Mass transfer equation error function

Ind. Eng. Chem. Res. 41,4911 (2002)] developed two correlations for reconciling the gas-liquid mass-transfer coefficient and interfacial area in randomly packed towers. The correlation for the interfacial area was a function of five dimensionless groups, and yielded a relative error of 22.5 percent for 325 data points. That equation, when combined with a correlation for Nsh as a function of four dimensionless groups, achieved a relative error of 24.4 percent, for 3455 data points for the product k cfl. 

The right side of Equation 2.25 contains known data when the weight of the wet material is measured as a function of time and when we have already determined, according to the previons section, the mass transfer coefficient K from data obtained in the constant rate drying period. The first eigen-valne can be determined numerically (by trial aud error or by iteratiou) from the transcendental equation. (The value of the V ranges between 0 and m. Ref. [2].) The mass diffnsivity coefficient can be calculated directly from Equation 2.22 if t-i is known. When the moisture capacity coefficient is determined separately [2,19], then the moisture conductivity coefficient can also be determined from Equation 2.23. 

For most chemical and biological processes first principles engineering methods can be applied to formulate balance equations that essentially provide the skeleton of an ordinary differential equation (ODE) model for such a process. What often remains to be determined, however, are functional relations in the constitutive equations for phenomena such as reaction rates and heat and mass transfer rates. These phenomena models are often difficult to determine due to the fact that finding a parametric expression with an appropriate structure to match the available experimental data is essentially a trial-and-error procedure with limited guidance and therefore potentially time-consuming. 

Having obtained (rc/R) at given 0 by trial and error from equation (7.68), (q/qo) may be obtained from equation (7.67b) and (Ct/C ) from equation (7.67). Hence (Ct/C ) may be obtained as a function of time. The only parameters required to fit data to the model are the effective diffusion coefficient De, and the film mass transfer coefficient k. The latter quantity can be estimated using equation (7.40). 

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