Numerical analysis of heat and mass transfer during freeze-drying

The transient-state external heat and mass-transfer during freeze-drying was investigated. The spaces between the heaters and porous product-surfaces were simulated as semi porous channels, with mass-injection into the channels from the sublimation of ice. The energy, vorticity, concentration, and stream function/vorticity equations were the governing equations used as the mathematical model. These partial differential-equations were solved by finite-difference, numberical methods. The Fromm, Alternating Direction Implicity, and Upwind Difference methods were used in solving the parabolic equations; and the Successive Over Relaxation method was adopted to solve the elliptic equation. Numerical solutions obtained from the digital computer for the external heat and mass-transfer during freeze-drying were computed for Reynolds numbers equal t0 0.1, 1.0, and 4.0 and Grashof numbers equal to 0, +/- 100, and +/- 1000. The Prandtl number selected for water vapor was 1.0. One set of these solutions were compared to a known, analytical solution, and good agreement was obtained. The external heat and mass-transfer mechanism was then combined with the internal-heat-transfer mechanism developed by Dyer and Sunderland (1968), and the equations describing the relation of heater temperatures and product surface-temperatures developed by Massey and Sunderland (1972). A thorough computer-simulation was carried out for the combined heat and mass-transfer mechanism during freeze-drying of food products.