A study of heat and mass transfer in porous material under equilibrium conditions
Theoretical Foundations of Chemical Engineering, Vol. 39, No. 2, 2005, pp. 200–203. From Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 2, 2005, pp. 216–219. Original English Text Copyright 2005 by Haghi.A Study of Heat and Mass Transfer in Porous Material under Equilibrium Conditions1 A. K. Haghi The University of Guilan, P.O. Box 3756, Rasht, IranAbstract—This paper surveys the heat and moisture transfer characteristics of fabric systems under equilib- rium conditions. Results are given for absorptive and nonabsorptive systems measured under conditions in which no excess moisture secretion or recondensation takes place. It is shown that, with an absorptive textile, the after-exercise chill is large and persists for a few hours, but with a nonabsorptive type it is negligible.
lower ranges of fabric density, the main path of watervapor transfer is through the air spaces between fibers
Manufacture of garments for specific activities is
and yarns. In order to determine the role of the fiber
growing worldwide. Many synthetic fibers produced by
itself in the passage of water vapor, its passage through
chemical processes are offered on the market, and
air spaces in fabric structures should be eliminated.
clothes can be manufactured from numerous combina-tions of natural and synthetic fibers. Many different
In cold climates, clothing is worn to restrict heat loss
kinds of clothing are adapted for particular uses, e.g.,
from the body. The fabrics used in apparel differ in
sports, industrial jobs, or very hot or very cold weather.
moisture sorption and thermal properties, and it is
The comfort of a garment is linked to several factors:
important to consider these properties when choosing
lightness, heat and vapor transport, sweat absorption
and drying, wind, and impermeability. For example,
However, trying to stay warm and dry while being
winter sport clothes must have good vapor transfer
active outdoors in winter has always been a challenge.
properties. However, some of the issues of clothing
In the worst case, an individual exercises strenuously,
comfort that are most readily understood involve the
sweats profusely, and then rests. During exercise, liquid
mechanisms by which clothing materials influence heat
water accumulates on the skin and starts to wet the
and moisture transfer from skin to the environment.
clothing layer above the skin. Some of the sweat evap-
Heat transfer by conduction, convection, and radiation
orates from both the skin and the clothing and moves
and moisture transfer by vapor diffusion are the most
out through the clothing. Depending on the temperature
important mechanisms in very cool or warm environ-
and humidity gradient across the clothing, the water
ments. There is much less certainty, however, about the
vapor either leaves the clothing or condenses and
important mechanisms under the small temperature
freezes somewhere in its outer layers.
gradients of ordinary clothing wear. It should be noted
When the individual stops exercising and begins to
that the moisture transport process in clothing under a
rest, active sweating soon ceases, allowing the skin and
humidity transient is one of the most important factors
clothing layers to eventually dry. During this time,
influencing the dynamic comfort of a wearer in a prac-
however, the heat loss from the body can be consider-
tical wear situation. The moisture transport process is
able. Heat is taken from the body to evaporate the
hardly a single process since it is coupled with the heat
sweat, both that on the skin and that in the clothing. The
transfer process under dynamic conditions [1].
heat flow from the skin through the clothing can be con-
Information on the transmission of water vapor by
siderably greater when the clothing is very wet since
textile fibers is desirable for better understanding of the
water decreases the thermal insulation of the clothing.
problems of comfort and as data for design in special
This post-exercise chill can be exceedingly uncomfort-
applications such as upholstery, footwear, immersion
able and can lead to dangerous hypothermia.
suits and other protective clothing, and wrapping or
A dry layer next to the skin is more comfortable than
packaging, where high resistance to liquid water is
a wet one. If one can wear clothing next to the skin that
desired, combined with considerable permeability to
does not pick up any moisture, but rather passes it
water vapor. Measurements of the water vapor perme-
through to a layer away from the skin, heat loss at rest
ability of woven fabrics have indicated that, in the
will be reduced. For such reasons, synthetic fibers havegained popularity with winter enthusiasts such as hikers
1 This article was submitted by the authors in English.
0040-5795/05/3902-0200 2005 MAIK “Nauka /Interperiodica”
A STUDY OF HEAT AND MASS TRANSFER IN POROUS MATERIAL
Advertising and the popular press would have us
the body responds with increased sweating to dissipate
believe that synthetic materials pick up very little mois-
excess thermal energy. Thus, the inability of a fabric to
ture and dry quickly, thus leaving the wearer warm and
remove liquid water seems to be the major factor caus-
dry. In contrast, warnings are given against wearing
ing uncomfortable feelings for the wearer.
cotton or wool next to the skin since these fibers absorb
Hollies [9] conducted wearer trials for shirts made
sweat and so lower the body temperature. A further
of various fibers and concluded that the largest factor
property credited to synthetics, in particular, polypro-
influencing wearing comfort was the ability of fibers to
pylene, is that they wick water away from the skin,
absorb water, regardless of whether fibers were syn-
All of these studies indicate that the transient state
phenomenon responding to the physiological demandto cause sweating is most relevant to the comfort or dis-
The literature describes some basic work. Osczevski
and Dolhan [2] and Farnworth et al. [3] reported a
When work is performed in heavy clothing, evapo-
strong dependency of water vapor resistance of hydro-
ration of sweat from the skin to the environment is lim-
philic membranes or coatings: the higher the relative
ited by layers of wet clothing and air. The magnitude of
humidity at the membrane, the lower the water vapor
decrement in evaporative cooling is a function of the
resistance (i.e., the higher the water vapor permeability,
resistance of the clothing to permeation of water vapor.
In a temperature-dependent experiment, Osczevski
[4] placed a hydrophilic film on an ice block. Water
vapor sublimating from the ice could diffuse only
When an absorbent material, such as a fabric, takes
through the film and was collected by a desiccant. Osc-
up water, diffusion and absorption occur simulta-
zevski measured mass transport through the film and
found that water vapor resistance is an exponentialfunction of temperature. In this experiment, water
vapor permeability varnishes nearly completely with
decreasing textile temperature. Because diffusion inhydrophilic materials is non-Fickian, Osczevski also
suffices to describe isothermal one-dimensional water
derived from the results a theory of diffusion speed
sorption by fabric. Here, θ is the volumetric water con-
depending on activation energy, and he accounted for
tent (liquid plus perceptible vapor); t is the time (s); x is
different relative humidities. Additionally, Gretton et al.
the distance (cm); and D(θ) is the isothermal water dif-
[5] reported an increase in the moisture vapor transmis-
fusivity, a parameter combining all forms of water
sion rate of hydrophilic and microporous textiles when
measuring was performed with a heated dish instead of
Assume that the sorption process satisfies the Bolt-
an unheated dish. They interpreted their results by the
increased motion of water vapor and polymer mole-
cules, which they claimed would also work for
Equation (1) can be integrated subject to boundary con-
Galbraith et al. [6] compared cotton, water repellent
cotton, and acrylic garments through wearing tests andconcluded that the major factor causing discomfort was
θ = θ , x ≠ 0, t = 0
the excess amount of sweat remaining on the skin sur-
face. Niwa [7] stated that the ability of fabrics to absorb
liquid water (sweat) is more important than water vapor
permeability in determining the comfort factor of fab-rics.
Morooka and Niwa [8] postulated physiological fac-
tors related to the wearing comfort of fabrics as fol-
lows: sweating occurs whenever there is a tendency forthe body temperature to rise, such as high temperature
thus enabling D(θ), the flow parameter controlling
in the surrounding air, physical exercise, etc. If liquid
sorption, to be evaluated from the distribution of water
water (sweat) cannot be dissipated quickly, the humid-
content with distance at any time. The total water taken
ity of the air in the space in between the skin and the
fabric contacting with the skin rises. This increased
humidity prevents rapid evaporation of liquid water on
the skin and gives the body the sensation of “heat” that
triggered the sweating in the first place. Consequently,
THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING Vol. 39 No. 2 2005
sheeting to prevent evaporation, so that the plate was
operated effectively like a dry plate. It was covered bythe textile system to be examined. When the systemreached thermal equilibrium, the polyethylene sheet
was pulled from between the wetted plate and the fabricsystem to allow evaporation from the plate to take
place. After a desired period of time, a second sheet ofpolyethylene was inserted between the plate and the
fabric system by being unrolled from a glass rod as itwas passed under the fabric system. Thus, evaporation
was stopped and the system was allowed to come toequilibrium again.
First, the plate was operated with the wetted cotton
covered and with and without the polyethylene evapo-ration barrier. Figure 1a shows that, when evaporationcommenced, heat input (which balanced heat loss) rose
suddenly. Similarly, on the cessation of evaporation,
there is a sharp drop to the original value.
Figure 1b shows the curve for the apparatus covered
Fig. 1. Heat loss vs. time.
with a layer of synthetic fabrics, which absorbed littlemoisture; the curve rises rapidly to a maximum valuewhen evaporation is initiated. Also, since the ambient
conditions were such that no condensation took place in
While the moisture permeability index and insula-
the fabric, the power drops to its original value when
tion value define the heat transfer characteristics of fab-
ric systems under equilibrium conditions, such condi-
Figure 1c shows the curve for a wool–nylon blend.
tions do not always occur. Moisture may accumulate in
The curve shows a peak in power loss at the initiation
clothing during periods of activity due to unevaporated
of sweating, which was unexpected. The power then
sweat or sweat that has evaporated from the skin and
drops to a minimum and gradually increases. The grad-
recondensed in cooler layers of clothing or due to mois-
ual increase is due to absorption of water by the wool,
ture that is absorbed by the textile fibers. Upon cessa-
which generates heat of absorption and decreases the
tion of activity and sweating, this moisture accumu-
power requirements from the plate. On cessation of
lated in the clothing will evaporate and produce undes-
evaporation from the plate, the moisture accumulated in
ired cooling, or after-exercise chill. A special
the wool gradually dries out and causes after-exercise
thermostated heated plate is described that is used to
measure rates of heat transfer through fabrics before,during, and after periods of simulated sweating. Theresults are shown for absorptive and nonabsorptive sys-
tems under conditions in which no excess moisturesecretion or recondensation takes place.
Bound water diffuses along the surface of fibers (all
kinds of fibers), mainly in the direction perpendicularto the fabric plane and into the wall of the fibers (hygro-
scopic fibers such as cotton, wool, etc.) in radial direc-
To examine the characteristics of fabric systems, a
special heated flat plate was made up. This flat plate
Free water is provided from external boundary con-
was a simple one without a guard ring. It had the usual
ditions of a garment (sweat, rain) or from internal con-
heating circuit, thermistor control, and thermocouple
densation depending on moist air properties. It is easy
attached to it. Power to the plate was measured by pass-
to observe sweat diffusion from particular places on the
ing the output through a short length of constantan
skin, as well as water diffusion through an external
wire. The plate itself was provided with a central hole
layer. This water moves from one point to another, fol-
through which water could be introduced from a con-
lowing the capillary properties of the fabric layers.
stant level source. The water was spread over the plate
However, it should be noted that, in practice, when
by wicking over a thin layer of cotton sheeting.
a clothed person sweats during activity, some of the
In typical operation, the plate was set up in a con-
sweat accumulates in the clothing. When the person
stant temperature and humidity box. The wetted cotton
returns to an inactive or resting state, the heat produc-
surface was covered with a thin layer of polyethylene
tion decreases and he or she no longer requires evapo-
THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING Vol. 39 No. 2 2005
A STUDY OF HEAT AND MASS TRANSFER IN POROUS MATERIAL
rative cooling. Sweating ceases, but the moisture that
range of climates to which any one system of clothing
was accumulated in the clothing continues to evaporate
is adaptable; this problem is applicable to all climates.
and provide unwanted cooling. This is the familiar sit-
The second is the devising of a system of fiber, yarn,
uation of a person standing inactive in damp clothing
fabric, and clothing properties that will reduce after-
after exercising vigorously and getting cold that is
termed after-exercise chill. It is a transient situationsince the clothing is gradually drying, and it cannot beinvestigated by any steady-state type of experiment.
1. Haghi, A.K., The Diffusion of Heat and Moisture
through Textiles, Int. J. Appl. Mech. Eng., 2003, vol. 8,
The proposed method has suggested many other
2. Osczevski, R.J. and Dolhan, P.A., Anomatous Diffusion
avenues of investigation in addition to the difference
in a Water Vapour Permeable, Waterproof Coating,
between absorptive and nonabsorptive textile fibers
J.Coated Fabrics, 1989, vol. 18, pp. 255–258.
under conditions of varying heat dissipation. For exam-
3. Farnworth, B., Lotens, W.A., and Wittgen, P., Variation
ple, a comparison can be made of the two types of fiber
of Water Vapour Resistance of Microporous and Hydro-
under conditions where it is desirable to have almost
philic Films with Relative Humidity, Textile Res. J.,
constant dissipation of heat under changing ambient
conditions, to typify going from indoors to outdoors.
4. Osczevski, R.J., Water Vapour Transfer through a
Yet another avenue is the problem of colder and damper
Hydrophilic Film at Subzero Temperatures, Textile Res. J., 1966, vol. 66, no. 1, pp. 24–29.
environments where condensation of free water occurs. The experiments here are used primarily to emphasize
5. Gretton, J.C., Brook, D.B., Dyson, H.M., and Har-
the fact that many problems of heat exchange through
lock, S.C., Moisture Vapour Transport through Water-proof Breathable Fabrics and Clothing Systems under a
textiles cannot be worked out on the assumption of
Temperature Gradient, Textile Res. J., 1998, vol. 68,
The sudden high heat demands on the initiation of
6. Galbraith, R.L., Werden, J.E., Fahnestock, M.K., Com-
evaporation, while interesting from a theoretical point
fort of Subjects Clothed in Cotton, Water Repellent Cot-
of view, probably do not have much practical applica-
ton and Orlon Suits, Textile Res. J., 1962, vol. 32, p. 236.
tion. Although the rate of heat transfer is very high, the
7. Niwa, M., Water Vapour Permeability of Underwear,
time duration is so short that the total heat extracted
J.Jpn. Res. Assn. Textile End Uses, 1968, vol. 9, p. 446.
from the plate is relatively small and not of much con-
8. Morooka, H. and Niwa, M., Moisture and Water Trans-
sequence to humans. Thus, in the field of functional and
port Properties of Clothing Materials and Comfort Sen-
protective clothing, there are two large areas for devel-
sations, J. Home Econ. Jpn., 1979, vol. 30, p. 320.
opment. The first is production of textiles with a high
9. Hollies, N., Improved Comfort Polyester, Textile Res. J.,
permeability index, the object being to increase the
THEORETICAL FOUNDATIONS OF CHEMICAL ENGINEERING Vol. 39 No. 2 2005
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