4. (28 pts.) Consider a thin cylindrical pore of length L and radius R (R <...

  

Transcribed Image Text:

4. (28 pts.) Consider a thin cylindrical pore of length L and radius R (R < < L). The lateral surface of the pore is coated with catalyst. Reactant A first diffuses through the external boundary layer (see figure below) and then it diffuses through the pore and reacts on the lateral surface by a first-order reaction: -r = kCA [=] mole/m.s. The effective diffusion coefficient, D[=] m/s, for axial diffusion of A through the pore may be assumed to be constant. Since the pore is thin, radial diffusion effects are negligible. Mass transfer of A through the external boundary layer is described by a mass transfer coefficient, kc [=] m/s. The concentration of A in the bulk is CA... (a) (14 pts.) Write the steady-state conservation statement for the moles of A and the boundary conditions that would allow one to obtain the concentration profile of A in the pore, CA = CA(z). Suppose that there are temperature variations in the pore due to the enthalpy of reaction, AHrxn which may assumed to be constant. The thermal conductivity, Ke [=] W/mK, associated with axial heat conduction through the pore may also assumed to be constant. Heat conduction in the radial direction is negligible because the pore is thin. The temperature in the bulk is T... Heat transfer through the external boundary layer is described by a heat transfer coefficient, h [=] W/mK. (b) (14 pts.) CA Too Write the steady-state energy conservation statement and the boundary conditions that would allow one to obtain the variation of temperature in the pore, T = T(z). -Boundary Layer (kc, h) Z CA(z) T(z) -L- 212 2R 4. (28 pts.) Consider a thin cylindrical pore of length L and radius R (R < < L). The lateral surface of the pore is coated with catalyst. Reactant A first diffuses through the external boundary layer (see figure below) and then it diffuses through the pore and reacts on the lateral surface by a first-order reaction: -r = kCA [=] mole/m.s. The effective diffusion coefficient, D[=] m/s, for axial diffusion of A through the pore may be assumed to be constant. Since the pore is thin, radial diffusion effects are negligible. Mass transfer of A through the external boundary layer is described by a mass transfer coefficient, kc [=] m/s. The concentration of A in the bulk is CA... (a) (14 pts.) Write the steady-state conservation statement for the moles of A and the boundary conditions that would allow one to obtain the concentration profile of A in the pore, CA = CA(z). Suppose that there are temperature variations in the pore due to the enthalpy of reaction, AHrxn which may assumed to be constant. The thermal conductivity, Ke [=] W/mK, associated with axial heat conduction through the pore may also assumed to be constant. Heat conduction in the radial direction is negligible because the pore is thin. The temperature in the bulk is T... Heat transfer through the external boundary layer is described by a heat transfer coefficient, h [=] W/mK. (b) (14 pts.) CA Too Write the steady-state energy conservation statement and the boundary conditions that would allow one to obtain the variation of temperature in the pore, T = T(z). -Boundary Layer (kc, h) Z CA(z) T(z) -L- 212 2R