Optimization Method for the Evaluation of Convective Heat and Mass Transfer Effective Coefficients and Energy Sources in Drying Processes

A new optimization method for the assessment of the coefficients existing in a model of drying kinetics is developed and presented in this article. This method consists of matching the drying kinetics resulting from the mathematical model with the drying kinetics resulting from the experiments. Both the heat and mass transfer coefficients, the critical relative humidity, and the additional ultrasound energy (heat) source are included in the optimization procedure. The Adams–Bashforth multistep method of solving nonlinear ordinary differential equations is used. The inverse problem of model parameter estimation is solved by the Rosenbrock optimization method. The methodology is illustrated by the example of the ultrasound-assisted convective drying of apple and carrot. A high level of agreement between the results obtained experimentally and numerically was found. The obtained results confirmed the great influence of ultrasound on the drying kinetics. It was found that ultrasound application improved the mass transfer by 20–80% and heat transfer by 30–90%. It was also found that the heating effect caused by the ultrasound’s absorption was very small, with a value below 1%.