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Two plates ofthe same area and the same ...

Two plates ofthe same area and the same thickness having thermal conductivities `k_(1)` and `k_(2)` are placed one on top of the other. Show that the thermal conductivity of the composite plate for conduction of heat is given by
`k=(2k_(1)k_(2))/((k_(1)+k_(2))`

Text Solution

Verified by Experts

Total heat flow through plates is given as
`(dQ)/(dt)=(T_(1)-T_(2))/((l)/(k_(1)).(x)/(A)+(1)/(k_(2)).(x)/(A))`
`(k_(1)k_(2))/(k_(1)+k_(2)).(A)/(x)(T_(1)-T_(2))`
Above expression can be written as
`(dQ)/(dt)=(2k_(1)k_(2))/(k_(1)+k_(2)).(A)/(2x)(T_(1)-T_(2))`
`implies (dQ)/(dt)=(k_(eq)A)/(2x)(T_(1)-T_(2))`
`implies k_(eq)= (2k_(1)k_(2))/(k_(1)+k_(2))`
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