Film theory with variable transport properties.

$($a$)$ Show that for systems in which the transport properties are functions of y$,$ Eqs. $19\mathrm{.}4-12$

and $13$ may be integrated to give for y a $6,$ or y $56,$ respectively,

$($b$)$ Make the corresponding changes in Eqs., $19\mathrm{.}4-16$ and $17$ as well as in Eqs. $22\mathrm{.}8-5$ and $6.$

Then verify that Eqs. $22\mathrm{.}8-7$ and $8$ remain valid. Thus it is not necessary to work with the inte grals in calculating transfer rates if hloc and kX$,,,,$ can be predicted.

$($c$)$ Show that h$,,,$ and kx$,$loc have to be evaluated in terms of the physical properties and flow

regime $($laminar or turbulent$)$ that prevail at the conditions for which hi$,,$ and k&$,$ are desired