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A carpenter builds an outer house wall w...

A carpenter builds an outer house wall with a layer of wood 2.0 cm thick on the outside and a layer of an insulation 3.5 cm thick as the inside wall surface. The wood has `K = 0.08 W//m-K` and the insulation has `K = 0.01 W//m-K` . The interior surface temperature is `19^@C` and the exterior surface temperature is `-10^@C`.
(a) What is the temperature at the plane where the wood meets the insulation?
(b) What is the rate of heat flow per square metre through this wall ?

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
(a) `H_1 = H_2`

`:. (19-theta)/R_1 = (theta+10)/R" "(H=(TD)/(R))`
or `(19-theta)/((l_1//K_1A)) = (theta + 10)/((l_2//K_2A))`
`:. (K_1(19-theta))/l_1 = (K_2(theta+10))/l_2`
`:. (0.01(19-theta))/3.5 = (0.08(theta + 10))/2.0`
Solving, we get
`theta = -8.1^@C`
(b) `H = H_1 = (19 - theta)/((l_1//K_1A))`
`=(K_1A(19-theta))/l_1`
`=((0.01)(19+8.1)(1))/(3.5 xx(10^-2))`
`=7.7 W//m^2`.
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