During the winter season a basement apartment collects water on its cold floor b

ID: 1859154 • Letter: D

Question

During the winter season a basement

apartment collects water on its cold floor because of vapor

condensation. To prevent this, a contractor suggested that

the floor be insulated to raise its temperature. She

recommended a 2.5 cm layer of polystyrene (k = 0.028

W/m^2C) and 1.5 cm layer of wood (k = 0.15 W/m^2C) for

rigidity. You are asked to evaluate this recommendation by

determining whether or not condensation will take place on the new wood flooring. Assume that

the temperature at the floor-polystyrene interface is 10%uF0B0C and that condensation takes place at a

temperature of 17C. The air temperature in the basement is 21C and the heat transfer

coefficient is 9 W/m2

-%uF0B0C. Assume 1-D heat transfer and steady state. (Hint: use thermal

resistance analysis)

Wood is directly on top of polysterene (sorry for lack of picture)

Thermal resistance=l/kA for conduction, 1/hA for convection.

Let the area of the floor be A

total resistance for conduction per unit area, R=l1/k1+l2/k2=0.992 m/W

Tamb=294K ; Tf1=283K ; Tf2:temp. on new wooden floor

Heat flux from surface=heat flux through the layers

h(-Tf2+Tamb)=(Tf2-Tf1)/R =>Tf2=[h*Tamb+Tf1/R]/(h+1/R)=292.89K=19.89 degC>17C. No condensation shall take place

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