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The figure shows (in cross section) a wall that consists of four layers. The thermal conductivities are k1 = 0.060 W/m = K, k3 = 0.050 W/m = K and k4 = 0.100 W/m = K (k2 is not known). The layer thicknesses are L1 = 1.8 cm, L3 = 1.6 cm and L4 = 1.2 cm. The hottest temperature on the extreme left is 30 degree C while the coldest is on the extreme right at -10 degree C. If we number the temperatures at the interfaces between different materials as 12, 23, 34, then T12 = 25 degree C. What is T34? (deg) Tries 2/7 Previous Tries What is T23? Tries 0/7 That is the ratio of k2 to L2? (enter no units) Tries 0/7
Explanation / Answer
Heat flux is constant throughout.
For constant flux, kA(T2-T1)/ALshould be constant. Since A is constant, k(T2-T1)/L should be constant.
1)Flux in L1=0.06*5/0.018=16.67
Matching flux in L4,
0.1*(T34+10)/0.012=16.67
T34=-8C
2)Similarly in L3,
0.05*(T23+8)/0.016=16.67
T23=-2.67C
3)k2/L2*(25+2.67)=60.24