The window of large vacuum chamber is fabricated from a material of prescribed spectral characteristics. A collimate beam of radiant energy from a solar simulator is incident on the window and has a flux of $3000\frac{W}{m^2}.$ The inside walls of the chamber, which are large compared to the window area, are maintained at $77K.$ The outer surface

Spring $2024$

of the window is subjected to surroundings and standard conditions for temperature and pressure with a convection heat transfer coefficient $28\frac{W}{m^2}K.$ The solar transmissivity $({}_s)$ of the window material to radiation from the solar simulator is $0\mathrm{.}748,$ the reflectivity $({}_s)$ is in the order of $0\mathrm{.}185,$ and the emissivity $()$ of $0\mathrm{.}85.$

a$.$ Determine the absorptivity of the material $({}_s)$

b$.$ Assuming that the window is insulated from its chamber mounting arrangements, what steady state temperature does the window will reach $(T_w)?$

c$.$ Calculate the net radiation transfer per unit area $(\frac{W}{m^2})$ of the window to the vacuum chamber wall $($exclude the transmitted simulated solar flux$)$