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In the modelling of heat, mass and momentum transfer phenomena which occur in a capillary porous medium during drying, the liquid and gas flows are usually described by the generalised Darcy laws. Nevertheless, the question of how to determine experimentally the relative permeability relations remains unanswered for most materials that consist of water and humid air, and as a result, arbitrary functions are used in the drying codes. In this paper, the emphasis is on deducing from both numerical and experimental studies a method for estimating pertinent relations for these key parameters. In the first part, the sensitivity of liquid velocity and, consequently, of drying kinetics in the variation of the relative permeabilities is investigated numerically by testing various forms. It is concluded that in order to predict a realistic liquid velocity behaviour, relative permeabiIities can be linked to a measurable quantity: the capillary pressure. An estimation technique, based on simulations coupled with experimental measurements of capillary pressure, together with moisture content kinetics obtained for low or middle temperature convective drying, is deduced. In the second part, the proposed methodology is applied to pine wood. It is shown that the obtained relations provide closer representation of physical reality than those commonly used. Nomenclature AV (AV)j aw By C Cp D D.C.Fm g ha hb hb averaging volume j phase volume within the averaging volume AV water activity resistance factor in the effective diffusitivity coefficient of vapour in the medium mass fraction of the vapour in the gaseous phase constant pressure heat capacity [J kg -1 K-1] diffusivity [m 2 s -1] convective drying condition assumed to remain constant during the overall process total moisture mass flux [kg m -2 s -1] gravity vector [m s -2] intrinsic averaged enthalpy of dry air [J kg-X]: h~ = Cp~(T -T~) specific averaged enthalpy of bound water [J kg-1]: hb = ht -Hb intrinsic averaged enthalpy of bound water [J kg-l]:hb = hz -p-~ jo Hbd(pb) 304 F. COUTURE ET AL. hi h~ h~ Hb H o I.C. J k K k~ L n P q Q RH T Tinfh T~ t S U v W z intrinsic averaged enthalpy of free water [J kg-l]: hz = CpL(7" --Tr) intrinsic averagedenthalpy of solid [J kg-1]: h~ = Cp~IT -T~) intrinsic averaged enthalpy of vapour [J kg-1]: h~ = Hv 4-Cp, (T -T~) heat of desorption [J kg -~] latent heat of vaporisation at the reference temperature T~ [J kg -1 ] Initial conditions of the medium flux intrinsic permeability [m 2] volumetric mass rate of evaporation [kg m -3 s -1] relative permeability thickness of the medium [m] exterior normal unit vector pressure [Pa] source term total heat flux [W m -2] external relative humidity [%] temperature [K or ~ C] wet bulb temperature [K or ~ reference temperature [K]: Tr = 273.16 K time [s] saturation conserved quantity velocity [ms -11 moisture content (in dry basis) space variable [m] Greek Symbols 6z space step [m] e porosity ej volume fraction for the phase j: ej = (AV)s/AV heat source [W m -3] ), effective thermal conductivity [W m -...

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