A laser beam sends a uniform radiation beam towards the hemispherical opening in a solid housing with dimensions as shown. The surface of the cavity is black and essentially insulated from the surrounding housing material. The hemispherical cavity is a thin-walled metal with a black surface. The temperature of the housing as well as that of the surroundings is 25°C. Determine the radiant flux of the laser beam, G0 [W/m2], if a thermocouple located on the hemispherical surface indicates a temperature of 10°C.

Question

GIVEN

• Laser beam sending uniform radiation beam towards the hemispherical opening.

• Temperature of housing and surrounding (T?)= 250C.

• Temperature difference on thermocouple in hemispherical surface (?Tc) = 100C.

FIND

• Radiant flux of the laser beam.

ASSUMPTIONS

• Cavity surface is black and perfectly insulated from its mounting material.

• Negligible convection heat transfer from cavity surface.

• Surroundings are large, isothermal.

Answer 1

The total area of the opening of the hemisphere (A0) is



The energy balance of the system gives



All the radiation energy entering and leaving the cavity passes through hypothetical surface. So Tc can be treated as black disk.



Thus, the energy balance becomes