Abstract
In this chapter we discuss various specific solutions of the heat equation for semi-infinite substrates. The irradiation geometry and the definition of the coordinate system shall be the same as in Fig. 6.1.1 but with \(\ensuremath{h_{\mathrm{s}}}\to\infty\). Any phase changes and chemical reaction energies are ignored. For many applications, the knowledge of the maximum laser-induced temperature rise is of great importance. With the beam shapes discussed in Sect. 6.4, the maximum surface temperature always occurs in the center of the laser beam at \(\textbf{\textit{x}}^\ast=0\). Subsequently, we present analytic expressions for semi-infinite substrates, stationary conditions, and temperature-independent material parameters.
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Bäuerle, D. (2011). Semi-infinite Substrates. In: Laser Processing and Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17613-5_7
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DOI: https://doi.org/10.1007/978-3-642-17613-5_7
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