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Transport Phenomena

Problem 2.253

The space between two large parallel plates separated by a distance l=5.0 mml=5.0 \mathrm{~mm} is filled with helium under a pressure pp =1.0 Pa.=1.0 \mathrm{~Pa} . One plate is kept at a temperature t1=17∘Ct_{1}=17^{\circ} \mathrm{C} and the other, at a temperature t2=37∘C.t_{2}=37^{\circ} \mathrm{C} . Find the mean free path of helium atoms and the heat flow density.

Reveal Answer
2.253.λ=23 mm>l, consequently, the gas is ultra-thin; q=p⟨v⟩(t2−t1)/6T(γ−1)=22 W/m2, where ⟨v⟩==8RT/πM,T=1/2(T1+T2)\begin{aligned} &2.253 . \lambda=23 \mathrm{~mm}>l, \text { consequently, the gas is ultra-thin; }\\ &q=p\langle v\rangle\left(t_{2}-t_{1}\right) / 6 T(\gamma-1)=22 \quad \mathrm{~W} / \mathrm{m}^{2}, \text { where }\langle v\rangle=\\ &=\sqrt{8 R T / \pi M}, T=1 / 2\left(T_{1}+T_{2}\right) \end{aligned}
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