Thus, for unfinned piles, natural convection, no wind:

= 26 F (from table)

a = 2.35 x 106/ft F for Tm = 26F

3

q = 0.13 Lair a1/3 A (Tv - Ta) 4/3

(d) For the case of unfinned piles,

(from table)

forced convection, induced either naturally by wind or

From a pile of 1 foot nominal diameter, the cooling

mechanically, the surface transfer coefficient is modified

area, At, is (rx 1.062) = 3.33 ft'/lineal foot. Thus:

and the equation is:

6

4/3

q = (0.13) (0.0138) (2.35 x 10 ) 1/3 (3.33) (32-20)

q = hc A (Tv - Ta) = air (0.82) VDρ 0.585 A(Tv -Ta)

K

= 21.8 BtuAin ft hr

D

(h) The freezeback time, relying

where:

exclusively on the thermal pile effect, for a pile length,

V = wind velocity, ft/hr

La, of 4 feet exposed to the air is:

D = outer diameter of pile, ft

iValues of factors p ,p , a and Kair for various values of Tm

200,000 9

are given below:

21.8 x 4 x 24 = 96 days

ρ

Tm

a

Kair

(i) This assumes that none of the

(F)

(1/ft F)

3

3

(lb/ft )

(Ibm/ft hr)

(Btu/ft hr)

slurry heat is extracted by the surrounding permafrost,

which, of course, is not the case. During the 20-day

6

32

.0807

.0417

2.21 x 10

.0140

period required to naturally freeze back the slurry, heat

6

.0136

20

.0827

.0408

2.50 x 10

removal via the thermal pile effect is (21.8 x 4x 20 x 24)

6

.0131

0

.0863

.0394

3.00 x 10

= 42,000 Btu. This represents 2100 Btu/lineal ft of pile.

6

.0129

-10

.0882

.0387

3.47 x 10

Again referring to figure 4-72 and using a volumetric

6

.0126

-20

.0902

.0380

3.93 x 10

latent heat of slurry of (10,000 2100) = 7900 Btu per

6

.0123

-30

.0923

.0373

4.53 x 10

lineal foot, it is noted that 7900 Btu can be removed in

6

.0121

-40

.0945

.0366

5.21 x 10

about 15.5 days. Thus, the thermal pile will influence

6

.0118

-50

.0968

.0358

5.74 x 10

freezeback over a shorter time than 20 days and by

6

.0115

-60

.0992

.0351

6.47 x 10

successive approximations the appropriate freezeback

6

.0113

-70

.1018

.0344

7.24 x 10

time is established. In 16.5 days, the thermal pile

extracts 1740 Btu/ft and about (10,000 1740 = ) 8260

(f) Computation of heat transfer

Btu/ft is dissipated into the permafrost in the same time

during freezeback. The thermal pile may be used to

interval (fig. 4-72). This represents a reduction in

accelerate freezeback of the slurry in a preaugered hole.

freezeback time of about 17 percent.

It would thus tend to supplement the in-situ permafrost's

(j) Had the air temperature averaged

freezeback capability. As noted in figure 4-72, a wet

0 F, rather than 20F, the thermal pile heat removal rate

slurry of 10,000 Btu/ft in a relatively warm permafrost at

would have increased to 81 Btu/lineal ft hr and the

28F would require about 20 days to freeze back

overall freezeback time would have been reduced to

naturally for the numerical values assumed in that

about 10 days (a 50% reduction in time). It should be

example. An indication of the reduction in freezeback

noted that these calculations assume that heat is also

time afforded by the thermal pile is developed below.

extracted by the pile from that portion of the slurry in the

(g) Example. Assuming a pile length

annual frost zone. If the pile is placed at the end of the

of 20 feet below ground surface (i.e., including the

winter, the annual frost zone will be at a lower

annual frost zone), this represents a total of 200,000

temperature than the permafrost and thus more slurry

Btu's of latent heat to be-removed during slurry

heat will be removed per linear foot by the surrounding

freezeback. Further, assuming that an unfinned pile is

ground in the annual frost layer than is the than is the

placed during the late fall when the average daily air

case in the permafrost zone. Thus, the procedure will

temperature is 20F and no wind exists, the following

tend to estimate the freezeback benefit of the thermal

estimation of freezeback under the thermal pile

pile somewhat conservatively. However, the opposite

mechanism may be made:

situation develops should the pile be placed at the end of

the summer period when the active zone is above

1/3

q = 0.13 Kair a Al (Tv - Ta) 4/3

freezing. At this time a large percentage of the pile's

Tv = 32F (assumed to be the temperature of

heat sink ability is used to extract heat from the annual

slurry during freeze-up)

frost zone.

Ta = 20F

Kair = 0.0138 Btu/ft hr F for Tm = 1/2

(Tv + Ta)