Heat and mass transfer heterogeneous model applied for mathematical representation of Aloe vera extracts spray drying

Abstract

Punctual heterogeneous and homogeneous state-space dynamic models for mathematical representation of Aloe vera extracts spray drying were proposed. Punctual heterogeneous model considers 2 partial derivatives di ff erential equations (PDDE) for particles in terms of Fourier’s and Fick’s laws, 2 ordinary di ff erential equations (ODE) for drying air and 3 thermodynamic relations at interface. Homogeneous model considers 4 ODE for air and particles with the same 3 thermodynamic relations at interface. Punctual heterogeneous model was theoretically validated with divergence theorem. On the other way, fresh and concentrated Aloe vera extracts, obtained from plant expression (with 0.43% and 3.93% of total solids), were experimentally spray dried with 180-170 ºC, 100-80 ºC air input-output temperatures. Heterogeneous model solution produced a periodic chaotic dynamic behavior around homogeneous model results which moisture profile within 6.7-7.1 × 10 − 5 m diameter particles. Simulated outlet particle moistures reproduced moderately the experimental ones