New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media

Rogério José Marczak, Mitsunori Denda

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This work presents two new methods to derive the fundamental solution for three-dimensional heat transfer problems in the general anisotropic media. Initially, the basic integral equations used in the definition of the general anisotropic fundamental solution are revisited. We show the relationship between three, two and one-dimensional integral definitions, either by purely algebraic manipulation as well as through Fourier and Radon transforms. Two of these forms are used to derive the fundamental solutions for the general anisotropic media. The first method gives the solution analytically for which the solution for the orthotropic case agrees with the well known result obtained by the domain mapping, while the fundamental solution for the general anisotropic media is new. The second method expresses the solution by a line integral over a semi-circle. The advantages and disadvantages of the two methods are discussed with numerical examples.

Original languageEnglish (US)
Pages (from-to)3605-3612
Number of pages8
JournalInternational Journal of Heat and Mass Transfer
Volume54
Issue number15-16
DOIs
StatePublished - Jul 1 2011

Fingerprint

Anisotropic media
anisotropic media
Heat conduction
conductive heat transfer
derivation
Radon
radon
Integral equations
integral equations
manipulators
heat transfer
Heat transfer

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Keywords

  • Fourier and Radon transforms
  • Fundamental solutions
  • General anisotropic solids
  • Heat transfer

Cite this

@article{eac7b59ef7a54ec29156fa0576ea8ce4,
title = "New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media",
abstract = "This work presents two new methods to derive the fundamental solution for three-dimensional heat transfer problems in the general anisotropic media. Initially, the basic integral equations used in the definition of the general anisotropic fundamental solution are revisited. We show the relationship between three, two and one-dimensional integral definitions, either by purely algebraic manipulation as well as through Fourier and Radon transforms. Two of these forms are used to derive the fundamental solutions for the general anisotropic media. The first method gives the solution analytically for which the solution for the orthotropic case agrees with the well known result obtained by the domain mapping, while the fundamental solution for the general anisotropic media is new. The second method expresses the solution by a line integral over a semi-circle. The advantages and disadvantages of the two methods are discussed with numerical examples.",
keywords = "Fourier and Radon transforms, Fundamental solutions, General anisotropic solids, Heat transfer",
author = "Marczak, {Rog{\'e}rio Jos{\'e}} and Mitsunori Denda",
year = "2011",
month = "7",
day = "1",
doi = "10.1016/j.ijheatmasstransfer.2011.03.023",
language = "English (US)",
volume = "54",
pages = "3605--3612",
journal = "International Journal of Heat and Mass Transfer",
issn = "0017-9310",
publisher = "Elsevier Limited",
number = "15-16",

}

New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media. / Marczak, Rogério José; Denda, Mitsunori.

In: International Journal of Heat and Mass Transfer, Vol. 54, No. 15-16, 01.07.2011, p. 3605-3612.

Research output: Contribution to journalArticle

TY - JOUR

T1 - New derivations of the fundamental solution for heat conduction problems in three-dimensional general anisotropic media

AU - Marczak, Rogério José

AU - Denda, Mitsunori

PY - 2011/7/1

Y1 - 2011/7/1

N2 - This work presents two new methods to derive the fundamental solution for three-dimensional heat transfer problems in the general anisotropic media. Initially, the basic integral equations used in the definition of the general anisotropic fundamental solution are revisited. We show the relationship between three, two and one-dimensional integral definitions, either by purely algebraic manipulation as well as through Fourier and Radon transforms. Two of these forms are used to derive the fundamental solutions for the general anisotropic media. The first method gives the solution analytically for which the solution for the orthotropic case agrees with the well known result obtained by the domain mapping, while the fundamental solution for the general anisotropic media is new. The second method expresses the solution by a line integral over a semi-circle. The advantages and disadvantages of the two methods are discussed with numerical examples.

AB - This work presents two new methods to derive the fundamental solution for three-dimensional heat transfer problems in the general anisotropic media. Initially, the basic integral equations used in the definition of the general anisotropic fundamental solution are revisited. We show the relationship between three, two and one-dimensional integral definitions, either by purely algebraic manipulation as well as through Fourier and Radon transforms. Two of these forms are used to derive the fundamental solutions for the general anisotropic media. The first method gives the solution analytically for which the solution for the orthotropic case agrees with the well known result obtained by the domain mapping, while the fundamental solution for the general anisotropic media is new. The second method expresses the solution by a line integral over a semi-circle. The advantages and disadvantages of the two methods are discussed with numerical examples.

KW - Fourier and Radon transforms

KW - Fundamental solutions

KW - General anisotropic solids

KW - Heat transfer

UR - http://www.scopus.com/inward/record.url?scp=79956214398&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956214398&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2011.03.023

DO - 10.1016/j.ijheatmasstransfer.2011.03.023

M3 - Article

AN - SCOPUS:79956214398

VL - 54

SP - 3605

EP - 3612

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

IS - 15-16

ER -