Problem #$4$

$4$ points

Consider two rectangular surfaces perpendicular to each other with a common edge which is $1\mathrm{.}6$ m long. The horizontal surface is $0\mathrm{.}8$ m wide, and the vertical surface is $1\mathrm{.}2$ m high. The horizontal surface has an emissivity of $0\mathrm{.}75$ and is maintained at $450$ K $.$ The vertical surface is black and is maintained at $700$ K $.$ The back sides of the surfaces are insulated.

The surrounding surfaces are at $290$ K and can be considered to have an emissivity of $0\mathrm{.}85.$ Determine the net rate of radiation heat transfer:

A$)$ Between the two surfaces $(2$ points$)$

B$)$ Between the horizontal surface and the surroundings $(2$ points$)$

$T_3=290K$

${}_3=0\mathrm{.}85$