited to a narrow class for laws of evolution of growth boundaries. Semianalytical solutions have a wider range of applications. The calculation and analysis of temperature fields in the ball under the condition of central symmetry are provided. An analysis of the temperature behavior on the growth boundary shows that, depending on the accretion rate, the boundary can be considered as an isothermal boundary (for high values of the accretion rate) or a boundary with variable effective temperature determined in the process of solving the problem.
Author Manzhirov, A.
Shatalov, M.
Fedotov, I.
Lychev, S.
Author_xml – sequence: 1
  givenname: S.
  surname: Lychev
  fullname: Lychev, S.
  email: lychevsa@mail.ru
  organization: Institute for Problems in Mechanics RAS,Vernadsky Ave. 101-1, 119526, Moscow, Russia
– sequence: 2
  givenname: A.
  surname: Manzhirov
  fullname: Manzhirov, A.
  organization: Tshwane University of Technology, Staatsartillerie St, Pretoria, 0183, South Africa
– sequence: 3
  givenname: M.
  surname: Shatalov
  fullname: Shatalov, M.
  organization: Tshwane University of Technology, Staatsartillerie St, Pretoria, 0183, South Africa
– sequence: 4
  givenname: I.
  surname: Fedotov
  fullname: Fedotov, I.
  organization: Tshwane University of Technology, Staatsartillerie St, Pretoria, 0183, South Africa
BookMark eNqFkMFKAzEQhoMoWGvfwENeoGuSbbMbD4JWW4WCoPUcs9nZmqWblCSr-Pam1oN40LnMwPD9zHwn6NA6CwidUZJRQvl5m21NH1WXMUKLjPCMUHaABoxRMhZlXh7-mI_RKISWpOKkZGw6QC8rr2wwYCNeQbcFr2LvAc8NbOqAjcUL796NXeNrVxsI-KmvWtARR4dvTNAeImBlazxzNhrbuz58EfEVP8LadBBO0VGjNgFG332Inue3q9ndePmwuJ9dLcc6n7I4VpRw3TSqULQkILQuc9HUhSiYqokWZdmkjda84EWlCBeqAgGNysWkyoHlkA_RxT5XexeCh0ZqE1U06S6vzEZSIne6ZCv3uuROlyRcJl0JnvyCt950yn_8h13uMUiPvRnwMuikUkNtfJIka2f-DvgEbbaLGg
CitedBy_id crossref_primary_10_1080_15376494_2022_2048324
crossref_primary_10_18287_2541_7525_2020_26_3_63_90
crossref_primary_10_37972_chgpu_2023_56_2_012
crossref_primary_10_1002_zamm_202100519
crossref_primary_10_1080_15376494_2022_2048325
Cites_doi 10.1017/CBO9780511762673
10.3103/S0025654413050117
10.3103/S0025654411060124
10.3103/S0025654412060106
10.1002/andp.18912780206
10.1016/j.jappmathmech.2013.11.011
10.1007/s001610050124
ContentType Journal Article
Copyright 2017 The Authors
Copyright_xml – notice: 2017 The Authors
DBID 6I.
AAFTH
AAYXX
CITATION
DOI 10.1016/j.piutam.2017.06.012
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
EISSN 2210-9838
EndPage 129
ExternalDocumentID 10_1016_j_piutam_2017_06_012
S2210983817300779
GroupedDBID --K
0R~
0SF
4.4
457
6I.
AACTN
AAEDT
AAEDW
AAFTH
AAIKJ
AALRI
AAXUO
ABMAC
ACGFS
ADBBV
ADEZE
AEXQZ
AFTJW
AGHFR
AITUG
ALMA_UNASSIGNED_HOLDINGS
AMRAJ
EBS
EJD
FDB
HZ~
IXB
J1W
KQ8
M41
M~E
NCXOZ
O-L
O9-
OK1
RIG
ROL
SES
SSZ
AAYWO
AAYXX
ACVFH
ADCNI
ADVLN
AEUPX
AFPUW
AIGII
AKBMS
AKRWK
AKYEP
CITATION
ID FETCH-LOGICAL-c352t-a106cffa7a180e9cc839fd7972ad0c988f7a1cc6767ba069abe9efa394b3e23e3
IEDL.DBID IXB
ISSN 2210-9838
IngestDate Tue Jul 01 02:03:43 EDT 2025
Thu Apr 24 23:00:10 EDT 2025
Wed May 17 00:06:02 EDT 2023
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords eigenfunctions
continuous growth
discrete growth
semianalytical solution
analytical solution
Galerkin method
heat transfer
Growing bodies
Language English
License This is an open access article under the CC BY-NC-ND license.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c352t-a106cffa7a180e9cc839fd7972ad0c988f7a1cc6767ba069abe9efa394b3e23e3
OpenAccessLink https://www.sciencedirect.com/science/article/pii/S2210983817300779
PageCount 10
ParticipantIDs crossref_citationtrail_10_1016_j_piutam_2017_06_012
crossref_primary_10_1016_j_piutam_2017_06_012
elsevier_sciencedirect_doi_10_1016_j_piutam_2017_06_012
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2017
2017-00-00
PublicationDateYYYYMMDD 2017-01-01
PublicationDate_xml – year: 2017
  text: 2017
PublicationDecade 2010
PublicationTitle Procedia IUTAM
PublicationYear 2017
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Cambridge University Press; 2010.
Lychev, Manzhirov (bib0005) 2013; 77
2012;6:130-7.
Danilovskaya (bib0030) 1950; 14
Stefan J. Uber die Theorie der Eisbildung, insbesondere uber die Eisbildung im Polarmeere
2012;47(6):677-89.
Epstein M.
1891;42:269-86.
Kuznetsov, Manzhirov, Fedotov (bib0035) 2011; 46
Fried E, Shen AQ. Generalization of the Stefan model to allow for both velocity and temperature jumps
Levitin AL, Lychev SA, Manzhirov AV, Shatalov MY. Nonstationary Vibrations of a Discretely Accreted Thermoelastic Parallelepiped
1999;11(5):277-96.
Manzhirov AV, Lychev SA, Kuznetsov SI, Fedotov I. Analytical study for the heat conduction in growing ball
Lychev, Manzhirov (bib0010) 2013; 48
10.1016/j.piutam.2017.06.012_bib0025
Danilovskaya (10.1016/j.piutam.2017.06.012_bib0030) 1950; 14
10.1016/j.piutam.2017.06.012_bib0015
Lychev (10.1016/j.piutam.2017.06.012_bib0010) 2013; 48
10.1016/j.piutam.2017.06.012_bib0040
10.1016/j.piutam.2017.06.012_bib0020
Lychev (10.1016/j.piutam.2017.06.012_bib0005) 2013; 77
Kuznetsov (10.1016/j.piutam.2017.06.012_bib0035) 2011; 46
10.1016/j.piutam.2017.06.012_bib0045
References_xml – reference: . Cambridge University Press; 2010.
– reference: 2012;47(6):677-89.
– reference: 1891;42:269-86.
– reference: Epstein M.
– reference: Manzhirov AV, Lychev SA, Kuznetsov SI, Fedotov I. Analytical study for the heat conduction in growing ball,
– reference: Levitin AL, Lychev SA, Manzhirov AV, Shatalov MY. Nonstationary Vibrations of a Discretely Accreted Thermoelastic Parallelepiped,
– volume: 77
  start-page: 421
  year: 2013
  end-page: 432
  ident: bib0005
  article-title: The mathematical theory of growing bodies. Finite deformations
  publication-title: J. Appl. Math. Mech
– volume: 48
  start-page: 553
  year: 2013
  end-page: 560
  ident: bib0010
  article-title: Reference configurations of growing bodies
  publication-title: Mech. Solids
– reference: Stefan J. Uber die Theorie der Eisbildung, insbesondere uber die Eisbildung im Polarmeere,
– reference: 2012;6:130-7.
– volume: 14
  start-page: 316
  year: 1950
  end-page: 324
  ident: bib0030
  article-title: Thermal stresses in an elastic half-space due to abrupt heating of its boundary
  publication-title: Prikl. Mat. Mekh.
– volume: 46
  start-page: 929
  year: 2011
  end-page: 936
  ident: bib0035
  article-title: Heat Conduction Problem for a Growing Ball
  publication-title: Mech. Solids
– reference: Fried E, Shen AQ. Generalization of the Stefan model to allow for both velocity and temperature jumps,
– reference: 1999;11(5):277-96.
– ident: 10.1016/j.piutam.2017.06.012_bib0015
  doi: 10.1017/CBO9780511762673
– volume: 48
  start-page: 553
  issue: 5
  year: 2013
  ident: 10.1016/j.piutam.2017.06.012_bib0010
  article-title: Reference configurations of growing bodies
  publication-title: Mech. Solids
  doi: 10.3103/S0025654413050117
– volume: 46
  start-page: 929
  issue: 6
  year: 2011
  ident: 10.1016/j.piutam.2017.06.012_bib0035
  article-title: Heat Conduction Problem for a Growing Ball
  publication-title: Mech. Solids
  doi: 10.3103/S0025654411060124
– ident: 10.1016/j.piutam.2017.06.012_bib0045
  doi: 10.3103/S0025654412060106
– volume: 14
  start-page: 316
  issue: 3
  year: 1950
  ident: 10.1016/j.piutam.2017.06.012_bib0030
  article-title: Thermal stresses in an elastic half-space due to abrupt heating of its boundary
  publication-title: Prikl. Mat. Mekh.
– ident: 10.1016/j.piutam.2017.06.012_bib0020
  doi: 10.1002/andp.18912780206
– volume: 77
  start-page: 421
  issue: 4
  year: 2013
  ident: 10.1016/j.piutam.2017.06.012_bib0005
  article-title: The mathematical theory of growing bodies. Finite deformations
  publication-title: J. Appl. Math. Mech
  doi: 10.1016/j.jappmathmech.2013.11.011
– ident: 10.1016/j.piutam.2017.06.012_bib0025
  doi: 10.1007/s001610050124
– ident: 10.1016/j.piutam.2017.06.012_bib0040
SSID ssj0000608225
Score 2.0365996
Snippet The heat transfer problems for growing bodies is the is the subject of present research. Temperature distributions in growing bodies that appear during...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 120
SubjectTerms analytical solution
continuous growth
discrete growth
eigenfunctions
Galerkin method
Growing bodies
heat transfer
semianalytical solution
Title Transient Temperature Fields in Growing Bodies Subject to Discrete and Continuous Growth Regimes
URI https://dx.doi.org/10.1016/j.piutam.2017.06.012
Volume 23
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NS8NAEF1KT15EUbF-sQevS5PdNMkebW0tQj1oC73FyWZXI5IWTa_-dmfyURREwUsgHwNhWGbeLO-9ZezSBS401ijhKYsDivKlQJTgBNgQZOrrNHUkTp7dhdNFcLscLDts1GphiFbZ1P66plfVunnSb7LZX-d5_0HitKJjcphTZEpDIj4VxJWIbznc7rN4IXmaE5ORvhcU0CroKprXOt-UQJJ0P6qMPH35c4f60nUme2y3gYv8qv6jfdaxxQF7rBoMCRn53CLsrW2R-YTIaO88L_gNztbYkvhwRRxBjsWBdlt4ueLXOZYJxMkcioyTM1VebHD2ryLKZ35vn0gScsgWk_F8NBXNSQnCIIAqBeBgZ5yDCPzYs9oYhD0ui3QkIfOMjmOHb4whc7YUvFBDarV1oHSQKiuVVUesW6wKe8x4rJSEAIzL3CBA9AEK7EDR0WTYxkwMPaba7CSmsRGn0yxek5Yv9pLUOU0opwnR5nzZY2Ibta5tNP74PmoTn3xbDglW-l8jT_4decp26K7eXzlj3fJtY88RcZTpRbWk8Dr7GH8CzAnXoQ
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NT8MwDI3GOMAFgQAxPnPgGq1turY5ssHYYNsBNmm3kKYJFKFugu7_Y_djAgmBxLWppcpK7Wfr-ZmQS-vbQBvNmcMNFCjc9RigBMuUCZQXuyKOLQ4njyfBYObfzTvzBunVszBIq6xifxnTi2hdPWlX3mwv07T96EG1IiJUmOMoSiM2yCaggRD_zuG8u260OAGKmiOVEQ0YWtQjdAXPa5mucoUz6W5YKHm63s8p6kva6e-SnQov0qvyk_ZIw2T75KnIMDjJSKcGcG-pi0z7yEb7oGlGb6G4hpxEuwskCVKIDthuofmCXqcQJwAoU5UlFKWp0mwFxX9hkb_QB_OMMyEHZNa_mfYGrFqVwDQgqJwpqOy0tSpUbuQYoTXgHpuEIvRU4mgRRRZOtEZ1tlg5gVCxEcYqLvyYG48bfkia2SIzR4RGnHvKV9omtuMD_FBcmQ7H3WSQx3SkWoTX3pG60hHHdRZvsiaMvcrSpxJ9KpE353otwtZWy1JH44_3w9rx8tt9kBDqf7U8_rflBdkaTMcjORpO7k_INp6UzZZT0szfV-YM4EcenxfX6xOW4dmQ
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=Transient+Temperature+Fields+in+Growing+Bodies+Subject+to+Discrete+and+Continuous+Growth+Regimes&rft.jtitle=Procedia+IUTAM&rft.au=Lychev%2C+S.&rft.au=Manzhirov%2C+A.&rft.au=Shatalov%2C+M.&rft.au=Fedotov%2C+I.&rft.date=2017&rft.issn=2210-9838&rft.eissn=2210-9838&rft.volume=23&rft.spage=120&rft.epage=129&rft_id=info:doi/10.1016%2Fj.piutam.2017.06.012&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_piutam_2017_06_012
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2210-9838&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2210-9838&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2210-9838&client=summon