1. The problem statement, all variables and given/known data
An oak slab (ρ=545 kg/m3, k=0.17 W/(m-K), and c=2385 J/(kg-K)) of thickness 10 cm is exposed on one side to irradiation (1x10^5 W/m2) from a laser, which starts heating it up. Convection is negligible (i.e., h is small). The slab is initially at 23°C. (a) If the oak surface temperature reaches 260°C, it will start burning. How long can the slab be irradiated before it starts burning? (b) As an approximate first analysis, assume that once the slab surface reaches the burning temperature, it immediately vaporizes. If the energy required to vaporize oak is 14.5 kJ/kg, how long would it take to vaporize the oak slab to a depth of 2 mm?
2. Relevant equations
I'm not really sure. Energy Balance (Ein - Eout + Egeneration = Estored)
3. The attempt at a solution
I'm not sure where to start. I know multiplying the irradiation value by the area will give me the Ein term. And I'm pretty sure the irradiation travels through the slab as conduction. But I'm not really sure where to go from there.
An oak slab (ρ=545 kg/m3, k=0.17 W/(m-K), and c=2385 J/(kg-K)) of thickness 10 cm is exposed on one side to irradiation (1x10^5 W/m2) from a laser, which starts heating it up. Convection is negligible (i.e., h is small). The slab is initially at 23°C. (a) If the oak surface temperature reaches 260°C, it will start burning. How long can the slab be irradiated before it starts burning? (b) As an approximate first analysis, assume that once the slab surface reaches the burning temperature, it immediately vaporizes. If the energy required to vaporize oak is 14.5 kJ/kg, how long would it take to vaporize the oak slab to a depth of 2 mm?
2. Relevant equations
I'm not really sure. Energy Balance (Ein - Eout + Egeneration = Estored)
3. The attempt at a solution
I'm not sure where to start. I know multiplying the irradiation value by the area will give me the Ein term. And I'm pretty sure the irradiation travels through the slab as conduction. But I'm not really sure where to go from there.
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