Calculate the mass transfer coefficient and molar flux for flow of a fluid over a flat plate.

Part A$.$ Pure water at $50C$ is flowing parallel over a flat plate of solid benzoic acid that is $0\mathrm{.}25m$ long at a velocity of $0\mathrm{.}0667\frac{m}{s}.$ The benzoic acid is dissolving and diffusing into the water at steady$-$state. The density of water at $50C$ is $988\mathrm{.}07k\frac{g}{m^3},$ the viscosity is $5\mathrm{.}49{10}^{-4}Pa*s,$ and the solubility of benzoic acid in water is $0\mathrm{.}07kg-mo\frac{l}{m^3}.$ The diffusivity of benzoic acid in water at $25C$ is $1\mathrm{.}21x{10}^{-9}\frac{m^2}{s}$ and the viscosity of water at $25C$ is $8\mathrm{.}94{10}^{-4}Pa.$s$.$ Calculate the mass transfer coefficient $k_C$ and the molar flux of benzoic acid $(N_A)$

Part B$.$ Pure dry air at $70C$ is flowing parallel over a volume of liquid water with a length $0\mathrm{.}25m$ with a velocity of $1\mathrm{.}333\frac{m}{s}.$ The water, which completely wets the surface that is blotting paper, is diffusing into the air at steady state. The density of air at $70C$ is $1\mathrm{.}0376k\frac{g}{m^3},$ the viscosity is $2\mathrm{.}049{10}^{-5}Pa*s,$ and the vapor pressure of water is $0\mathrm{.}3075$atm. The diffusivity of water vapor in air at $25C$ is $2\mathrm{.}60{10}^{-5}\frac{m^2}{s}.$ The total pressure of the system can be assumed to be constant at $1$atm. Calculate the mass transfer coefficient $k_G$ and the molar flux of water $(N_A).$

Part C$.$

A sphere of naphthalene $2$ inch in diameter is placed in air at $115F$ flowing with a velocity of $1\mathrm{.}1f\frac{t}{sec}.$ The vapor pressure of solid naphthalene is $0\mathrm{.}565mmHg$ and the diffusivity of naphthalene in air and at $115F$ is $7\mathrm{.}5{10}^{-5}f\frac{t^2}{sec}.$ Determine the mass transfer coefficient $(($:$k{G}_G\}$ in lbmol$/(($:$f{t}^2-hr-$atm$\}$ and the mass transfer flux of naphthalene to air $(N_A)$ and the total mass evaporated $($WA$)$ in Ibmol$/$hr in this stagnant air at $115F$ and $1$atm.

Data:

Properties $of$ air $at1$atm and $115F$ are:

Density $()=0\mathrm{.}0692l\frac{b}{f}{t}^3$

Viscosity $()=0\mathrm{.}0469l\frac{b}{ft-hr}$

$R=0\mathrm{.}73\frac{(atm)-f{t}^3}{\text{l}\text{b}\text{m}\text{o}\text{l}-R},K_G=k\frac{c}{R}T$

$N_A=K_G(P_{A1}-P_{A2})$