Question $4$

$($Please show every step in the process of calcualtions with explanations and assumptions$)$

a$)$ A hollow cylinder of naphthalene inner diameter and $0\mathrm{.}6m$

long$)$ has a stream of carbon dioxide flowing inside at an average

velocity $6m{s}^{-1}.$ The vapour pressure of naphthalene at the operating

temperature of $373K$ is $10mmHg$ and the diffusivity of naphthalene in

carbon dioxide is $0\mathrm{.}083c{m}^2{s}^{-1}.$ Density and viscosity of carbon dioxide

are $0\mathrm{.}946kg{m}^{-3}$ and $0\mathrm{.}021$mPa s respectively. The friction factor may

be considered equal to $0\mathrm{.}046R{e}^{-0\mathrm{.}2}.$ The system pressure is $101\mathrm{.}3$kPa

$($which is $760mmHg).$ Explain the applicability of analogy theory to this

situation. Calculate the rate of naphthalene sublimation. The universal

gas constant is $8\mathrm{.}314Jmo{l}^{-1}{K}^{-1}.$

b$)$ A tube of $100mm$ diameter has its outer surface $($grey$,$ emissivity $0\mathrm{.}8)$

maintained at $393K$ by an inner steam flow. It is surrounded by a thin

cylinder $($grey$,$ emissivity $0\mathrm{.}1),$ whose inner diameter is $120mm$ and

inner surface temperature is $308K.$ What is the net radiant heat transfer

from the tube per unit length? If the cylinder was removed, the tube

would be in surroundings $($black$)$ at $293K.$ Calculate the net radiant

heat transfer rate per unit length for the uncovered tube and discuss the

effect of the cylinder on the radiant heat transfer.

The general interchange factor for grey$-$body radiation is:

$F_{12}=\frac{1}{(\frac{1}{{}_1}-1)+\frac{A_1}{A_2}(\frac{1}{{}_2}-1)+\frac{1}{\frac{?}{\text{b}\text{a}\text{r}}(F_{12})}}$

The Stefan$-$Boltzmann constant is $5\mathrm{.}67{10}^{-8}W{m}^{-2}{K}^{-4}.$

$($There is a bar on top of the F$12$ in the equation. P$.$s check the imagine for the correct formula.$)$