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 (C_A,out) from the tube. The model should contain the following process variables: gas-phase inlet concentration of A, C_A,in; gas-phase outlet concentration of A, C_A,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, k_c, at an inlet He volumetric flow rate of 110 cm³/s?

c. What is the outlet mole fraction of POCl₃ vapor (y_A,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 y_A,out? 

e. What is the maximum possible outlet mole fraction of POCl₃ vapor for an infinitely long tube?

Transcribed Image Text:

Porous ceramic tube innerd = 2.0 cm L = 60 cm Heated liquid POCI3 reservoir 50 C He + POCI, vapor (CA,Out) ↑ Helium (He) inlet gas 50 C, 1.0 atm v₂ = 110 cm³/sec Makeup liquid POCIĄ