Question

If Da is diffusivity, CT is tracer concentration and UT is overall heat transfer coefficient, then the pulse tracer balance with dispersion is obtained as ____

(a) \(\frac{∂^2 C_T}{∂z^2} – \frac{∂U_T}{∂z} = \frac{∂C_T}{∂z} \)

(b) Da\(\frac{∂^2 C_T}{∂z^2} – \frac{∂U_T}{∂z} =\frac{∂C_T}{∂z} \)

(c) Da\(\frac{∂^2 C_T}{∂z^2} + \frac{∂U_T}{∂z} =\frac{∂C_T}{∂z} \)

(d) Da\(\frac{∂C_T}{∂z^2} – \frac{∂U_T}{∂z} =\frac{∂C_T}{∂z} \)

I got this question in a national level competition.

The origin of the question is Solid Catalysed Reactions in portion Solid Catalysed Reactions & Transport Processes with Reactions Catalyzed by Solids of Chemical Reaction Engineering

Answer 1

Correct choice is (a) \(\frac{∂^2 C_T}{∂z^2} – \frac{∂U_T}{∂z} = \frac{∂C_T}{∂z} \)

Explanation: The equation \(\frac{∂^2 C_T}{∂z^2} – \frac{∂U_T}{∂z} = \frac{∂C_T}{∂z} \) is obtained by a combination of mole balance on inert tracer and the molar flow rate of tracer by both convection and dispersion.