A scientist performs mass transfer experiments by coating a structure of complex geometry $($with total surface area As and the characteristic length L$)$ with a thin layer of oily chemical coated on the surface. This structure is equipped with embedded heaters that maintain the surface temperature above the freestream temperature. Air flows over the structure and the oily chemical vaporizes through convective mass transfer. After analysis of experimental data, the scientist proposes a correlation for average Nusselt number as NuL$=0\mathrm{.}5$ReL$^0\mathrm{.}5*$Pr$^0\mathrm{.}3$

$(1)$ Write an expression for the average mass transfer coefficient $($m$,$L$),$ inspired by the Nusselt number correlation, in terms of the velocity U$\backslash$infty and some or all of the known fluid and geometrical parameters: L$,$ As$,\backslash$rho $,$ k$,$ Cp$,$ Pr$,$ Sc$,$ Dab, $\backslash$mu $,$ v$.$

$(2)[$Each answer must be correct with valid justification for credit for that sub$-$question$]$ In this scenario, the three boundary layers $($hydrodynamic$,$ thermal, and concentration$)$ grow simultaneously. If Pr $=0\mathrm{.}7$ and Sc $=7\mathrm{.}0,$ which boundary layer is the thickest for each flow regime? Provide brief justifications $($with equations and$/$or text$).($Mark an $$x$$next to the correct answer$)$