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 temperatures of the forms: (i)T 1(t)=T 0(1+a cos ωt), and (ii)T 2(t)=T 0(1+b t cos ωt), wherea andb are controlling factors of the periodic oscillations about the constant surface temperatureT 0. The dimensionless (or reduced) temperature and heat flux solutions are presented in terms of decompositionsC Γ andS Γ 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 temperatures.
Zusammenfassung
Die Untersuchung liefert analytische Lösungen für das Temperatur- und Wärmeflußfeld in einem halbunendlichen Körper mit konstanten Stoffwerten. Die Lösungen werden in dimensionsloser Form für veränderliche Oberflächentemperaturen ermittelt, welche nach folgenden Zeitgesetzen oszillieren: (i)T 1(t)=T 0(1+a cos ωt), (ii)T 2 (t)=T 0 (1+b t cos ωt). Die Darstellung erfolgt unter Verwendung der ZerlegungsfunktionenC Γ undS Γ für die unvollständige Gammafunktion. Für große Zeiten münden die hier mitgeteilten Ergebnisse in die bekannten quasistationären periodischen Lösungen ein.
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Chaudhry, M.A., Zubair, S.M. Temperature and heat flux solutions due to steady and non-steady periodic-type surface temperatures in a semi-infinite solid. Warme - Und Stoffubertragung 29, 205–210 (1994). https://doi.org/10.1007/BF01539751
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DOI: https://doi.org/10.1007/BF01539751