Copper is purified by a process known as electrorefining. In this process, copper mixed with impurities is oxidized at one electrode and reduced at the other. The purity can be improved from $99\%$ to $99\mathrm{.}99\%$ through this method. The concentration of CUSO$4$ is $0\mathrm{.}35$M and the supporting electrolyte is $2$M sulfuric acid. Impurities more difficult to reduce than copper will not oxidize appreciably, and therefore will not pass into the electrolyte. Therefore, if the potential difference is properly controlled, the cathode will be significantly purer than the material initially placed on the anode.

The following information is available:

$\backslash$rho e$=1106$ kgm$-3$

D$=5\mathrm{.}33$x$10-10$m$^2$s$-1$

L$=1\mathrm{.}5$m

A$\backslash$rho $=38$ kgm$-3$

v $=1\mathrm{.}31$x$10-6$m$^2$s$-1$

a$)$ Estimate the limiting current and electrode area required to produce $10$ t$/$day of copper. For a vertical electrode free of convection the following correlation is suggested:

Sh $=0\mathrm{.}31($Sc$*$Gr${)}^{0\mathrm{.}28}$

b$)$ Calculate the mass transport coefficient based on natural convection using the electrode height as the characteristic length.

c$)$ The aim is to increase the mass transport coefficient in a factor of $10$ e and increase the limiting current so

consequent. When using forced convection, what velocity of the fluid and Re required? The following correlations are suggested to calculate the coefficients using flat parallel plates. The distance between electrodes is $3$ cm$.$ Assume they are electrodes

Laminar flow: Sh $=1\mathrm{.}85($ReSc$)0\mathrm{.}333$

Turbulent flow: Sh $=0\mathrm{.}0789(\frac{0\mathrm{.}079}{R{e}^{0\mathrm{.}25}}{)}^{0\mathrm{.}5}Re*S{c}^{0\mathrm{.}25}$

Consider the hydraulic diameter as the characteristic length for these models

d$)$ For this case, air spraying with a flow of $2$L$/$min per square meter of electrode area generates a coefficient of $2$x$10^-5$ m$^2/$s$.$ Calculate the surface speed of the air.