Question

Air flowing through a tube of 75-mm diameter passes over a 150-mm-long roughened section that is constructed from naphthalene having the properties M=128.16kg/kmol\mathcal{M}=128.16 \mathrm{kg} / \mathrm{kmol} and psat (300K)=1.31×104p_{\text {sat }}(300 \mathrm{K})=1.31 \times 10^{-4} bar. The air is at 1 atm and 300 K, and the Reynolds number is ReD=35,000R e_{D}=35,000. In an experiment for which flow was maintained for 3 h, mass loss due to sublimation from the roughened surface was determined to be 0.01 kg. What is the associated convection mass transfer coefficient? What would be the corresponding convection heat transfer coefficient? Contrast these results with those predicted by conventional smooth tube correlations.

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Air properties at the temperature T=300T=300K are taken from Table A.4:

*  Prandtl number, $Pr=0.707$
*  Density, $\rho=1.1614 \frac{\mathrm{kg}}{\mathrm{m^3}}$
*  Specific heat, $c_p=1007 \frac{\text{J}}{\text{kgK}}$
*  Kinematic viscosity, $\nu=15.89 \cdot 10^{-6} \frac{\text{Ns}}{\mathrm{m^2}}$
*  Thermal conductivity, $k=0.0263 \frac{\mathrm{W}}{\mathrm{mK}}$

From Table A.8 for Naphthalene-air mixture at 300300K,11 atm:

DAB=0.62105m2sSc=νBDAB=2.563\begin{align*} D_{AB}&=0.62 \cdot 10^{-5} \frac{\mathrm{m^2}}{\mathrm{s}}\\ Sc &=\frac{\nu_B}{D_{AB}}=2.563 \end{align*}

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