The convective mass-transfer device shown in the figure (right column) is used to generate a gas stream
Question:
The convective mass-transfer device shown in the figure (right column) is used to generate a gas stream containing a mixture of phosphorous oxychloride (POCl3) vapor diluted in inert helium (He) gas. This gas mixture is sent to a diffusion furnace to serve as the primary dopant for the manufacture of silicon-based solar cells. In the present process, pure (100%) He gas at a volumetric flow rate of 110 cm3/s enters the 2.0-cm inner diameter tube at 50 C and 1.0 atm. The length of the tube is 60 cm. Liquid POCl3 enters a reservoir that surrounds the porous ceramic tube. The liquid POCl3 enters into the porous ceramic like a wick. At the inner surface of the tube, the POCl3 liquid vaporizes, with its vapor pressure determined by the process temperature. The process is maintained at a constant temperature of 50 C by a controlled heater surrounding the POCl3 reservoir. Therefore, the transfer of POCl3 to the gas stream is limited by diffusion across the convective boundary layer on the inside of the tube. The process can be considered dilute. The diffusion coefficient of POCl3 vapor (A) inHe gas (B) is 0.37 cm2/s at 1.0 atm and 50 C. The vapor pressure of POCl3 is PA 0.15 atm at 50 C. The kinematic viscosity of He gas at 1.0 atm and 50 C is 1.4 cm2/s.
a. Propose a model in final algebraic form to predict the outlet concentration of POCl3 vapor (CA,out) from the tube. The model should contain the following process variables: gas-phase inlet concentration of A, CA,in; gas-phase outlet concentration of A, CA,out; kc, tube mass-transfer coefficient; L tube length; D, tube inner diameter; ν∞, gas velocity; C*A, equilibrium vapor concentration in the gas stream.
b. What is the convective mass-transfer coefficient, kc, at an inlet He volumetric flow rate of 110 cm3/s?
c. What is the outlet mole fraction of POCl3 vapor (yA,out) at an inlet He volumetric flow rate of 110 cm3/s?
d. If the inlet volumetric flow rate remains fixed at 110 cm3/s, but the diameter d is doubled, what is the new kc and yA,out?
e. What is the maximum possible outlet mole fraction of POCl3 vapor for an infinitely long tube?
Step by Step Answer:
To address your questions lets start by formulating a model for the outlet concentration of POCl 3 vapor ...View the full answer
Fundamentals Of Momentum Heat And Mass Transfer
ISBN: 9781119723547
7th Edition
Authors: James Welty, Gregory L. Rorrer, David G. Foster
