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= 2. (Total 35 points) Assume a stream of carbon dioxide at a free-stream velocity of U. (m/s) at 1 atm and 100C blows across a 1-mm diameter naphthalene (CH3) sphere that is rotating along its axis with the speed of n rpm. The vapor pressure of naphthalene at the surface temperature is 10 mmHg. Its diffusivity in carbon dioxide at 1 atm and 0C is 5.15x10-6 m/s. Mco2 = 1.75*104 poise at 1 atm and 100C. Density of solid naphthalene at 100C is 962.5 kg/m. If U.=10 m/s and n= 20 rpm, calculate the following: a) The initial sublimation rate of rotating naphthalene into the stream of pure carbon dioxide with the approaching velocity of U.. in terms of kilograms of naphthalene sublimed per hour. (15 points) b) The initial sublimation rate of stationary naphthalene in stagnant carbon dioxide under the same temperature and pressure condition. (5 points) c) Compare the results of parts (a) and (b) and comment on it. (3 points) d) Calculate the required time for the naphthalene to completely sublime for the cases of stationary naphthalene in stagnant carbon dioxide. (5 points) e) Develop an expression by which one can integrate to find the required time for the naphthalene to completely sublime in the case of rotating naphthalene sphere into a stream of pure carbon dioxide with approaching velocity of U.. Why is the integration not possible in this case? Which one is faster? (7 points) a For a rotating sphere in a fluid with approaching velocity of U., the mass transfer coefficient is found using the following equation: Although always the characteristic dimension for sphere is its diameter, exceptionally, for this specific equation, the characteristic dimension is the radius of the sphere (R) for Re and Sh definitions applicable to this equation only, w is the angular velocity in terms of radian per second, U, is the approaching velocity, and Re, is the stream Reynolds number (PU,R/u)