Overview
In this section, the analytical solution of the temperature distribution given by the hyperbolic heat conduction equation is presented. The model of irradiated one-dimensional, semi-infinite body is studied. The laser heating is modeled as an internal source which strength depends on time and position \(g(x,t)=I(t)(1-R)\mu \cdot {e^{{-\mu x}}}\). The temperature distribution in the semi-infinite body is studied for two different types of laser sources. For the first case, the source of the constant strength is assumed, and the exponential source is analyzed for the second case. Moreover, the effect of absorption coefficient β on the temperature distribution inside the semi-infinite body is studied. The analytical solution of the hyperbolic heat conduction equation is obtained using the Laplace transform method. This technique allows converting the partial differential equation to ordinary differential equation, which significantly simplifies the solution procedure. The...
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© 2014 Springer Science+Business Media Dordrecht
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Ocłoń, P., Łopata, S. (2014). Hyperbolic Heat Conduction Equation. In: Hetnarski, R.B. (eds) Encyclopedia of Thermal Stresses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2739-7_390
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DOI: https://doi.org/10.1007/978-94-007-2739-7_390
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2738-0
Online ISBN: 978-94-007-2739-7
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