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

• Published in: International journal of heat and mass transfer Vol. 38; no. 18; pp. 3393 - 3399
• Main Authors: Zubair, Syed M., Chaudhry, M.Aslam
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1995; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Physics; Temperature distribution; Heat flow; Semiinfinite solid; Malignant tumor; Periodic variations; Analytical solution; Medical application; Induced hyperthermia; Thermal conduction; Processing
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/0017-9310(95)00110-U

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) Q 1( t) = Q 0(1+ a cos ωt); and (ii) Q 2( t) = Q o (1+ bt cos ωt), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q 0. 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.