# HW4_sol - T in to the ambient air at T out is The area of...

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Thermal & Fluids Engineering I. Spring 2006. Homework #4 Solution. WebCT post date: 02/13/2006 3-44 The roof of a house is partially covered with snow. The roof is made from plywood covered with shingles ( k sh = 0.4 Btu/h·ft· o F). In the attic space, the heat transfer coefficient between the air and the plywood is 3.1 Btu/h·ft 2 · o F. The heat transfer coefficient over the snow and the exposed shingles on the outside of the roof is 7.6 Btu/h·ft 2 · o F. Assume the snow has a density of 12 lbm/ft 3 and it covers 64% of the roof area. Calculate the thermal resistance from the attic air to the outside air for the 30-ft by 60-ft roof panel shown below. Approach: Use the thermal resistance analogy, adding resistances in parallel and series as necessary. Assumptions: 1. The roof is very large so edge effects may be neglected. 2. The plywood and shingles are isothermal. 3. The heat transfer coefficient is uniform and independent of temperature. 4. Thermal conductivity is constant. Solution: A thermal resistance model for transport from the attic air at

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Unformatted text preview: T in to the ambient air at T out is: The area of the roof panel is ( )( ) 2 30ft 60ft 1800ft A = = With properties from Tables B-4 and B-5, the resistances are ( ) ( )( ) ( ) ( ) 4 o o 2 1 1 1.79 10 h F Btu 3.1Btu h ft F 1800ft o R hA-= = = × ⋅ ⋅ ⋅ Thermal & Fluids Engineering I. Spring 2006. Homework #4 Solution. Page 2 ( ) ( )( ) ( ) 4 o 1 2 0.75 ft 12 4.96 10 h F Btu 0.07Btu h ft R 1800ft L R kA- = = = × ⋅ ⋅ ⋅ ( )( ) ( ) 5 o 2 0.5 12 5.79 10 h F Btu 0.4 1800 L R kA- = = = × ⋅ ( )( )( ) ( )( )( ) ( )( )( ) 4 o 3 4 o 4 4 o 5 3 12 48.2 10 h F Btu 0.045 1800 0.64 1 1 1.14 10 h F Btu 7.6 1800 0.64 1 1 2.03 10 h F Btu 7.6 1800 0.36 L R kA R hA R hA--- = = = × ⋅ = = = × ⋅ = = = × ⋅ Adding resistances in series and parallel gives ( ) 5 3 4 4 o 1 2 5 3 4 9.28 10 h F Btu tot o R R R R R R R R R R-+ = + + + = × ⋅ + + Answer...
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HW4_sol - T in to the ambient air at T out is The area of...

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