Thermodynamics HW Solutions 179

Thermodynamics HW Solutions 179 - Chapter 3 Steady Heat...

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Chapter 3 Steady Heat Conduction 3-38E A thin copper plate is sandwiched between two layers of epoxy boards. The effective thermal conductivity of the board along its 9 in long side and the fraction of the heat conducted through copper along that side are to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat transfer is one-dimensional since heat transfer from the side surfaces are disregarded 3 Thermal conductivities are constant. Properties The thermal conductivities are given to be k = 223 Btu/h ft °F for copper and 0.15 Btu/h ft °F for epoxy layers. Analysis We take the length in the direction of heat transfer to be L and the width of the board to be w . Then heat conduction along this two-layer plate can be expressed as (we treat the two layers of epoxy as a single layer that is twice as thick) [] L T w kt kt L T kA L T kA Q Q Q Δ + = Δ + Δ = + = epoxy copper epoxy copper epoxy copper ) ( ) ( & & & Heat conduction along an “equivalent” plate of thick ness t = t copper + t epoxy and thermal conductivity k eff can be expressed as L T w t t
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