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HW1 Solutions

# HW1 Solutions - Problem 2 The thermal conductivity of a...

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ME 364 HW 1 Solutions Problem 1: The range of U-factors for windows are given. The range for the rate of heat loss through the window of a house is to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat losses associated with the infiltration of air through the cracks/openings are not considered. Analysis The rate of heat transfer through the window can be determined from ) ( window overall window o i T T A U Q where T i and T o are the indoor and outdoor air temperatures, respectively, U overall is the U-factor (the overall heat transfer coefficient) of the window, and A window is the window area. Substituting, Maximum heat loss: W 378 C )] 8 ( 20 )[ m 8 . 1 C)(1.2 W/m 25 . 6 ( 2 2 max window, Q Minimum heat loss: W 76 C )] 8 ( 20 )[ m 8 . 1 C)(1.2 W/m 25 . 1 ( 2 2 min window, Q Discussion Note that the rate of heat loss through windows of identical size may differ by a factor of 5, depending on how the windows are constructed.
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Unformatted text preview: Problem 2: The thermal conductivity of a material is to be determined by ensuring one-dimensional heat conduction, and by measuring temperatures when steady operating conditions are reached. Assumptions 1 Steady operating conditions exist since the temperature readings do not change with time. 2 Heat losses through the lateral surfaces of the apparatus are negligible since those surfaces are well-insulated, and thus the entire heat generated by the heater is conducted through the samples. 3 The apparatus possesses thermal symmetry. Analysis For each sample we have C 8 74 82 m 01 . m) 1 . m)( 1 . ( W 5 . 12 2 / 25 2 T A Q Then the thermal conductivity of the material becomes C W/m. 0.781 ) C 8 )( m 01 . ( m) W)(0.005 5 . 12 ( 2 T A L Q k L T kA Q Q Window 20 C -8 C Q Q L L A...
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