Chapter 3 Steady Heat Conduction3-38EA 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. Assumptions1Steady operating conditions exist. 2 Heat transfer is one-dimensional since heat transfer from the side surfaces are disregarded 3 Thermal conductivities are constant. PropertiesThe 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) LTwktktLTkALTkAQQQΔ+=⎟⎠⎞⎜⎝⎛Δ+⎟⎠⎞⎜⎝⎛Δ=+=epoxycopperepoxycopperepoxycopper)()(&&&Heat conduction along an “equivalent” plate of thick ness t = tcopper+ tepoxyand thermal conductivity keffcan be expressed as LTwtt
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