# Heat Transfer: Finding temperature at the junction

#### paulie

1. Homework Statement
A furnace is constructed with 0.5 m of fire brick, 0.15 m of insulating brick and 0.25 m of ordinary building brick. The inside surface-temperature is 1530K and the outside surface temperature is 525K. The thermal conductivities of the fire, insulating and building bricks are 1.4, 0.21, and 0.7 W/m-K, respectively. Calculate the following per square meter area:
(a) Total resistance of the wall in K/W
(b) Rate of heat flow in W
(c) The temperatures at the junctions of the bricks.

2. Homework Equations
Q/T = kAΔT / L

3. The Attempt at a Solution
(a) Total resistance of the wall in K/W: answer 1.43 K/W
(b) Rate of heat flow in W: answer 703.5 W
(c) The temperatures at the junctions of the bricks.

(Temperature drop over firebrick+insulating brick)/(Total temperature drop) = (0.3571+0.7143/1.43)
Temperature drop over firebrick+insulating brick:
(1530K-525K) ⋅ (0.3571+0.7143/1.43) = 752.9769 K
Hence the temperature at the (firebrick & insulating)-ordinary brick interface = (1530K - 752.9769 K) = 777.0231 K

The correct answer according to the answer sheet is 778 K, there might be a slight difference but I want to make sure that my computation is right?

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Mentor
Looks OK.

E

#### Eucle

why is the solution on letter C like that? i tried equating by (1530 - X) / (0.5 / 1.4) = (X - 525) / (0.25 / 0.7) but its not showing the correct answer...

#### Chestermiller

Mentor
My heat flow rate equations for the three layers are as follows:
$$Q=1.4\frac{(1530-T_1)}{0.5}$$
$$Q=0.21\frac{(T_1-T_2)}{0.15}$$
$$Q=0.7\frac{(T_2-525)}{0.25}$$
What is the solution to these equations for $T_1$ and $T_2$?

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