This is a steady-state problem. a slab has thickness l and thermal conductivity k. the slab is irradiated by a laser beam which is absorbed exponentially, leading to a heat generation, g(x) g exp( x /l) = 0 − , where g0 is a known constant with si units [w/m3 ]. the absorption depth l is also known, and you are also given that l < < l. the x=l face of the slab is well-insulated. the x=0 face is exposed to fluid with a known convection coefficient h and an unknown fluid temperature t∞. your job is to specify t∞ so that the hottest temperature of the slab never exceeds a critical value tcrit. (a) obtain an expression for the temperature profile t(x), for arbitrary t∞. your expression here can contain t∞ , but should not involve tcrit. (b) sketch your result for t(x). (c) now obtain an expression for t∞, such that the maximum of t(x) does not exceed a specified tcrit.