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# Thermal phys: heat flow

The multi-layer wall system consisting of three plane walls "A", "B", and "C" as shown in the figure, which is transferring heat from fluid I at 100oC to fluid II at 20oC. These fluids are in contact with its left and right surfaces respectively. Estimate the heat flow form fluid I to fluid II through a unit width of the multi-layer wall system by assuming one-dimensional steady-state conduction and negligible radiation. Thermal conductivities of the wall materials are kA=0.6W/mK, kB=1.5W/mK, kC=0.8W/mK.

Ans: 83.96W

What can I solve this? The figure is so complicated....

Please help.

Sorry, I just found the solution. But sttill have questions about it.

total resistance = resistance of I + resistance of A + resistance of BC + resistance of II

= 1/[(15)(8.4)] + (0.8)/[(0.6)(8.4)] + 1/[ (1.5)(3)/(1.2) + (0.8)(5.4)/(1.2) ] + 1/[(8)(8.4)]

=0.3176

total heat transfer = (100-20)/0.3176=251.9W

So do you know why resistance of I and II are also included and what are the values 8.4, 3, and 5.4? Area??

Thank you very much!!

### 1 Answer

- 天同Lv 76 years agoFavorite Answer
Thermal conductivity of composite wall B and C

= (1 x 1.5 + 1.8 x 0.8)/(1+1.8) w/m^2.K = 1.05 w/m.K

Resistance of composite wall B and C = 1.2/1.05 m^2.K/w = 1.143 m^2K/w

Resistance of wall A = 0.8/0.6 m^2K/w = 1.333 m^2K/w

Total resistance of walls A, B and C = (1.333 + 1.143) m^2K/w = 2.476 m^2K/w

Hence, heat flow by conduction pe unit width

= (100 - 20)/2.476 w = 32.3 w

Please check if your given answer is correct.

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