Page 24 - ICJ Jan 2026

TECHNICAL PAPER

conductivity of pore would increase. The contribution of solid
portions to effective conductivity of moist porous material
Solid
remains unchanged with increase in moisture content from continuity Pendular water
dry state. Moisture contents, both mass and volumetric basis,
involve dry mass and volume of the sample, respectively. The
Pore
density, i.e. mass / volume, varies from material to material continuity Nearly enclosed
depending upon solid type and their specific gravity. Hence, solid
as a general concept, relative degree of saturation is a better Wide pore Pores without
parameter that can be related to thermal conductivity of with narrow narrow neck
necks
partially saturated porous material against moisture content.
Degree of saturation or relative moisture content is defined as Figure 25: Pendular water in porous material at lower degree of
saturation
the ratio of moisture content divided by saturation moisture
content. Thus, degree of saturation, θ = , where M stands
2
for mass of the sample and subscripts m, d, and s represent where, q W is the vapor flux in kg/m s; C W is the vapor
3
moist, dry and saturated states, respectively. The degree of concentration in kg/m ; x is the space dimension along direction
2
saturation is normalized with respect to maximum absorption of heat flow, and D W is the vapor diffusion coefficient in m /s.
possible, general to all material and non-dimensional. Jakob C W is expressed in terms of partial pressure of vapor i.e. vapor
factor increases at a faster rate initially with moisture content pressure and temperature as vapor follows Ideal Gas Law.
compared to the rate at higher moisture content. This is (46)
a general observation reported in literature [31,52] . It follows
therefore that as θ increases from 0 towards 1, initially the where, M W is the mass of water vapor, V is the volume, p W is the
rate of increase of moist thermal conductivity with degree of vapor pressure, and R W is the specific gas constant of water
saturation dk/dθ of porous material such as concrete or brick vapor. Thus,
etc., is high and tends to reduce gently near θ, when equals
to unity. Convection in small pores is negligible as ratio of size (47)
of the pores to molecular size of water is not large enough Consider s pW as the exposed surface area of pendular water in
for occurrence of convective circulation of water. Temperature the pores available for evaporation per unit area of the material,
difference across the pore under ambient condition is small and L is the latent heat of evaporation. Then the heat flux and
for significant radiative heat transfer manifestation. There contribution of evaporation-condensation to equivalent pore
are three possible contributing mechanisms to effective heat conductivity are q and k v as given below,
conduction in pores in partially saturated pores. The first one
is heat conduction through water occupying the pore space by
displacing the air. The second mechanism is heat conduction (48)
through yet to be replaced air in the pore. The third possible
mechanism of heat transfer is evaporation and absorption of
latent heat at the water surface inside pore and transport of The D W , L, dp W /dT are function of temperature and the value of
vapor under pressure gradient to cooler pore space followed k' v at 25 °C and 60 °C are given in Table 17; with universal gas
by latent heat transfer by condensation. At lower degree of constant(R) = 8.314 J/K.mol, and hence R W = 8.314 / 18.015 ×
saturation initially, pores partially filled with water are in a 1000 = 461.5 J/kg.K.
pendular state, and the liquid water adheres to the solid surface
as illustrated in Figure 25. The water evaporates at the surface The s pW is the surface area of water per unit area of material
due to concentration difference, and the vapor flux can be normal to the direction of flow and depends upon porosity,
written according to Fick’s Law as follows, pores size distribution, shape of pores, and degree of saturation.
Mean pore size for cylindrical pores from MIP generally is of the
(45) order of 15-40 nm for concrete [16-18] . Assuming spherical pores

Table 17: Properties of water vapor and equivalent conductivity
2
TEMPERATURE (°C) L (J/kg) D W (m /s) d pw /dT (N/m .K) k' v (W/m.K) k v (θ) (W/m.K)
2
20 2450 2.42 × 10 –5 0.149 × 10 –3 6.53324 × 10 −11 0.013
60 2350 3.0 × 10 –5 0.927 × 10 –3 4.25258 × 10 −10 0.085

THE INDIAN CONCRETE JOURNAL | JANUARY 2026 29