Semi-analytical method for heat and moisture transfer in packed bed of silica gel

A semi-analytical model for the heat and mass transfer of adsorption and desorption processes of the vertical solid desiccant packed bed dehumidifier is presented on the basis of quasi-steady state assumption, and is solved using close form integration with the limits equivalent to bed and time increments, and numerically by Runge-Kutta Fehlberg and forward scheme finite difference techniques. The most important parameters during the dehumidifier operation, namely, (i) exit air temperature and humidity, (ii) axial temperature distribution in the bed and (iii) water content are evaluated. Stability of the semi-analytical method is investigated and found that the main parameters affecting the model stability are the bed and time increments size. A dimensionless parameter combining time and bed increments size and air velocity named velocity ratio is defined and investigated. It is found that when the velocity ratio equals the ratio of particle diameter to bed length, the method is stable, and as the velocity ratio is made smaller beyond the stable velocity ratio, the results remain unchanged. The results of semi-analytical and numerical models agree well with the experimental results for both desorption and adsorption processes. Using the proposed semi-analytical model, the minimum and maximum relative errors for exit air temperature are 2.24% and 11.78%, respectively and for exit air humidity the minimum and maximum errors are 3.79% and 27.17% respectively.