Design of a furnace enclosure

The inside dimensions of a furnace are $700mm($length$),500mm($width$),$ and $400mm($height$).$ The inside of the furnace is surrounded by $6$ walls, each consisting of two layers in series: a layer of fireclay brick with thickness $x_B$ and a layer of steel with thickness $x_S=6\mathrm{.}25mm.$ The inner surface of the brick layer $($which faces the inside of the furnace$)$ is at a temperature of $500C.$ The outer surface of the steel layer faces the air in the room. The air temperature in the room is $20\mathrm{.}0C.$ The thermal conductivities of the brick and steel are $0\mathrm{.}160W*m^{-1}*K^{-1}$ and $45\mathrm{.}0W*m^{-1}*K^{-1},$ respectively. $($See the specifications sheet for the insulating firebrick$).$ The convective heat transfer coefficient of the air in contact with the steel is $15\mathrm{.}0W*m^{-2}*K^{-1}.$

a$.$ For safety reasons, the temperature of the outer surface of the steel layer must not exceed $50\mathrm{.}0C.($A higher temperature could cause burns to people working near the furnace if they touch it$).$ What is the maximum heat transfer rate $($W$)$ through all six faces of the furnace together? $($Hint: Neglect the heat transfer through the corners of the furnace$).$

b$.$ Calculate the minimum thickness required for the brick layer.