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A black plane surface at a constant high temperature T_h, is parallel to another black plane surface at constant lower temperature T_l. Between the plates is vacuum. In order to reduce the heat flow due to radiation, a heat shield consisting of two thin black plates, thermally isolated from each other, it placed between the warm and the cold surfaces and parallel to these. After some time stationary conditions are obtained. By what factor neta is the stationary heat flow reduced due to the presence of the heat shield? Neglect end effects due to the finite size of the surfaces. |
Answer» Solution :`(DH)/(dt)=A sigma(Th^(4)-T_(L)^(4))`  `(dh)/(dt)=A sigma(T_(H)^(4)-T_(1)^(4))=A sigma(T_(1)^(4)-T_(2)^(4))` `=Asigma(T_(2)^(4)-T_(l)^(4))` `T_(h)^(4)-T_(1)^(4)=T_(1)^(4)-T_(2)^(4)=T_(2)^(4)-T_(1)^(4)=C` `T_(2)^(4)=C+T_(l)^(4)` `T_(l)^(4)=T_(2)^(4)+C=2C+T_(l)^(4)` `T_(h)^(4)-(2C+T_(l)^(4))=C` `T_(h)^(4)-T_(l)^(4)=3C ` `(dH')/(dt)=A sigmaC=(dH)/(3dt)` |
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