1、51.1CHAPTER 51SNOW MELTING AND FREEZE PROTECTIONSnow-Melting Heat Flux Requirement 51.1Slab Design . 51.8Control 51.10Hydronic System Design . 51.10Electric System Design 51.13Freeze Protection Systems 51.18HE practicality of melting snow or ice by supplying heat to theTexposed surface has been demo
2、nstrated in many installations,including sidewalks, roadways, ramps, bridges, access ramps, andparking spaces for the handicapped, and runways. Melting elimi-nates the need for snow removal by chemical means, providesgreater safety for pedestrians and vehicles, and reduces the labor andcost of slush
3、 removal. Other advantages include eliminating piledsnow, reducing liability, and reducing health risks of manual andmechanized shoveling.This chapter covers three types of snow-melting and freeze pro-tection systems:1. Hot fluid circulated in slab-embedded pipes (hydronic)2. Embedded electric heate
4、r cables or wire3. Overhead high-intensity infrared radiant heatingDetailed information about slab heating can be found in Chapter6 of the 2012 ASHRAE HandbookHVAC Systems and Equipment.More information about infrared heating can be found in Chapter 16of the same volume.Components of the system desi
5、gn include (1) heat requirement,(2) slab design, (3) control, and (4) hydronic or electric systemdesign.1. SNOW-MELTING HEAT FLUX REQUIREMENTThe heat required for snow melting depends on five atmosphericfactors: (1) rate of snowfall, (2) snowfall-coincident air dry-bulbtemperature, (3) humidity, (4)
6、 wind speed near the heated surface,and (5) apparent sky temperature. The dimensions of the snow-melt-ing slab affect heat and mass transfer rates at the surface. Other fac-tors such as back and edge heat losses must be considered in thecomplete design.Heat BalanceThe processes that establish the he
7、at requirement at the snow-melting surface can be described by terms in the following equation,which is the steady-state energy balance for required total heat flux(heat flow rate per unit surface area) qoat the upper surface of asnow-melting slab during snowfall.qo= qs+ qm+ Ar(qh+ qe)(1)whereqo= he
8、at flux required at snow-melting surface, Btu/hft2qs= sensible heat flux, Btu/hft2qm= latent heat flux, Btu/hft2Ar= snow-free area ratio, dimensionlessqh= convective and radiative heat flux from snow-free surface, Btu/hft2qe= heat flux of evaporation, Btu/hft2Sensible and Latent Heat Fluxes. The sen
9、sible heat flux qsis theheat flux required to raise the temperature of snow falling on the slabto the melting temperature plus, after the snow has melted, to raisethe temperature of the liquid to the assigned temperature tfof the liq-uid film. The snow is assumed to fall at air temperature ta. The l
10、atentheat flux qmis the heat flux required to melt the snow. Under steady-state conditions, both qsand qmare directly proportional to the snow-fall rate s.Snow-Free Area Ratio. Sensible and latent (melting) heat fluxesoccur on the entire slab during snowfall. On the other hand, heat andmass transfer
11、 at the slab surface depend on whether there is a snowlayer on the surface. Any snow accumulation on the slab acts to par-tially insulate the surface from heat losses and evaporation. The in-sulating effect of partial snow cover can be large. Because snow maycover a portion of the slab area, it is c
12、onvenient to think of the insu-lating effect in terms of an effective or equivalent snow-covered areaAs, which is perfectly insulated and from which no evaporation andheat transfer occurs. The balance is then considered to be the equiv-alent snow-free area Af. This area is assumed to be completely c
13、ov-ered with a thin liquid film; therefore, both heat and mass transferoccur at the maximum rates for the existing environmental con-ditions. It is convenient to define a dimensionless snow-free arearatio Ar:Ar= (2)whereAf= equivalent snow-free area, ft2As= equivalent snow-covered area, ft2At= Af +
14、As= total area, ft2Therefore,0 Ar 1To satisfy Ar= 1, the system must melt snow rapidly enough thatno accumulation occurs. For Ar= 0, the surface is covered with snowof sufficient thickness to prevent heat and evaporation losses. Prac-tical snow-melting systems operate between these limits. Earlierst
15、udies indicate that sufficient snow-melting system design informa-tion is obtained by considering three values of the free area ratio: 0,0.5, and 1.0 (Chapman 1952).Heat Flux because of Surface Convection, Radiation, andEvaporation. Using the snow-free area ratio, appropriate heat andmass transfer r
16、elations can be written for the snow-free fraction ofthe slab Ar. These appear as the third and fourth terms on the right-hand side of Equation (1). On the snow-free surface, maintained atfilm temperature tf, heat is transferred to the surroundings and massis transferred from the evaporating liquid
17、film. Heat flux qhincludesconvective losses to the ambient air at temperature taand radiativelosses to the surroundings, which are at mean radiant temperatureTMR. The convection heat transfer coefficient is a function of windThe preparation of this chapter is assigned to TC 6.5, Radiant Heating andC
18、ooling.AfAt-51.2 2015 ASHRAE HandbookHVAC Applicationsspeed and a characteristic dimension of the snow-melting surface.This heat transfer coefficient is also a function of the thermody-namic properties of the air, which vary slightly over the temperaturerange for various snowfall events. The mean ra
19、diant temperaturedepends on air temperature, relative humidity, cloudiness, cloudaltitude, and whether snow is falling.The heat flux qefrom surface film evaporation is equal to theevaporation rate multiplied by the heat of vaporization. The evapo-ration rate is driven by the difference in vapor pres
20、sure between thewet surface of the snow-melting slab and the ambient air. The evap-oration rate is a function of wind speed, a characteristic dimensionof the slab, and the thermodynamic properties of the ambient air.Heat Flux EquationsSensible Heat Flux. The sensible heat flux qsis given by thefollo
21、wing equation:qs= waterscp,ice(ts ta) + cp,water(tf ts)/c1(3)wherecp,ice= specific heat of ice, Btu/lbFcp,water= specific heat of water, Btu/lbFs = snowfall rate water equivalent, in/hta= ambient temperature coincident with snowfall, Ftf= liquid film temperature, Fts= melting temperature, Fwater= de
22、nsity of water, lb/ft3c1= 12 in/ftThe density of water, specific heat of ice, and specific heat ofwater are approximately constant over the temperature range ofinterest and are evaluated at 32F. The ambient temperature andsnowfall rate are available from weather data. The liquid film tem-perature is
23、 usually taken as 33F.Melting Heat Flux. The heat flux qmrequired to melt the snowis given by the following equation:qm= watershif /c1(4)where hif= heat of fusion of snow, Btu/lb.Convective and Radiative Heat Flux from a Snow-FreeSurface. The corresponding heat flux qhis given by the followingequati
24、on:qh= hc(ts ta) + s(T4f T4MR)(5)wherehc= convection heat transfer coefficient for turbulent flow,Btu/hft2FTf= liquid film temperature, RTMR= mean radiant temperature of surroundings, R = Stefan-Boltzmann constant = 0.1712 108Btu/hft2R4s= emittance of surface, dimensionlessThe convection heat transf
25、er coefficient over the slab on a plane hor-izontal surface is given by the following equations (Incropera andDeWitt 1996):hc= 0.037 Re0.8LPr1/3(6)where kair= thermal conductivity of air at ta, Btuft/hft2FL = characteristic length of slab in direction of wind, ftPr = Prandtl number for air, taken as
26、 Pr = 0.7ReL= Reynolds number based on characteristic length LandReL= c2(7)whereV = design wind speed near slab surface, mphair= kinematic viscosity of air, ft2/hc2= 5280 ft/mileWithout specific wind data for winter, the extreme wind data inChapter 14 of the 2013 ASHRAE HandbookFundamentals maybe us
27、ed; however, it should be noted that these wind speeds may notcorrespond to actual measured data. If the snow-melting surface isnot horizontal, the convection heat transfer coefficient might be dif-ferent, but in many applications, this difference is negligible.From Equations (6) and (7), it can be
28、seen that the turbulent con-vection heat transfer coefficient is a function of L0.2. Because ofthis relationship, shorter snow-melting slabs have higher convectiveheat transfer coefficients than longer slabs. For design, the shortestdimension should be used (e.g., for a long, narrow driveway or side
29、-walk, use the width). A snow-melting slab length L = 20 ft is usedin the heat transfer calculations that resulted in Tables 1, 2, and 3.The mean radiant temperature TMRin Equation (5) is theequivalent blackbody temperature of the surroundings of the snow-melting slab. Under snowfall conditions, the
30、 entire surroundings areapproximately at the ambient air temperature (i.e., TMR= Ta). Whenthere is no snow precipitation (e.g., during idling and after snowfalloperations for Ar 1), the mean radiant temperature is approxi-mated by the following equation:TMR= T4cloud Fsc+ T4sky clear (1 Fsc)1/4(8)whe
31、reFsc= fraction of radiation exchange that occurs between slab and cloudsTcloud= temperature of clouds, RTsky clear= temperature of clear sky, RThe equivalent blackbody temperature of a clear sky is primarilya function of the ambient air temperature and the water content ofthe atmosphere. An approxi
32、mation for the clear sky temperature isgiven by the following equation, which is a curve fit of data inRamsey et al. (1982):Tsky clear= Ta (1.99036 103 7.562Ta+ 7.407 103T2a 56.325 + 26.252)(9)whereTa= ambient temperature, R = relative humidity of air at elevation for which typical weather measureme
33、nts are made, decimalThe cloud-covered portion of the sky is assumed to be at Tcloud.The height of the clouds may be assumed to be 10,000 ft. Thetemperature of the clouds at 10,000 ft is calculated by subtractingthe product of the average lapse rate (rate of decrease of atmospherictemperature with h
34、eight) and the altitude from the atmospherictemperature Ta. The average lapse rate, determined from the tables ofU.S. Standard Atmospheres (COESA 1976), is 3.5F per 1000 ft ofelevation (Ramsey et al. 1982). Therefore, for clouds at 10,000 ft,Tcloud= Ta 35 (10)Under most conditions, this method of ap
35、proximating the tem-perature of the clouds provides an acceptable estimate. However,when the atmosphere contains a very high water content, the tem-perature calculated for a clear sky using Equation (9) may bewarmer than the cloud temperature estimated using Equation (10).When that condition exists,
36、 Tcloudis set equal to the calculated clearsky temperature Tsky clear.Evaporation Heat Flux. The heat flux qerequired to evaporatewater from a wet surface is given bykairL-VLair-Snow Melting and Freeze Protection 51.3qe= dry airhm(Wf Wa)hfg(11)wherehm= mass transfer coefficient, ft/hWa= humidity rat
37、io of ambient air, lbvapor/lbairWf= humidity ratio of saturated air at film surface temperature, lbvapor/lbairhfg= heat of vaporization (enthalpy difference between saturated water vapor and saturated liquid water), Btu/lbdry air= density of dry air, lb/ft3Determination of the mass transfer coeffici
38、ent is based on the anal-ogy between heat transfer and mass transfer. Details of the analogyare given in Chapter 5 of the 2013 ASHRAE HandbookFunda-mentals. For external flow where mass transfer occurs at the con-vective surface and the water vapor component is dilute, thefollowing equation relates
39、the mass transfer coefficient hmto theheat transfer coefficient hcEquation (6):hm= (12)where Sc = Schmidt number. In applying Equation (11), the val-ues Pr = 0.7 and Sc = 0.6 were used to generate the values inTables 1 to 4.The humidity ratios both in the atmosphere and at the surface ofthe water fi
40、lm are calculated using the standard psychrometric rela-tion given in the following equation (from Chapter 1 of the 2013ASHRAE HandbookFundamentals):W = 0.622 (13)where p = atmospheric pressure, psipv= partial pressure of water vapor, psiThe atmospheric pressure in Equation (13) is corrected for alt
41、i-tude using the following equation (Kuehn et al. 1998):p = pstd(14)wherepstd= standard atmospheric pressure, psiA = 0.00356R/ftz = altitude of the location above sea level, ftTo= 518.7RAltitudes of specific locations are found in Chapter 14 of the 2013ASHRAE HandbookFundamentals.The vapor pressure
42、pvfor the calculation of Wais equal to thesaturation vapor pressure psat the dew-point temperature of the air.Saturated conditions exist at the water film surface. Therefore, thevapor pressure used in calculating Wfis the saturation pressure atthe film temperature tf. The saturation partial pressure
43、s of watervapor for temperatures above and below freezing are found intables of the thermodynamic properties of water at saturation or canbe calculated using appropriate equations. Both are presented inChapter 1 of the 2013 ASHRAE HandbookFundamentals.Heat Flux Calculations. Equations (1) to (14) ca
44、n be used to de-termine the required heat fluxes of a snow-melting system. However,calculations must be made for coincident values of snowfall rate,wind speed, ambient temperature, and dew-point temperature (or an-other measure of humidity). By computing the heat flux for eachsnowfall hour over a pe
45、riod of several years, a frequency distributionof hourly heat fluxes can be developed. Annual averages or maxi-mums for climatic factors should never be used in sizing a systembecause they are unlikely to coexist. Finally, it is critical to note thatthe preceding analysis only describes what is happ
46、ening at the uppersurface of the snow-melting surface. Edge losses and back losseshave not been taken into account.Example 1. During the snowfall that occurred during the 8 PM hour onDecember 26, 1985, in the Detroit metropolitan area, the followingsimultaneous conditions existed: air dry-bulb tempe
47、rature = 17F,dew-point temperature = 14F, wind speed = 19.7 mph, and snowfallrate = 0.10 in. of liquid water equivalent per hour. Assuming L = 20 ft,Pr = 0.7, and Sc = 0.6, calculate the surface heat flux qofor a snow-freearea ratio of Ar= 1.0. The thermodynamic and transport properties usedin the c
48、alculation are taken from Chapters 1 and 33 of the 2013ASHRAE HandbookFundamentals. The emittance of the wet surfaceof the heated slab is 0.9.Solution:By Equation (3),qs= 62.4 0.49(32 17) + 1.0(33 32) = 4.3 Btu/hft2By Equation (4),qm= 62.4 143.3 = 74.5 Btu/hft2By Equation (7),ReL= = 4.24 106By Equat
49、ion (6),hc= 0.037 (4.24 106)0.8(0.7)1/3= 4.44 Btu/hft2FBy Equation (5),qh= 4.44(33 17) + (0.1712 108)(0.9)(4934 4774)= 83.5 Btu/hft2By Equation (12),hm= = 247 ft/hObtain the values of the saturation vapor pressures at dew-pointtemperature 14F and film temperature 33F from Table 3 in Chapter 1of the 2013 ASHRAE HandbookFundamentals. Then, use Equation(13) to obtain Wa= 0.00160 lbvapor/lbairand Wf= 0.00393 lbvapor/lbair.By Equation (11),qe= 0.083 247(0
