A region at 60 0 C is separated from a region at 25 ?0 ? C by a .01m wrought iro

Question

A region at 600C is separated from a region at 25?0? C by a .01m wrought iron wall. What is the rate of heat transfer between the regions? Now suppose the wall is changed to a three layer wall. The first, with a width of .005m is wrought iron, the second, with a width of .004m is air, and the third, with a width of .005m is wrought iron. What is the rate of heat transfer now (per area)? What properties / constants in this problem (implicitly or explicitly given) are additive. Identify 3 properties or contants (used in the problem) as either intensive or extensive.

Explanation / Answer

given Th = 600 C
Tc = 25 C
t = 0.01 m
heat conductovoty of iron, kc = 59 W/m K
rate of heat transfer per unit area , q' = kc*(Th - Tc)/t = 3392500 W/m^2

for three layer wall
let temperaure on one side of the air wall be T1 and on the other side be T2
then
q' = kc*(Th - T1)/t1 = kc*(T2 - Tc)/t2 = k*(T1 - T2)/t
t1 = t2 = 0.05 m
t = 0.04 m
k = 2 W /m K
hence

59(600 - T1)/0.05 = 59(T2 - 25)/0.05 = 2(T1 - T2)/0.04
T1 + T2 = 575
-T1 + T2 = -23.6(T2 - 25)
2T2 = 575 - 23.6T2 + 23.6*25
T2 = 45.5078 C
T1 = 529.492 C
hence q' = 83199 W/m^2
in this case, the temeprature difference is an additive property

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