The figure below shows (in cross section) a wall consisting of four layers, with

Question

The figure below shows (in cross section) a wall consisting of four layers, with thermal conductivities k1 = 0.060 W/m · K, k3 = 0.040 W/m · K, and k4 = 0.12 W/m · K (k2 is not known). The layer thickness are L1 = 1.7 cm, L3 = 2.8 cm, and L4 = 3.5 cm (L2 is not known). The known temperature are T1 = 25°C, T12 = 22°C, and T4 = 10°C. Energy transfer through the wall is steady. What is interface temperature T34? Give your answers in C degrees.

http://www.webassign.net/hrw10/18-p-063.gif -- image URL

Explanation / Answer

Because the conduction is steady, the conduction rate P4 through the brick must equal the conduction rate P1 through the pine.

T34 = k1*L4 / k4*L1 (T1-T12) + T4

Putting L4 = 3.5, L1 = 1.7, k1 = 0.060, k4 = 0.12

T34 = (0.060 * 3.5 / 0.12 * 1.7 ) (25-22) - 10

T34 = (0.060 * 3.5 / 0.12 * 1.7 ) (3) - 10

T34 = (0.060 * 3.5 * 3 / 0.12 * 1.7 ) - 10

T34 = -1.07 degree C

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