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, Iran Abstract—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.
, 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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