Mathematical modeling and dimensional analysis of hot-air tray drying kinetics of Khoa

Abstract:

This study investigates the transport phenomena and drying kinetics of khoa (heat-coagulated milk solids) during hot-air tray drying to produce a shelf-stable khoa powder. Experiments were conducted at three drying temperatures (55°C, 60°C and 65°C) at a constant air velocity of 2.0 m/s with a 0.5 cm product thickness. The results indicated a non-linear decrease in moisture content over time, showing that the dehydration occurred entirely within the falling-rate period. Elevating the temperature from 55°C to 65°C significantly accelerated the moisture removal rate, reducing the total drying time from 6.0 hours to 5.0 hours, and yielding a final moisture content ranging from 4.83% to 3.17% (dry basis). To predict drying behavior, moisture ratio (MR) data were fitted to two semi-empirical models: Henderson and Pabis, and Wang and Singh. The Wang and Singh model demonstrated superior predictive accuracy, achieving the highest correlation coefficient (R²=0.998). Using Fick’s second law of diffusion, the effective moisture diffusivity (D_eff) was determined to increase with temperature, ranging from 1.11× 10^-9 m²/s at 55°C to 1.55 × 10^-9 m²/s at 65°C. Dimensional analysis validated these transport mechanisms; the mass transfer Biot numbers (Bi_m) exceeded 9.0 ×10⁶, confirming that internal moisture diffusion, rather than surface evaporation, is the process bottleneck. Furthermore, mass transfer Fourier numbers (Fo_m) surpassed the critical threshold of 0.2 within 1.0 to 1.5 hours, indicating a rapid progression of the drying front to the core of the product. These universal dimensionless parameters offer a robust foundation for scaling up and optimizing industrial khoa drying operations.