A furnace wall is comprised of insulating brick with a thermal conductivity that exhibits a linear dependence on temperature. If the inside wall of the furnace is at 2500 °F and the outside wall is at 100 °F and the following information is available for the thermal conductivity:

Material: Insulating Brick

Thickness (ft): 1.00

Thermal Conductivity (Btu/hr*ft*F): at 100 F = 0.90, at 2000 F= 1.80

a. For steady-state operation, determine an expression for the temperature within the wall.

b. Determine the heat flux through the wall [Btu / ft2 ]