The steady-state temperature distribution in a semitransparent material of thermal conductivity [tex]k[/tex] and thickness [tex]L[/tex] exposed to laser irradiation is of the form
[tex]
T(x)=-\frac{A}{k a^2} e^{-a r}+B x+C
[/tex]
where [tex]A, a, B[/tex], and [tex]C[/tex] are known constants. For this situation, radiation absorption in the material is manifested by a distributed heat generation term, [tex]\dot{q}(x)[/tex].
(a) Obtain expressions for the conduction heat fluxes at the front and rear surfaces.
