A very thin polymeric coating of thickness 0.1 mm uniformly coats a rectangular
ID: 701675 • Letter: A
Question
A very thin polymeric coating of thickness 0.1 mm uniformly coats a rectangular surface. The rectangular surface has a length of 20 cm and a width of 10 cm. The coating contains a solvent that must be evaporated away from the coating in order to cure the coating. Initially, there is 0.001 mole of solvent for cm3 of coating loaded in the coating. A heated plate just beneath the surface maintains the coating at a uniform temperature of 40 C, and the vapor pressure exerted by the solvent is 0.05 atm at 40 C. Air gently flows parallel to the surface at a velocity of 5.0 cm/s. The surrounding air at 1.0 atm total system pressure and 20 C. The surrounding air acts as an infinite sink, so there is no solvent in the surrounding air. You may neglect any molecular diffusion of the solvent through the very thin polymeric film and focus only on the convection aspects of the problem. The diffusion coefficient of the solvent in air at 20 C is 0.1 cm2/s. The density of the air is 1.1769 kg/m3 and the kinematic viscosity (v) of the air is 157 x 10m2/s, both at 30 C, the average temperature of the system 4. Determine the Reynolds number associated with this process Determine the Schmidt number associated with this process at the average temperature of the system Determine the Sherwood number associated with this process What is the film mass transfer coefficient, ky (mole fraction based on driving force) associated with this process? How long will it take for the solvent to completely evaporate from the coating? a. b. c. d. e.Explanation / Answer
(a) Reynolds number Re = DV/ is a dimensioneless number.
Re=Inertial force/viscous force
Re= DV/kinematic viscosity
Re = (Characterestic length*velocity of medium)/ kinematic viscosity
Re = (5 cm/s *20 cm) / (0.157 cm2/sec) = 637.
(b) Schimidth Number (Sc) is a dimensionless number which is defined as the ratio of momentum diffusivity to mass diffusivity.
It is widely used in characterizing the fluid flows in which simultaneouus mass and momentum transfer is occuring.
Sc =/DAB = kinematic viscosity /DAB
Sc = (Kinemmatic viscosity/diffusivity) = (0.157 cm2/sec)/(0.1 cm2/sec) =1.57
(c) Sherwood Number (Sh) (also called the Nusselt number of mass transfer) is also a dimensionless number which is defiend as the ratio of convective mass transport to diffusive mass tranport.
Sh = KL/D,
or
Sh = 0.67 Re0.5Sc0.33
Sh = 0.664 (637)0.5(1.57)0.33 = 19.6
(d) Sh = Kc/LDAB
19.6 = Kc/LDAB
Kc= 19.6*0.1/20 = 0.098.
Ky= Kc(M.W/RT) . pAB
=0.098(29/8.314*298)*5066.25 = 5.811
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