To reduce heat transfer losses through a glass window, you consider replacing the window with one of three alternatives: a sheet of tin 0.50-cm thick, a layer of brick 8.0- cm thick, and a combination of wood and insulation 4.0-cm thick. The original thickness of the glass is 1.0-cm. Consider the thermal conductivities of each to be the following: glass – 1.40 W/m-K; tin – 66.6 W/m-K; brick – 1.20 W/m-K; wood/insulation combination – 0.09 W/m-K. Considering the inside temperature of the surface to be 20.0°C, and the outside temperature to be -5.0°C, determine the heat conduction rate per unit area for the glass and the three alternatives, and discuss the relative merits of the three alternatives (ignoring material and installation costs).
Given: Ti = 20.0°C; To = -5.0°C
What will be an ideal response?
For the each material, approximate: dT/dx = ti-t0/?x
For Glass: k = 1.40 W/m-K; ?x = 1.0 cm = 0.01 m
Qcond/A = -k T1-T0/?x = -3,500 W/m2
Tin: ? = 66.6 W/m-K; ?x = 0.5 cm = 0.005 m
Qcond/A = -k T1-T0/?x = 266,400 W/m2
Brick: ? = 1.20 W/m-K; ?x = 8.0 cm = 0.08 m
Qcond/A = -k T1-T0/?x = 375 W/m2
Wood/Insulation: ? = 0.09 W/m-K; ?x = 4.0 cm = 0.04 m
Qcond/A = -k T1-T0/?x = 56.3 W/m2
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