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The quantities φ in equation (44) represents the phase potentials and χ is the depth scalar. The nomenclature section of this report defines all other symbols. This formulation accounts for the evolution of internal pressure through the air balance (equation (43)) and is thus able to deal with high temperature convective drying, vacuum drying and dielectric drying. 3.5.4 Closure conditions Wood is a highly hygroscopic porous medium; therefore, we must separate bound water from (45) ε g = φ (1 − Sw ) , ε w + ε g = φ , where φ is the porosity. We define the intrinsic phase air density as ρ a = ε g ρ a and the gaseous phase is a binary mixture of air and vapour, which we assume to behave like an ideal gas. The saturation variable involved in the relative permeability functions is calculated according to the free water content only: free water as defined by: X=Xw+Xb ≡εwρw +min(Xfsp,X). ρo The volume fractions of the liquid and gaseous phases are defined as: εw =φSw , Sw=XXw . w max (46) As both liquid and gaseous water phases are present during drying of wood, and because of the curvature of the interface that exists between the liquid and gas phases within the pores of the medium, the liquid pressure is less than the gas pressure. The capillary pressure represents the difference: P=P−P. wgc (47) The values for fibre saturation point (Xfsp) are essential wood properties for the development of an accurate wood drying model and were therefore, measured as part of this study. The methodology for which is detailed in section 3.4 Drying modelling - Measurement of essential wood properties. 3.5.5 Boundary Conditions The boundary conditions for the external drying surfaces are assumed to be of the following form (Turner and Perré, 2004): (48) (49) (50) 39 Evaluation of super–heated steam vacuum drying viability and development of a predictive drying model for Australian hardwood species – Final report 1−x Jw +⋅nˆ=kmcMvln v∞ x=0 1−xv |x=0+ + ⋅nˆ=q(T−T∞)+hvkmcMvln v∞ 1−x x=0 1−xv |x=0+ Je P|=P, gx=0+ ∞PDF Image | Evaluation of super-heated steam vacuum drying
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