Problem 2: Liquid with zero initial solute concentration enters a long cylindrical tube of radius a, along which a single species solute is supplied at a constant flux jwz(molm2sec1). It is assumed that the velocity profile is fully developed at the entrance of the tube, and we are interested in determining the behavior of the concentration profile from the axial position at which the concentration boundary layer becomes fully developed. (a) Taking the origin of the axial coordinate x to be at the position where the concentration profile becomes fully developed, find an expression for the concentration c in terms of x,r,jw,a,u and D, where r is the radial coordinate measured from the tube center, D is the diffusion coefficient and u is the mean fluid velocity. The velocity profile is given by: u=2u(1a2r2). (b) Determine the Nusselt number for mass transfer, often called Sherwood number defined by: NuD=D(cwcm)2ajw where cw is the concentration at the wall and cm is the mixing cup or bulk average concentration at any cross section defined by: cm=a2u10auc2rdr