Laser heating of a slab having temperature‐dependent surface absorptance

The exact solution obtained here for the temperature in a laser‐heated slab with surface absorptance A=A_i+A₁ T (0,t) proportional to temperature and with negligible radial heat flow, shows that the temperature is considerably greater in general than for A₁=0. In the limit of long time, for negligible cooling, the surface temperature increases exponentially as T_A{ exp[(I/I_l)(t/τ_l)]−1} for I≲I_l and as T_A{2 exp[(I/I_l)²(t/τ_l)]−1} for I≳I_l, where T_A=A_i/A₁, I_l=K/lA₁, τ_l=Cl²/K, K is the thermal conductivity, C is the heat capacity per unit volume, and l is the slab thickness. The limiting temperature derived here for t≳τ_l/5 and that derived by Sparks and Loh for t≲τ_l/5 afford simple closed‐form expressions for T (z,t) for all z and t. With cooling, the temperature increases without bound (thermal runaway) for I≳I_hl, where I_hl=I_l[H_s+H/(1+H)] with H_s and H normalized heat‐transfer coefficients at the front and rear surfaces of the slab. The intrinsic cw damage threshold, which is slightly less than I_hl, can be quite low—from 100 W/cm² to 150 kW/cm² for the examples considered. The ability to withstand a given irradiance in a small beam does not imply the ability to withstand the same irradiance in a large beam.