Problem 2. (6 pts)

A furnace wall is to be designed to transmit a maximum heat flux of 200 Btu/hr ft² of wall area.

The inside and outside wall temperatures are to be 2000 and 300°F, respectively.

(a) Use the shell-balance approach to derive the differential equation that governs heat

conduction through an insulated wall. Derive two equations, one in terms of heat flux (q)

and the other in terms of temperature (T).

(b) Determine the most economical arrangement of bricks measuring 9 by 4.5 by 3 inches if

the bricks are made from one of two materials, one with a k of 0.44 Btu/hr ft °F and a

maximum usable temperature of 1500°F and the other with a k of 0.94 Btu/hr ft °F and a

maximum usable temperature of 2200°F. Bricks made of each material cost the same

amount and may be laid in any manner.

Problem 3. (6 pts)