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MIT4_42JF10_assn06 (1)

# MIT4_42JF10_assn06 (1) - Fall10 1.044J 2.45J 4.42J Homework...

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Fall’10 1.044J, 2.45J, 4.42J Homework Set #6 1 1. A low density fiberglass insulation has an R value of 11 (BTU/hr ft 2 o F) -1 when used in a standard 2x4 wall cavity. To achieve a higher insulation, a contractor compresses the fiberglass so that there are two layers of the insulation in the 2 x 4 wall cavity. He states that the wall has an R value of 22. Do you agree? Explain. 2. A flat roof insulation system uses aluminum screws to hold down flat insulation panels. The screws are 1/4 inch diameter, 2 inches long and spaced 4 inches on center in a square array. The top of the insulation uses a thin aluminum sheet as a weather barrier and a reflective layer. Underneath the insulation is a corrugated steel roof. The insulation is two inches thick and has a conductivity of 0.015 BTU/hr ft o F. The screws pass through the insulation and are anchored in the corrugated roof. The effective U value of the insulation system plus screws is defined as U=q(total)/A(total)ΔT where q(total) is the sum of the heat transfer through the aluminum screws and the insulation. Assume that the convective heat transfer coefficient on the inside of the corrugated surface and on the outside over the top of the thin aluminum sheet is 2BTU/hr ft 2 o F. Calculate the U value for two limiting cases: 1) There is large lateral heat transfer and the corrugated sheet and the thin aluminum are each at a uniform temperature and ; 2) there is no lateral heat transfer through the corrugated sheet and the aluminum panel, heat transfer through the screws and the insulation occur in parallel with no interaction between the heat flows in the respective cross-sections. 3. A window has two vertical panes of glass separated by an one inch air gap. The glass panes can be considered black bodies at uniform temperatures of 40 o F and 60 o F, respectively. Estimate the total heat transfer, convection plus radiation, through the window space. Note:

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