(Mass transfer). Consider steady-state slug flow (i.e., flow with uniform velocity equal to U) of an incompressible and constant-property fluid in a flat channel, shown in Figure P 4.36. The system is...

(Mass transfer). Consider steady-state slug flow (i.e., flow with uniform velocity equal to U) of an incompressible and constant-property fluid in a flat channel, shown in Figure P 4.36. The system is isothermal. Assume that the walls of the channel contain a slightly soluble substance, so that downstream from location x = 0, a species designated by subscript 1 diffuses into the fluid. The boundary condition downstream the location where x = 0 is thus UWM (i.e., m₁
= m_1,s
at surface for x ≥ 0), while upstream from that location, the concentration of the transferred species is uniform and equal to m1,in (m₁= m₁,in for x ≤ 0 and all y). Assume that the diffusion of the transferred species in the fluid follows Fick’s law