Consider the room problem above in problem 25 . Of the four walls in the room, two are external walls with surface temperatures of \(17^{\circ} \mathrm{C}\). The other two are internal walls whose temperatures are at \(20^{\circ} \mathrm{C}\).

a. Set up the equations describing radiative heat transfer between the walls, floor, and ceiling.

b. What are the view factors?

c. Solve the set of equations to obtain the heat flows between the walls, floor, and ceiling.

d. How much energy must be supplied to the floor?

Problem 25

A new radiant heating system is installed in the floor of a room \(4 \mathrm{~m}\) long by \(3 \mathrm{~m}\) wide. The floor is held at a temperature of \(35^{\circ} \mathrm{C}\) and the ceiling, located \(2.75 \mathrm{~m}\) from the floor, is well insulated. The walls leak heat and have a surface temperature of \(17^{\circ} \mathrm{C}\). If all the surfaces have an emissivity of 0.9 , how much heat is transferred via radiation from the floor?