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Transport Phenomena

Problem 2.253

The space between two large parallel plates separated by a distance \(l=5.0 \mathrm{~mm}\) is filled with helium under a pressure \(p\) \(=1.0 \mathrm{~Pa} .\) One plate is kept at a temperature \(t_{1}=17^{\circ} \mathrm{C}\) and the other, at a temperature \(t_{2}=37^{\circ} \mathrm{C} .\) 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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