Question $7[13$ Points$]$: The Sherwood number $($Sh$)$ is a dimensionless number used in mass$-$transfer operation, representing the ratio of the convective mass transfer to the rate of diffusive mass transport. Use your knowledge of dimensions to determine the proper form of the Sherwood number.

a$)Sh=\frac{h}{DL}$

b$)Sh=\frac{hL}{D}$

c$)Sh=\sqrt[\phantom{2}]{\frac{h{L}^{0\mathrm{.}5}}{D}}$

d$)Sh=\frac{h^{2}L}{D^{0\mathrm{.}5}}$

where $L$ is a characteristic length $(m),D$ is the mass diffusivity $(m^2{s}^{-1}),$ and $h$ is the convective mass transfer film coefficient $(m{s}^{-1}).$