An analytical study of transient heat conduction in an infinite medium with gamma-type, spherical-surface-heat sources

Syed M. Zubair; M. Aslam Chaudhry

doi:10.1016/0735-1933(92)90027-F

An analytical study of transient heat conduction in an infinite medium with gamma-type, spherical-surface-heat sources

Syed M. Zubair^*, M. Aslam Chaudhry

^*Corresponding author for this work

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

Abstract

A close-form model for the computation of temperature distribution, in an infinitely extended isotropic body with Gamma-type, spherical-surface-heat sources is discussed. The temperature solutions are presented for time-dependent heat sources of the forms: (i) Q dot₁(t) = q₀exp(-λt), and (ii) Q dot₂(t) = q₀texp(-λt), where λ is a real number. The dimensionless (or reduced) temperature solutions are presented in terms of the generalized representation of an incomplete Gamma function I_α(b,χ), which can also be expressed by the complementary error functions. It is also demonstrated that the classical solution given in the literature can easily be recovered from the present analysis.

Original language	English
Pages (from-to)	155-163
Number of pages	9
Journal	International Communications in Heat and Mass Transfer
Volume	19
Issue number	2
DOIs	https://doi.org/10.1016/0735-1933(92)90027-F
State	Published - 1992

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
General Chemical Engineering
Condensed Matter Physics

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10.1016/0735-1933(92)90027-F

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title = "An analytical study of transient heat conduction in an infinite medium with gamma-type, spherical-surface-heat sources",

abstract = "A close-form model for the computation of temperature distribution, in an infinitely extended isotropic body with Gamma-type, spherical-surface-heat sources is discussed. The temperature solutions are presented for time-dependent heat sources of the forms: (i) Q dot1(t) = q0exp(-λt), and (ii) Q dot2(t) = q0texp(-λt), where λ is a real number. The dimensionless (or reduced) temperature solutions are presented in terms of the generalized representation of an incomplete Gamma function Iα(b,χ), which can also be expressed by the complementary error functions. It is also demonstrated that the classical solution given in the literature can easily be recovered from the present analysis.",

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

year = "1992",

doi = "10.1016/0735-1933(92)90027-F",

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journal = "International Communications in Heat and Mass Transfer",

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T1 - An analytical study of transient heat conduction in an infinite medium with gamma-type, spherical-surface-heat sources

AU - Zubair, Syed M.

AU - Aslam Chaudhry, M.

PY - 1992

Y1 - 1992

N2 - A close-form model for the computation of temperature distribution, in an infinitely extended isotropic body with Gamma-type, spherical-surface-heat sources is discussed. The temperature solutions are presented for time-dependent heat sources of the forms: (i) Q dot1(t) = q0exp(-λt), and (ii) Q dot2(t) = q0texp(-λt), where λ is a real number. The dimensionless (or reduced) temperature solutions are presented in terms of the generalized representation of an incomplete Gamma function Iα(b,χ), which can also be expressed by the complementary error functions. It is also demonstrated that the classical solution given in the literature can easily be recovered from the present analysis.

AB - A close-form model for the computation of temperature distribution, in an infinitely extended isotropic body with Gamma-type, spherical-surface-heat sources is discussed. The temperature solutions are presented for time-dependent heat sources of the forms: (i) Q dot1(t) = q0exp(-λt), and (ii) Q dot2(t) = q0texp(-λt), where λ is a real number. The dimensionless (or reduced) temperature solutions are presented in terms of the generalized representation of an incomplete Gamma function Iα(b,χ), which can also be expressed by the complementary error functions. It is also demonstrated that the classical solution given in the literature can easily be recovered from the present analysis.

UR - https://www.scopus.com/pages/publications/0026835066

U2 - 10.1016/0735-1933(92)90027-F

DO - 10.1016/0735-1933(92)90027-F

M3 - Article

AN - SCOPUS:0026835066

SN - 0735-1933

VL - 19

SP - 155

EP - 163

JO - International Communications in Heat and Mass Transfer

JF - International Communications in Heat and Mass Transfer

IS - 2

ER -

An analytical study of transient heat conduction in an infinite medium with gamma-type, spherical-surface-heat sources

Abstract

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