Analytical solution for a class of flat plate conjugate convective heat transfer problems

Antti Lehtinen, Reijo Karvinen (Corresponding Author)

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows: transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with Pr ≥ 1. The solutions in the paper are based on the superposition principle and analytical expressions are used to couple the temperature and the heat flux distributions on the surface of the plate. The results of the Luikov problem and transient plate are also compared to other solutions presented earlier in the literature.
Original languageEnglish
Article number043004
Number of pages6
JournalFrontiers in Heat and Mass Transfer
Volume2
Issue number4
DOIs
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed

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convective heat transfer
flat plates
Heat transfer
heat generation
Heat generation
heat transfer
thin plates
forced convection
Forced convection
laminar flow
Laminar flow
turbulent flow
Turbulent flow
Heat flux
heat flux
convection
Temperature
temperature

Keywords

  • Flat plate
  • conjugate heat transfer
  • Luikov problem
  • fractional calculus

Cite this

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abstract = "Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows: transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with Pr ≥ 1. The solutions in the paper are based on the superposition principle and analytical expressions are used to couple the temperature and the heat flux distributions on the surface of the plate. The results of the Luikov problem and transient plate are also compared to other solutions presented earlier in the literature.",
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Analytical solution for a class of flat plate conjugate convective heat transfer problems. / Lehtinen, Antti; Karvinen, Reijo (Corresponding Author).

In: Frontiers in Heat and Mass Transfer, Vol. 2, No. 4, 043004, 2011.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Analytical solution for a class of flat plate conjugate convective heat transfer problems

AU - Lehtinen, Antti

AU - Karvinen, Reijo

PY - 2011

Y1 - 2011

N2 - Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows: transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with Pr ≥ 1. The solutions in the paper are based on the superposition principle and analytical expressions are used to couple the temperature and the heat flux distributions on the surface of the plate. The results of the Luikov problem and transient plate are also compared to other solutions presented earlier in the literature.

AB - Analytical solutions for three different flat plate conjugate heat transfer cases are presented. The cases are as follows: transient heat transfer of a thin plate with uniform heat generation; the Luikov problem in which one plate surface is kept in a constant temperature and the other one is cooled by forced convection; and a modified Luikov problem with heat generation on one surface and convection on both surfaces of the plate. All the cases are solved for both laminar and turbulent flows with Pr ≥ 1. The solutions in the paper are based on the superposition principle and analytical expressions are used to couple the temperature and the heat flux distributions on the surface of the plate. The results of the Luikov problem and transient plate are also compared to other solutions presented earlier in the literature.

KW - Flat plate

KW - conjugate heat transfer

KW - Luikov problem

KW - fractional calculus

U2 - 10.5098/hmt.v2.4.3004

DO - 10.5098/hmt.v2.4.3004

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JO - Frontiers in Heat and Mass Transfer

JF - Frontiers in Heat and Mass Transfer

SN - 2151-8629

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