Document LpGrzM6pGZNKa13GBZ3OMYko3
m
CHAPTER 24
1956 Guide
A i = 1; commercial areas (e.g? sidewalks wound stores,, etc.) may be designed with A r - 0.5'; and private driveways, oriareas where low instal
lation cbsts are imperative, may>be designed with A, -- 0. For a more complete discussion of free area) rati6 and; its effect on system performance,
see. Reference 6. . .The .equations for .the heating requirements of a snow melting system have been derived and thoroughly explained in Reference 7. The general
equation for slab output, is : r; !.
;
? = ?. +
+ ?h)
-
(7)
where
"qt -- sensible heat transferred to snow, Btu per (hour) (square foot). qm = heat of fusion', Btu per (hour) (square foot). A r -- ratio of s:nov- free are to total area, ^dimensionless.
= heat of vaporization, Btu per (hour) (square foot). Qh = heat transfer by convection ail'd radiation, Btu per (hour) (square foot).
net. om i* ih.
> a; CCKTEM
' ' i i ---------- -- - -
^ r. o r. : .
i ;7J
-V-
i J
"*> ** 0 ; -*''' V *
Fig. 16. Detail of Snow Melting Panel F === Depth of Finish Coat--Assumed as in. of concrete'. Finish Coat may be asphalt but then cover
slab should be reduced from 3 in. Depth of slab should always keep thermal resistance equal to 3 in.
of concrete. S =? Depth required by structural design.
The sensible heat, q,, to raise the temperature of the snow to 32 F is
'
'^' '
q. - 2.6s (32 - (.)
"(8)
where j
'
a = fate of snowfall, see Table 3, inches of water equivalent per hour. - air temperature, Fahrenheit.
The heat of fusion, qm, to melt the snow is
'. <?,,' = 746s .
;
. (9)
The heat of vaporization, qe, (mass transfer) is 9. - 1074(0.020h> -1 0.055)(0.185 - p..)A,
(10)
where p,. = vapor pr6ssure of moist air, inches of mercury.
The heat transfer, (convection'and radiation) is ' V ' ' ' qh = 11.4(0.0201v + 0.055)((, - u)A,
(11)
where
v = wind velocity, miles per hour. I, - water film temperature, Fahrenheit.
Panel Heating
587
In addition to determining the four heating requirements, it is neces sary to make allowance for back and edge losses. These losses vary from 30 to 50 percent, depending upon the slab construction.
The equation for the required fluid temperature to provide an output q,,
has been derived in Reference 7. For construction similar to Fig. 16, the
equation is
'
= 0.5?o +1,
(12)
where
' tm = mean fluid temperature (antifreeze solution), Fahrenheit.
Equation 12 will, suffice for 1 in. IP'S as well as % in. -- see Fig. 16.
Table 4: Heat Output And Fluid Tempebatube fob Snow Melting Systems
s Rate of Snowfall
At
t* = 0 F ^ Velocity 9 5 10 15
U = 10 F Velocity V 5 10 15
li = 20 F Velocity 9 5 10 15
U = 30 F Velocity 9 5 10 15
0.08
F.0 - Qo
151 205 260 127 168 209 102 128 154 75 84 94
> fm 108 135 162 97 117 138 85 97 110 70 75 79
0.0 Qo
66 66 66 64 64 64 62 62 62 60 60 60 66 66 66 65 65 65 64 64 64 63 63 63
0.16 1.0 Qo >218 273 327 193 233 274 165 191 217 135 144 154 tm 142 169 198 129 149 170 117 129 142 100 105 109
0.0 Qo
133 133 133 129 129 129 125 125 125 121 121 121
*m 99 99 99 97 97 97 95 95 95 93 93 93
0.25 1.0 Qo 292 347 401 265 305 346 235 261 287 203 212 221 tm 179 206 234 165 186 206 151 163 176 134 139 144
0.0 Qo >208 208 208 202 202 202 195 195 195 188 188 188 137 137 137 134 134 134 131 131 131 127 127 127
Note: This table is based on a relative humidity of 80 percent for all air temperatures = Rate of snowfall, inches of water equivalent per hour (See Table 3). Ar = Free area ratio. 9o19 Slab output, Btu per (hour) (square foot). U ~ Air temperature, Fahrenheit. tm -- Fluid temperature, Fahrenheit. Based on construction as shown is Fig. 16. = Wind velocity, miles per hour.
Values for $ for certain cities are given in Table 3. Using the values for s given in Table 3, the appropriate values for (a and v, the values for 5 may be found in Table 4. In preparing Table 4, only values of pov for relative humidities of 80 percent , were used. The variation in q0 and tm for humidities of 75, 80, 85 and 90 percent are given in Reference 6, and may be calculated by solving Equations 13 and 14.
~ = -537 (0.0201k + 0.055) Ar dptv
(13)
d~p*r = -1074 (0.0201n + 0.055) At
* (14)
When selecting the heat exchanger, it will be necessary to allow for the thermal properties of the anti-freeze solution. The manufacturer should be given data on the type and concentration of anti-freeze, the tempera-