Experimental study of water evaporation from nanoporous cylinder surface in natural convective airflow

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1 Avance Computationa Methos in Heat Transfer IX 67 Experimenta stuy of water evaporation from nanoporous cyiner surface in natura convective airfow S. Hara Department of Mechanica Engineering, Toyo University, Japan Abstract Ungaze porous cyiners were use to stuy experimentay the evaporation features of water from the cyiner surfaces in natura convective airfows. Seto semi-porceain cay No.6 was empoye to make the ungaze porous cyiners. The firing temperature was change from 77 to 5 K to reguate the pore size of the porous. The iameter was from 80 to 85 mm, the thickness 7 mm, an the span 90 mm. The experiment was mae at constant air temperature an the reative humiity. The air temperature range from 8 to 97 K an the reative humiity from 0 to 7%. The firing temperature ha itte effects on the evaporation characteristics. The evaporation rates were aways.5 to times as high as those of non-porous cyiners. The Grashof number, which shows macroscopic natura convection, i not have any appreciabe effects on the evaporation. The evaporation rates were affecte by the ambient temperature an reative humiity. Therefore, the foowing two concusions were acquire: the evaporation on the nanoporous was shou be argey taken into account with the interaction between water an surface moecues which etermines the evaporation energy of moecues, an the nanoporous oes not consist of the pores among partices of the semi-porceain, but of the nanoscae pores of a partice. Keywors: water evaporation, natura convection, nanoporous surface, ungaze semi-porceain cyiner, moecuar interaction, firing temperature, nanoscae pore, experiments, air temperature, reative humiity. 006 WIT Press oi:0.95/ht0605

2 68 Avance Computationa Methos in Heat Transfer IX Introuction Water evaporation phenomenon has been observe for water containe in an ungaze semi-porceain cyiner. The mechanism of the evaporation from the nanoporous surface is unknown. If the porous passage is arge enough for water moecues moving to surface, the evaporation on the porous surface goes on in the same manner as on the surface of water fim, showing the same evaporation rate of the ater. If the passage is resistive for the water moecues, the moecuar interaction must be appreciabe between the passage an the passer-by moecues. The evaporation atent heat is macroscopicay efine as the energy ifference between gaseous an iqui states of the moecuar assembes at the same temperature an pressure. This means that it is the energy require for moecues to eave away the iqui-state custer of the same homogeneous moecues. If the thir moecues are reate to the process of evaporation as in the soi-state custer, the evaporating energy of the moecues must be ifferent from that of the homogeneous moecues as shown in references [ ~ 6]. Whether the change is positive or negative epens on the thir-boy interaction with the evaporating moecues. Concerning the water evaporation on the nanoporous surface of the ungaze pottery cyiner in force convective airfow as shown in the references [7, 8], the evaporation rates were.5 times as high as those of non-porous cyiners at first. However, these evaporation rates ecrease to the equiibrium vaue of.5 after 0 minutes. This is why the surface ry causes the water suppy rate from the insie of the cyiner to be ess than the evaporation rate from the surface of the cyiner. Therefore, the water evaporation on the surface of the nanoporous cyiners was not abe to be etaiey anayze. But in the natura convective airfow the cyiner surface oes not get ry because the evaporation rate is ow, an the evaporation rate remains steay as the time passes. It was, therefore, experimentay investigate how the water evaporation wi be affecte by the nanoscae pore size of the cyiner surface. The experiment was carrie out in natura convective evaporation on the groun-base nanoporous cyiner with water insie. Experimenta apparatus an proceure Figure shows the experiment apparatus use. The nanoporous cyiner of 80 mm in iameter an 90 mm in ength is surroune by mm cross-sectiona area an 000 mm high was for getting stabe natura convection. The was are 700 mm away from the groun. The cyiner is ocate on the supporting cyiner of 80 mm in iameter an 000 mm in height from the groun. Distie water was absorbe up into the hoow cyiner of 7 mm in thickness from the storage tank, where the water surface eve is 00 mm beow the unerneath en of the cyiner. Seto semi-porceain cay No.6 is use to make the cyiner an the firing temperature was change between 77 an 5 K. The firing temperature causes the size of porous pores to change between 5 nm an 00 nm. The experiment was carrie out uner the stabe 006 WIT Press

3 Avance Computationa Methos in Heat Transfer IX 69 conitions of the room temperature an reative humiity an with possibe reuction of goba natura convections in the room. The experiment starte on the wette surface of the cyiner. The evaporation rate was measure by the water fow suppie into the porous cyiner with a fow meter of Petier eement. The air temperature was measure with Pt 00 thermometer. The reative humiity was measure with HUMICAP of Vaisaa (thin-fim poymer sensor). The experimenta air temperature T was 8 to 97 K an the reative humiity RH 0 to 7%. Unit: mm Natura Convective Air Fow Nanoporous Cyiner Nanoporous Cyiner Cosures Stop Vave Cyiner Support Mass Meter Distie Water Groun Fow Figure : Experimenta apparatus. Experimenta resuts The experimenta resuts obtaine are summe up using two non-imensiona parameters, Sh; the Sherwoo number for evaporation rate an Gr; the Grashof number for natura convection. The Sherwoo number shows the evaporation rate, compare with the moecuar iffusion rate uner the same moecuar-ensity conitions at the bounary. The evaporation rate can be expresse as hd ( ρ - ρw ) S, () an the moecuar iffusion rate is given by ρ - ρw D S, () 006 WIT Press

4 70 Avance Computationa Methos in Heat Transfer IX where ρ w an ρ are the water concentrations or air ensities at the cyiner-wa surface an its infinity, h D the tota mass transfer rate at the cyiner surface, D the moecuar iffusion coefficient, the cyiner iameter, an S the tota surface area causing the evaporation. Then the Sherwoo number is shown as h D Sh. () D The Grashof number is an inertia force compare with the viscous force ike as the Reynos number, athough the inertia force without any force fows is given by the natura convection force as u ρ = g ( ρ ρw ) -, () an the viscous force is given by u ρ ν, (5) where u is the characteristic veocity an ν the kinematic viscosity. These give the non-imensiona number, Gr ; Grashof number as u u u ρ - ρ Gr ρ w ρ ν = = g, (6) ν ρ ν The heat transfer hanbook [9] shows the Nusset number for the cyinrica surface as ( Nu ) c / 0.8 ( Nu ) ( Nu ) = +, (7) p p where ( Nu ) c is the Nusset number for the circuar cyiner base on the cyiner ength an ( Nu is the Nusset number for the fat pate an with the ) p pate ength. Since the atter is given as Nu = 0 55Ra, (8) ( ). p 6 ( Nu ) Ra ( / ) 5 Ra c =, (9) 56 or eqn. (7) gives ( ) ( ) ( ) Nu = Ra Ra, (0) c where ( Nu an Ra are the Nusset number an Rayeigh number base on ) c the cyiner iameter. Since Ra is given as Ra = Gr Pr, () ( Nu ) 0 55 ( Gr Pr ) ( Gr Pr ) c =. (). 006 WIT Press

5 Avance Computationa Methos in Heat Transfer IX 7 Substituting Nu with Sh, an Pr with Sc to eqn. () by the anaogy between heat an mass transfer, then the Sherwoo number for the non-porous cyiner fuy wette by water is given by / Sh 0 55 Gr Sc 0 68 Gr Sc / =. +., () ( ) ( ) ( ) c where Sc is the Schmit number. It is the purpose of the present experiment how ifferent evaporation rates Sh wi be resute in the water evaporation from the nanoporous surfaces, uner the same natura convective conitions, Gr. The evaporation rates resute are a given in the term of the ratio compare with the Sherwoo number for the fuy wette cyinrica surfaces at the same Grashof number, Sh / Sh vs. Gr.. Effects of the firing temperature on the cyiner porous.. Effects of the firing temperature on the cyiner iameter Figure shows the effect of the firing temperature on the cyiner iameter. The shape, size an porosity istribution wi be affecte by the firing temperature to make the ungaze porous cyiner from the cay. The iameter of the semi-porceain cyiner remaine stabe by 7 K, an then the iameter ecrease rapiy as the firing temperature increase Cyiner Diameter [mm] Firing Temperature [K] Figure : Effects of the firing temperature on the cyiner iameter... Effects of the firing temperature on the water eakage mass rate Figure shows the effect of the firing temperature on the water eakage mass rate at the oae pressure of 500 mm Aq. The water eakage mass rate raise as the firing temperature increase by 7 K, an then the water eakage mass rate fe rapiy as the temperature increase. At 5 K, there was no eakage. 006 WIT Press

6 7 Avance Computationa Methos in Heat Transfer IX Specificay, the size of the pore among the semi-porceain partices came to be smaer as the temperature increase by 7 K, then the size of the pore rapiy ecrease, an at the temperature of 5 K there was no eakage. This shows that the pore size among the semi-porceain partices change ue to the firing temperature. 0.5 Leakage mass rate [kg/(m h )] T = 9 K, RH = 70 % Firing temperature [K] Figure : Effects of firing temperature on the water eakage mass rate.. Effects of the firing temperature on the evaporation rate Figure shows the effect of the firing temperature on the water evaporation rates. It is cear from the figure that the firing temperature has itte effect on the water evaporation from the porous cyiners at the firing temperature of 97 ~ 7 K. At 5 K there was no evaporation because of no water suppy to the cyiner surface. The size of the pore among the partices of semiporceain then affects no evaporation rate, an the nanoporous with evaporation characteristics oes not consist of the pores among partices of the semiporceain, but of the nanoscae pores of a partice.. Effects of air temperature an humiity Figures 5 an 6 show the effects of the temperature an reative humiity of the ambient air surrouning the cyiner. The air temperature an reative humiity must be incue in the terms of non-imensiona parameters, but they sti have some effects on the evaporation rates. It is not known whether this comes from the insufficient estimation of physica properties such as the iffusion coefficients, viscosity an ensity or funamentay from the evaporation from the porous cyiner surface. 006 WIT Press

7 Avance Computationa Methos in Heat Transfer IX 7 Sh/Sh T=9 K, RH=55~60 % T=9 K, RH=5~50 % T=8 K, RH=5~55 % Firing Temparature [K] Figure : Effects of firing temperature on the Sherwoo number ratio. Sh/Sh RH=70 ~75 % RH=50 ~55 % RH=0 ~5 % Gr=(.8~.) 0 Gr=(.8~.) 0 Gr=(.9~5.) T [K] Figure 5: Effects of air temperature on the Sherwoo number ratio. 006 WIT Press

8 7 Avance Computationa Methos in Heat Transfer IX Sh/Sh T=95 ~ 97 K T=90 ~ 9 K T=8 ~ 85 K Gr=(.8~5.) 0 Gr=(.~.5) 0 Gr=(.9~.) RH [%] Figure 6: Effects of reative humiity on the Sherwoo number ratio. Sh/Sh 0 T=9 ~ 98 K, RH=6 ~7% T=9 ~ 98 K, RH=50 ~59 % T=9 ~ 98 K, RH=5 ~9 % T=89 ~ 9 K, RH=70 ~ 7 % T=89 ~ 9 K, RH=60 ~6 % T=89 ~ 9 K, RH= ~ 55 % T=8 ~ 89 K, RH=60 ~ 6 % T=8 ~ 89 K, RH=50 ~ 58 % T=8 ~ 89 K, RH=0 ~ 9 % 0 5 Gr 0 - Figure 7: Effects of Grashof number on the Sherwoo number ratio. 006 WIT Press

9 Avance Computationa Methos in Heat Transfer IX 75. Effects of Grashof number As shown in figure 7, the evaporation rate increases.5 to times compare with the fuy wette cyiner surfaces in the range of the Grashof number (~5) 0. In this range, the Grashof number oes not show an appreciabe effect on the evaporation characteristics. Specificay the macroscopic fow ue to the natura convection is the same as that of the evaporation from the nonporous cyiner fuy wette by water, but those microscopic features of evaporation must be appreciaby affecte by the interaction of water moecues with porous materia of nanoscae configuration, which gives constants.5 to times as arge as those in eqn. (). Concuing remarks () Foowing figures 5, 6 an 7, the evaporation features epen on the ambient temperature an reative humiity, amost inepenent of the Grashof number. Due to this inepenency, the same convective fows wi appear if inuce by the buoyancy force by the ifference of ensity istribution. As far as the macroscopic fows, the same fows wi appear even when the evaporation mechanism itsef is ifferent from each other. If the nanoporous surface affects ony the microscopic mechanism of evaporation, that is, the interaction between water an porous-surface moecues, the evaporation features must be infuence by the ambient temperature an reative humiity, inepenent of the Grashof number which gives the macroscopic fow fie. The particuar evaporation mechanism on the porous surface is not straightforwary eucibe because the moecuar interaction incues the quantum effects which cannot be expecte by the moecuar ynamics with a constant potentia of interfacia moecues. () Foowing figure, the nanoporous reate to the evaporation characteristics oes not consist of the pores among partices of the semi-porceain, but of the nanoscae pores of a partice of the semi porceain. Nomencature : iameter of cyiner, m D : iffusion coefficient, m /s g : gravitationa acceeration, m/s Gr : Grashof number, Gr = g ( ρ - ρ )/ ( ρ ν ) w h D : mass transfer rate, m/s : ength of cyiner, m RH : reative humiity, % S : tota surface area causing evaporation, m Sh : Sherwoo number, Sh = h D / D. Sh : Sherwoo number of fuy wette surface cyiner in the hanbook, 006 WIT Press

10 76 Avance Computationa Methos in Heat Transfer IX ( Gr Sc / ) ( Gr Sc / ) Sh = Sc : Schmit number, Sc = ν / D. T : temperature, K u : characteristic veocity, m/s ν : kinematic viscosity, m /s ρ : ensity at wa surface, kg/m w ρ : ensity of main fow, kg/m References [] Krim, J., Couomb, J.P. & Bouzii, J., Tripe-Point Wetting an Surface Meting of Oxygen Fims Asorbe on Graphite, J. Phys. Review Letters, 58 (6), pp , 987. [] Soko, P.E., Ma, W.J., Herwig. K.W., Snow, W.M., Wang, Y., Kopic, J. & Banavar, J.R., Freezing in Confine Geometries, App. Phys. Lett. 6 (7), pp , 99. [] Moz, E., Wong, A.P.Y., Chan, M.H.W. & Beamish, J.R., Freezing an Meting of Fuis in Porous Grasses, Phys. Review B, 8 (9), pp , 99. [] Unruh, K.M., Huber, T.E. & Huber, C.A., Meting & Freezing Behaviour of Inium Meta in Porous Gasses, Phys. Review B, 8 (), pp , 99. [5] Hansen, E.W., Stöcker, M. & Schmit, R., Low-Temperature Phase Transition of Water Confine in Mesopores Probe by NMR. Infuence on Pore Size Distribution, J. Chem. Phys., 00 (6), pp , 996. [6] Maox, M.W. & Gubbins, K.E., A Moecuar Simuation Stuy of Freezing/Meting Phenomena for Lennar-Jones Methane in Cyinrica Nanoscae Pores, J. Chem. Phys. 07 (), pp , 997. [7] Hara, S. & Suzuki, T., Water Evaporation on a Nanoporous Cyiner in Force Airfows, Therma Science & Engineering, 6(), pp. -8, 998. [8] Hara, S., Water Evaporation on a Nanoporous Cyiner in Force Airfows, Therma Science & Engineering, 8(), pp. -7, 000. [9] JSME, Heat Transfer Hanbook, Japan Society of Mechanica Engineer, pp. -5, WIT Press