Variable heat generation (Wiedemann-Franz law) in a heated source

O. Bautista, F. Méndez, I. Campos

Research output: Contribution to journalArticle

Abstract

In the present work, we study analytically and numerically the variable heat generation of a source immersed in a laminar channel cooling flow. We assume this internal heat generation is proportional to the local electrical resistivity, represented through the well-known Wiedemann-Franz law. It provides a relationship between the local electrical resistivity and the temperature of the source. Taking into account a finite thermal conductivity of the source's material, the nondimensional temperature profile and maximum longitudinal temperature and average temperature differences have been obtained as functions of the nondimensional parameters α, γ and Pe. α is the heat conduction parameter and represents the competition between the longitudinal heat conduction in the material to the heat convection in the laminar cooling flow. γ is a nondimensional parameter associated with the temperature's dependence on the electrical resistivity. Pe is the characteristic Peclet number of the cooling flow. The numerical and asymptotic results of the above nondimensional variables show a very sensible dependence of the parameters α, γ and Pe. Therefore, this set of nondimensional parameters controls directly the thermal performance of this simplified generating-heat strip model.
Original languageAmerican English
Pages (from-to)7-15
Number of pages9
JournalInternational Journal of Heat and Technology
StatePublished - 1 Jan 2006

Fingerprint

heat generation
Heat generation
Cooling
Heat conduction
conductive heat transfer
electrical resistivity
Temperature
heat
Heat convection
Peclet number
temperature profiles
Thermal conductivity
strip
temperature gradients
convection
thermal conductivity
temperature dependence
temperature
Hot Temperature

Cite this

@article{43c48b811d6543c4935d71907619afd7,
title = "Variable heat generation (Wiedemann-Franz law) in a heated source",
abstract = "In the present work, we study analytically and numerically the variable heat generation of a source immersed in a laminar channel cooling flow. We assume this internal heat generation is proportional to the local electrical resistivity, represented through the well-known Wiedemann-Franz law. It provides a relationship between the local electrical resistivity and the temperature of the source. Taking into account a finite thermal conductivity of the source's material, the nondimensional temperature profile and maximum longitudinal temperature and average temperature differences have been obtained as functions of the nondimensional parameters α, γ and Pe. α is the heat conduction parameter and represents the competition between the longitudinal heat conduction in the material to the heat convection in the laminar cooling flow. γ is a nondimensional parameter associated with the temperature's dependence on the electrical resistivity. Pe is the characteristic Peclet number of the cooling flow. The numerical and asymptotic results of the above nondimensional variables show a very sensible dependence of the parameters α, γ and Pe. Therefore, this set of nondimensional parameters controls directly the thermal performance of this simplified generating-heat strip model.",
author = "O. Bautista and F. M{\'e}ndez and I. Campos",
year = "2006",
month = "1",
day = "1",
language = "American English",
pages = "7--15",
journal = "International Journal of Heat and Technology",
issn = "0392-8764",
publisher = "Edizioni E.T.S.",

}

Variable heat generation (Wiedemann-Franz law) in a heated source. / Bautista, O.; Méndez, F.; Campos, I.

In: International Journal of Heat and Technology, 01.01.2006, p. 7-15.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Variable heat generation (Wiedemann-Franz law) in a heated source

AU - Bautista, O.

AU - Méndez, F.

AU - Campos, I.

PY - 2006/1/1

Y1 - 2006/1/1

N2 - In the present work, we study analytically and numerically the variable heat generation of a source immersed in a laminar channel cooling flow. We assume this internal heat generation is proportional to the local electrical resistivity, represented through the well-known Wiedemann-Franz law. It provides a relationship between the local electrical resistivity and the temperature of the source. Taking into account a finite thermal conductivity of the source's material, the nondimensional temperature profile and maximum longitudinal temperature and average temperature differences have been obtained as functions of the nondimensional parameters α, γ and Pe. α is the heat conduction parameter and represents the competition between the longitudinal heat conduction in the material to the heat convection in the laminar cooling flow. γ is a nondimensional parameter associated with the temperature's dependence on the electrical resistivity. Pe is the characteristic Peclet number of the cooling flow. The numerical and asymptotic results of the above nondimensional variables show a very sensible dependence of the parameters α, γ and Pe. Therefore, this set of nondimensional parameters controls directly the thermal performance of this simplified generating-heat strip model.

AB - In the present work, we study analytically and numerically the variable heat generation of a source immersed in a laminar channel cooling flow. We assume this internal heat generation is proportional to the local electrical resistivity, represented through the well-known Wiedemann-Franz law. It provides a relationship between the local electrical resistivity and the temperature of the source. Taking into account a finite thermal conductivity of the source's material, the nondimensional temperature profile and maximum longitudinal temperature and average temperature differences have been obtained as functions of the nondimensional parameters α, γ and Pe. α is the heat conduction parameter and represents the competition between the longitudinal heat conduction in the material to the heat convection in the laminar cooling flow. γ is a nondimensional parameter associated with the temperature's dependence on the electrical resistivity. Pe is the characteristic Peclet number of the cooling flow. The numerical and asymptotic results of the above nondimensional variables show a very sensible dependence of the parameters α, γ and Pe. Therefore, this set of nondimensional parameters controls directly the thermal performance of this simplified generating-heat strip model.

M3 - Article

SP - 7

EP - 15

JO - International Journal of Heat and Technology

JF - International Journal of Heat and Technology

SN - 0392-8764

ER -