A furnace wall is to be constructed of brick having standard dimensions 9 by 4.5 by 3 in. Two kinds of material are available. One has a maximum usable temperature of 1900°F and a thermal conductivity of 1 Btu/(h ft°F), and the other has a maximum temperature limit of 1600°F and a thermal conductivity of 0.5 Btu/(h ft°F). The bricks cost the same and can be laid in any manner, but we wish to design the most economical wall for a furnace with a temperature on the hot side of 1900°F and on the cold side of 400°F. If the maximum amount of heat transfer permissible is 300 Btu/h for each square foot of area, determine the most economical arrangements for the available bricks.
GIVEN
Furnace wall made of 9 A? 4.5 A? 3 inch bricks of two types
Type 1 bricks Maximum useful temperature (T1,max) = 1900°F
Thermal conductivity (k1) = 1.0 Btu/(h ft°F)
Type 2 bricks Maximum useful temperature (T2,max) = 1600°F
Thermal conductivity (k2) = 0.5 Btu/(h ft°F)
Bricks cost the same
Wall hot side (Thot) = 1900°F and cold side (Tcold) = 400°F
Maximum heat transfer permissible (qmax/A) = 300 Btu/(h ft2)
ASSUMPTIONS
One dimensional, steady state heat transfer conditions
Constant thermal conductivities
The contact resistance between the bricks isnegligible
