A wet cylinder of agar gel at 278 K contains a uniform concentration of urea of 0.1 kg mol/m. The cylinder has a diameter of 45.76 mm and is 57.2 mm long with flat parallel ends. The diffusivity of the urea in agar is 7.27 x 10-40 m/s. The cylinder is suddenly immersed in turbulent pure water which initially contains no urea. For radial mass transfer only, listing your assumptions, calculate, (a) the concentration at a distance of 9.152 mm from the midpoint of the cylinder after 100 hours of mass transfer [5 Marks) (b) the time by which the concentration, c, at the centre of the cylinder is 5 x 104 kg mol/m. (5 Marks) Table (1) and Graph (1) are attached in the next two pages 1.0 cylinder * N=1.0 0.8 0.6 0.4 0.2 0.0 0.10 7,-T Ti - T. 0.5 Y, 1.0 0.8 0.6 0.4 0.2 0.0 0 0.010 OOOOO 1.0 0.8 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 mo 0.0010 105 0.5 1.0 1.5 2.5 3.0 3.5 2.0 at Graph 1 Unsteady-state heat conduction in a long cylinder. (From H. P. Gurney and J. Lurie, Ind. Eng. Chem., 15, 1170(1923).) Table 1 Relation Between Mass- and Heat-Transfer Parameters for Unsteady-State Diffusion Mass Transfer Heat Transfer K = c/c = 1.0 K = c/c# 1.0 C-C C-Co c./K-c C,/K - Co T; -T Y, T; - To T-T 1-Y T. -T C-Co C-Co DAB! C-CO C/K - Co DAB! 21 X X 2. Vai 2/DABI k DAB mi, hx 2/D18! DAB Kk x, Kk / h I a ke DA AB Det DABI DAB X X X, x is the distance from the center of the slab, cylinder, or sphere; for a semiinfinite slab, x is the distance from the surface.co is the original uniform concentration in the solid, C, the concentration in the fluid outside the slab, and the concentration in the solid at position x and limet