Mass Transfer Coefficients in Laminar Flow Extraction from the PDE Model

2 Mass Transfer Coefficients in Laminar Flow Extraction from the PDE Model 

Mass transport in laminar flow in a tubular geometry or around simple submerged shapes is generally modeled by PDEs because Ihere is more than 

Let us demonstrate its derivation using transport in a tube as an example. The situation here is one in which solute diffuses in the radial direction, either as a result of release from the wall, or in consequence of transporf to and ultimately through a permeable wall. The model for this case has been presented in Section 2.8 and there referred to as the Graetz problem in mass transfer. 

The concentration profiles that arise in this case are distributed in both the radial and axial directions, as diffusion in one direction is superposed on convective transport in the other direction. To obtain a mass transfer coefficient from this information, we perform a mass balance at the tubular wall, equating diffusional transport rate to an equivalent convective rate expressed by means of a mass transfer coefficient. Thus, 

To evaluate k, two quantities need to be obtained from the primary concentration profile. One is tiie derivative at the tubular wall given above, which is obtained by differentiating the solution C r,z) the second is the mean integral concentration C in the flowing fluid. This latter quantity is obtained from fhe expression 

---