Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes

Syed M. Zubair; M. Aslam Chaudhry

doi:10.1016/0017-9310(95)00110-U

Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes

Syed M. Zubair^*
, M. Aslam Chaudhry

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface heat fluxes of the forms: (i) Q₁(t) = Q₀(1+a cos ωt); and (ii) Q₂(t) = Q_o(1+bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q₀. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositions C_r and S_r of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. In addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.

Original language	English
Pages (from-to)	3393-3399
Number of pages	7
Journal	International Journal of Heat and Mass Transfer
Volume	38
Issue number	18
DOIs	https://doi.org/10.1016/0017-9310(95)00110-U
State	Published - Dec 1995

Bibliographical note

Funding Information:
Acknowledgement--Tahuet horsa cknowledgthee support providedb y the King Fahd Universityo f Petroleuman d Mineralsfo r thisr esearcphr oject.

ASJC Scopus subject areas

Condensed Matter Physics
Mechanical Engineering
Fluid Flow and Transfer Processes

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10.1016/0017-9310(95)00110-U

Cite this

@article{85c1b9eec7d344548d3b321174063b0c,

title = "Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes",

abstract = "An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface heat fluxes of the forms: (i) Q1(t) = Q0(1+a cos ωt); and (ii) Q2(t) = Qo(1+bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q0. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositions Cr and Sr of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. In addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.",

author = "Zubair, \{Syed M.\} and Chaudhry, \{M. Aslam\}",

note = "Funding Information: Acknowledgement--Tahuet horsa cknowledgthee support providedb y the King Fahd Universityo f Petroleuman d Mineralsfo r thisr esearcphr oject.",

year = "1995",

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doi = "10.1016/0017-9310(95)00110-U",

language = "English",

volume = "38",

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journal = "International Journal of Heat and Mass Transfer",

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T1 - Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes

AU - Zubair, Syed M.

AU - Chaudhry, M. Aslam

N1 - Funding Information: Acknowledgement--Tahuet horsa cknowledgthee support providedb y the King Fahd Universityo f Petroleuman d Mineralsfo r thisr esearcphr oject.

PY - 1995/12

Y1 - 1995/12

N2 - An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface heat fluxes of the forms: (i) Q1(t) = Q0(1+a cos ωt); and (ii) Q2(t) = Qo(1+bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q0. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositions Cr and Sr of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. In addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.

AB - An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface heat fluxes of the forms: (i) Q1(t) = Q0(1+a cos ωt); and (ii) Q2(t) = Qo(1+bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q0. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositions Cr and Sr of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. In addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.

UR - https://www.scopus.com/pages/publications/0029141102

U2 - 10.1016/0017-9310(95)00110-U

DO - 10.1016/0017-9310(95)00110-U

M3 - Article

AN - SCOPUS:0029141102

SN - 0017-9310

VL - 38

SP - 3393

EP - 3399

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

IS - 18

ER -

Heat conduction in a semi-infinite solid subject to steady and non-steady periodic-type surface heat fluxes

Abstract

Bibliographical note

ASJC Scopus subject areas

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