A factory has a sheet metal wall with a thermal conductivity of 105 Btu/h-ft-oF. The wall thickness is 1 inch. (a) If the inside temperature of the wall is 80.0oF and the outside temperature of the wall is 10.0°F, determine the heat transfer rate per unit area from conduction (the conductive heat flux) for the wall. (b) For an inside wall temperature of 80.0°F, plot the conductive heat flux through the wall for outside wall temperatures ranging from 90.0°F to 0.0°F. (c) For an outside wall temperature of 10.0°F, plot the conductive heat flux for inside wall temperatures ranging from 50.0°F to 85.0°F. Discuss how this relates to gaining cost savings by heating a building to a lower temperature in the winter.
Given: ? = 105 Btu/h-ft-°F; ?x = 1 in = 0.0833 ft
What will be an ideal response?
(a) To = 10.0°F, Ti = 80.0°F
Qcond = - ?A dT/dx
For the wall, approximate: dT/dx = T1-T0/?x = 840.3 °F/ft
Qcond/A = -(105 Btu/hr-ft-°F) (840.3 °F/ft) = -88,200 Btu/hr-ft2
b)
c)
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