wi&kMm

'Mimim

NAT'L INST. OF STAND & TECH R.I.C.

NBSIR 81-2378

AlllOl 77bfiMD

AlllDS LI&73S

TT >leat Transfer Analysis of

Underground Heat and

Chilled-Water Distribution Systems

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, DC 20234

November 1981

Prepared for Naval Facilities Engineering Council

U.S. Navy

Washington, DC 20390

Directorate of Civil Engineering

U.S. Air Force

Washington, DC 20330

and

f-QClOQ

• U56

81-2378

1981

Office of Chief of Engineers

As. Army

'ashington, DC 20304

V.

MATlOlfAL BUKKAT' or standABUS LIRRART NBSIR 81-2378 DEC 7 1981

HEAT TRANSFER ANALYSIS OF

UNDERGROUND HEAT AND

CHILLED-WATER DISTRIBUTION SYSTEMS

T. Kusuda

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, DC 20234

November 1981

Prepared for Naval Facilities Engineering Council

U.S. Navy

Washington, DC 20390

Directorate of Civil Engineering

U.S. Air Force

Washington, DC 20330

and

Office of Chief of Engineers

U.S. Army

Washington, DC 20304

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
* . ^¥ ^ I ?

'

> HQ
Heat Transfer Analysis of Underground Heat and

Chilled-Water Distribution Systems

T. Kusuda

National Bureau of Standards

ABSTRACT

Simplified calculation procedures for determining heat exchange between the

earth and a multiplicity of buried pipes having different temperature and

thermal insulation are presented. The procedures deal with cases where pipes

are burled side by side, as well as those when several pipes are bundled in a conduit. The effects of seasonal variation of earth temperature are treated in

a quasi-steady-state equation that includes the soil thermal properties, depth

of burial, pipe sizes, and relative locations of pipes. Sample calculations

are included, together with the Fortran program listing and thermal properties

of earth to be used for the calculations.

Key words: computer program; earth temperature; heat transfer; pipes; thermal

Insulation; thermal properties; underground systems.

lii
TABLE OF CONTENTS

Page

Abstract Ill

1. Introduction 1

2. Theoretical Background for Underground Pipe Heat Transfer 2

2.1 Single Shallow Pipe System 2

2.2 Multiple Pipe System 5

2.3 Pipes In an Underground Conduit 13

2.4 Underground Pipe In an Insulated Trench 18

3. Earth Temperature Data 20

4. Sample Problems and Solutions 22

5. Summary 23

6. References 25

7 . Unit Conversion Factor 26

Appendix A. Earth Temperature Tables for Underground Heat-DlstrlbutlonSystem Design A-1

Appendix B. Computer Program Listing for Multiple Pipe Heat Transfer

and Economic Analysis B-1

Iv
1 . INTRODUCTION

Although underground heat distribution systems for a complex of buildings,

such as college campuses and military bases, have been widely used in the

United States for the past several decades, not much attention has been given

to heat transfer analysis other than to such technical problems as the possibility of failure of the piping system from corrosion, thermal expansion

difficulties, or moisture penetration through the thermal insulation. This

is largely because many of the underground installations designed to distribute steam or hot water are purposely well insulated. Until recently, heat

loss from these pipes has been considered small when compared with the total

heat energy being transmitted through the pipe, providing that the thermal

insulation is not damaged and rendered ineffective by leaking pipe fluid or from ground moisture. Thus, the main emphasis is placed on the preservation

of a dry insulation around the pipe, corrosion protection of the conduit which

houses the piping system, and the design of the piping system to minimize

stress caused by the thermal expansion and contraction.

Since the early part of the 1960 ’s when underground chilled water distribution

systems began to gain popular acceptance for district cooling, the economic

consideration as to whether the chilled water pipes should be Insulated or not

has required a careful reevaluation of the heat transfer problem [1].

Underground chilled water pipes are sometimes installed uninsulated, allowing

a considerable savings in capital investment, especially for a large district

cooling system. The uninsulated chilled water system appears justified on

the following basis:

a. Ground temperature is not severely affected by the presence of a deeply buried uninsulated chilled water pipe, and soil ecology and

plant life are not unduly affected.

b. Heat gain from the surrounding earth to large chilled-water pipes is

usually a very small part of the total refrigeration load, and

Increases in the temperature of the chilled water being circulated

in the underground piping network are not significant.

c. There is no heat source such as an underground heat distribution system

in the vicinity of the chilled water pipe.

Although item a is unquestionably valid, item b may be less so, particularly

when the pipe diameter is small, long lengths of pipe are used, and when the

earth surrounding the pipe remains warm and conductive for long periods of

time. Item c is often invalid because in many instances underground chilled

water lines run parallel and close to the steam and/or hot water lines.

The question is under what conditions is it necessary to insulate underground

chilled-water pipes? If insulation becomes necessary, how much is needed?

In order to answer this question, a comprehensive heat transfer calculation

methodology is needed to analyze the situation whereby several underground pipes

of different temperatures are buried side by side. This report presents a

1
recommended procedure and sample calculation to solve multiple pipe underground

heat and chilled water distribution systems.

2. THEORETICAL BACKGROUND FOR UNDERGROUND PIPE HEAT TRANSFER

Except for the work of Loudon [2]

,

very few papers have been published in the

past treating the realistic conditions applicable to the analysis of underground pipe heat transfer. Most of the analytical solutions readily available

for estimating heat transfer to and from underground pipes are either steadystate solutions for a pipe at shallow depths or transient heat conduction solutions for a single deep underground pipe. All of these solutions are based

upon the assumption that the earth surrounding the pipe is homogeneous, the

thermal properties of the earth are constant, and the temperature of the earth

at reasonable distances from the pipe is constant and unaffected by the

existence of the pipe.

It has been well known that these assumptions are unrealistic because thermal

properties as well as earth temperatures change with respect to time and space

due to seasonal change of the earth surface temperature and also due to movement of the soil moisture or ground water around the pipe. Analytical solutions

which take into account these realistic situations are, however, extremely difficult to obtain and are not expected to be available in the near future.

Therefore, the approach here was to examine quasi-steady-state heat transfer

theories applicable to seasonal change of earth temperature. The method would

provide approximate solutions for several practical problems, inclusive of

multiple-pipe situations.

2.1 SINGLE SHALLOW PIPE SYSTEM (figure 1)

The solution for steady-state heat conduction from an underground pipe

Installed horizontally at a finite depth in homogenous soil of constant property

can be found in several heat transfer texts [3,4]. This solution is based upon

the potential flow theory and is obtained by the use of the "mirror- image”

technique [3]. According to this technique, the heat loss Q from the unit

length of the pipe of temperature Tp to the undisturbed ground at an average

temperature Tq can be approximated by following equation:

where kg = average thermal conductivity of earth surrounding the pipe (see

figure 2)

d = depth of the pipe measured from the ground surface to the centerline of the pipe

r = external radius of the pipe where the pipe temperature is Tp

£n = natural logarithm

Another form of the above equation usually cited is

27ikc(Tp-Tp)

Q ( 1 )

)

2
GROUND SURFACE

Figure 1. Single-pipe system (Nomenclature).

3
3

ea

MOISTURE CONTENT |% of dry weigtitj

2.0

1.5

1.0

0.5

Figure 2. Thermal conductivity versus moisture content for soils.

4

THERMAL

CONDUCTIVITY

(W/m

• K)
2iTks(Tp~TG)

Q ( 2 ) =

r

which is a further approximate representation of equation (1) when d/r » 1, or when the radius of the pipe is sufficiently smaller than the depth.

Equations (1) and (2) were developed for the average pipe surface temperature

Tp and the average temperature Tq of the undisturbed earth at some distance

from the pipe inclusive of the ground surface.

When the pipe is insulated, a term for the thermal resistance of the insulation

layer must be added to the above equations. If the pipe is uninsulated and the

pipe material has high thermal resistance, such as non-metallic pipes, the thermal resistance term for the pipe wall should also be included in the pipe heat

transfer equation in such a way that

in consistent units where

Kp = pipe heat transfer factor

Tp = pipe fluid temperature

Tq = undisturbed average earth temperature surrounding the pipe

ry = inside radius of the pipe

r = external radius of the insulation

t = thickness of the pipe Insulation

hy = heat transfer coefficient of the pipe fluid

ks = thermal conductivity of the earth surrounding the pipe

ky = thermal conductivity of the pipe wall

kj = thermal conductivity of the pipe insulation .

The above expression is, however, only approximately correct since actual heat

flow is not radial and may result in error if kg/kj » 1. The extent of the error due to this approximation, is however, unknown.

Moreover, for the calculation of pipe heat transfer factor for metallic pipe

Kp, it is customary to ignore the terms involving hy and ky because of their

very small numerical value. Even for the non-metallic pipes, the term involving hy is usually neglected unless the pipe fluid velocity is extremely small.

2.2 MULTIPLE PIPE SYSTEM; (figure 3)

The foregoing discussion is for a single isolated underground pipe. In

practice, several pipes may be installed in the same vicinity. Thus, heat

1 ,

(3)

5
GROUND

SURFACE

X

UJ

q:3

h"<

(T

liJ CL

:sUJX

Ia:<

UJ

UJ

CD<

q:UJ><Q

UJ

CD

cr33

>-I 6

UNDISTURBED

AVERAGE

THERMAL

CONDUCTIVITY
transfer around each pipe is affected by the presence of its neighbor. The

steady-state heat transfer for a multiple- pipe system was explored in detail

during this study and is presented in this report because little information

was available from reference material. The multiple pipe system considered in

this section is shown schematically in figures 3 and 4. The undisturbed earth

temperature is designated by Tq, whereas the earth temperature at any point

(x, -y) in the region of pipe heat transfer is designated by T.

The difference in temperature T-Tq, due to M number of heat sources (or sinks) can be obtained by the superposition of mirror image technique employed for the

single pipe problem (such as found in reference 3) in consistent units as follows

T-Tg

1=1 (x-aj^)^ + (y+d^)2

(4)

where = strength of the i-th heat source (if plus) or sink (if minus). It

is the total heat loss (if plus) or heat gain (if minus) of the i-th

pipe per unit length.

k3 = thermal conductivity of earth surrounding all the pipes.

aj[ and dj^ = coordinates of the center of the i-th pipe referring to an arbitrary origin of the coordinate system (x, -y) . If, for instance,

the coordinates were so chosen that X]^ = 0 and yi = -d]^, the

origin of the coordinates for the multiple pipe system would be

at the ground surface above the centerline of the first pipe.

By denoting the exterior radius of the k-th pipe as rj^, the pipe surface can be

expressed as

(x-ak)^ + (y+dj^)^ = r^^ . (5)

Or with the use of the polar coordinate system

X = a]j^ + r^ sin 6 (6)

y

= r^j^ cos 6 - dj^

where 9 is the angular position of a point on the surface around the k-th pipe

as shown in figure 3. Equations (5)/(6) represent a point on a circle of radius

rj^, the center of which is the line heat source of strength Btu/hr.ft. The

temperature of the point defined by (x, -y), however, would be influenced by

all the other m lines heat sources such as (i=l> 2, . . . m) and would vary

from point to point over the circle as a function of 0 . By substituting (6)

into (4), the surface temperature distribution for the k-th pipe can be obtained

as a function of 6 as follows: m

Tk (6) - Tg = 2 i=l ^ ^ (ak sin 9)^ + (r^^ cos e-d^^-d.^^

(3k "a^+r^ sin 9)^ + (r^ cos 9-dj^+d^^)^ ^ (7)

7
By denoting further that

^ki “K

^2 _ Aki 2

tan =

a, -a.

. ^k"^i

^ik = A-r dk+df

equation (7) becomes

Tk (0) - Tg = m

Z i=l

l?^k

( 8 )

4irkf

A

^ - 2A cos (9+C ) + 1 Zn

^ik ” 2Aj[k ^

(9)

Qv r — r^^k'i 1 Zn {1-4 Ji cos 0 + [

4iTks r^

With the assumption also that the circle represented by equations (5)/(6) is

the cross section of a pipe which is losing heat Q Btu/hr.ft at average surface

temperature one can approximate the value of by integrating with respect

to 6 as follows:

T -T = _L

k "g 2TT

M

2tt / (Tj^(0)-Tg) d0

(10)

4irk Z Qi Zn

S i=l '^ik 4iTkf tn (!^)'

Although this equation is consistent with the approximate solution for the case

of the single-pipe heat transfer (equation 2) if M = 1, it is not recommended

for the shallow large pipe problems where d]^^/r^ « 1.

By defining matrix elements Pi^k such a manner that

2 Plk = (~)

^ik

( 11 )

8
2d ^ Pkk = to (—

the values of , Q2

• • *Qm can now be obtained as a solution of the following

simultaneous equations

P12 ••• Pim'' ^Qi

' "ti - Tg'I

P2I P22 ••• P2M

• •

•

Q2 T2 - Tg

• •

PmI Pm2 ••• PmM

^ / Tm Tg

provided that the values of T]^ , T2 . . . are known.

The above equations are for bare steel pipe systems where the average exterior

pipe surface temperature may safely be approximated as equal to the pipe fluid

temperature

.

When the system includes non-metallic pipes or insulated pipes, the external

surface temperatures (pipe-earth Interface temperatures) T;[, T 2 ••• must

be calculated first. Assuming, for the time being, that the values of , T 2 .

. . are known as well as the pipe fluid temperatures, Tp][, Tp2 » »

the heat transfer from the pipes Q]^, A2 ••• Qm then be calculated by

Qk ~^k^"^Fk ~

"^k^ for k=l, 2, . . . .M (13)

where = is the heat transfer coefficient for the k-th pipe for use with

the thermal resistance between the pipe fluid and the external

radius of the pipe or the pipe insulation where it interfaces with

soil. The value of may be approximated by

1- = 1 1 to (!l.) + 1- to + J_ . Ck 2tt kji^ rj]^ kj^l^ rj^

(14)

In equation (14), kj and and k^pi^ are the thermal conductivities of insulation

and wall for the k-th pipe, whereas rj]^ and rj^j^ are the external radii of the

insulation and the wall, respectively.

The symbol hy refers to the heat transfer coefficient between the pipe fluid

and the pipe wall. The value of h^j is usually very high unless the pipe fluid

velocity is extremely small, and consequently the last term of equation (14) is

usually neglected.

9
By substituting equation (13) into (12) and rearranging the terms with respect

to the pipe average surface temperature T^, T 2 ... the following simultaneous

equations can be derived.

11 12 IM

P' P" ... P"

21 22 2M

p''

\ Ml M2

’** mm/

where

Pik =

Pkk =

^k P

4 irk S ^k^kk ^

4irks

^ Ti N

®2

% ,

(15)

M

^ Pik Tpk

k=l

The solution of (15) yields a set of pipe-soil interface temperatures , T2 ... Tjq, thus permitting the calculation of pipe heat transfer by equation (13).

When equation (15) is to be solved for the multiple pipe system where some of

the pipes are non-insulated steel pipes, fictitious insulation of arbitrary

thickness with thermal conductivity identical to the surrounding soil may be

assumed for the bare pipes. This procedure is necessary because the values of

Pi,k ®i meaningless otherwise.

®i = Tg +

4irk<

Computer programs have been developed during the course of this study to

implement this derivation for the multiple pipe system. The Fortran listing of

this program is included in Appendix B, which includes the life-cycle cost

analysis of pipe insulation. A sample case selected is illustrated in figures

4 and 5 with the results of the calculations given in figure 5 to show relative

effect between heat transfer and distance between pipes. The values in parentheses indicate percentage change from case 5, where each pipe is considered to

be a single separate pipe system.

10
Tf = PIPE TEMPERATURE

Tq = EARTH TEMPERATURE, ®F

ks = THERMAL CONDUCTIVITY OF EARTH

BTU/HR, Ft2, *F/IN

kj = THERMAL CONDUCTIVITY OF PIPE INSULATION

BTU/HR, Ft2^ ®F/IN

THREE- PIPE SYSTEM

Figure 4. Multiple-pipe system (insulated pipes).

11
43

”

CASE ^1

in

^2

in

h

Btu/hr , ft

^2

Btu/hr, ft

<^3 Btu/hr, ft

1 60 110 -17.89 (16)* -20.30 (72) 81.24 (2)

2 55 100 -18.15 (12) -21.46 (98; 81.57 (3)

3 55 90 -18.48 (14) -22.82 (111) 82.00 (3)

4 45 80 -18.89 (16) -24.46 (126) 82.55 (4)

5 -16.23 (0) -10.82 (0) 79.40 (0)

* percentage change from the single-pipe system.

Figure 5. Sample calculation for multiple-pipe system (insulated pipe).

12
2.3 PIPES IN AN UNDERGROUND CONDUIT (figure 6 )

When a group of pipes (some Insulated and others non-insulated) are installed

in the unvented underground conduit such as illustrated in figure 3, the

following heat balance equation in consistent units would approximate the

overall heat transfer process

X 2wrk Uk (Tju - Ta) = KCT^ - Tg)

k-1

where M = total number of pipes in the conduit

r]^ = outside radius of insulated or non-insulated pipes (k-th pipe)

Uk = overall heat transfer coefficient of the k-th pipe calculated

by the following formula

1 = "k +

1 Ur ^Ik

(17)

kiDk = thermal conductivity of the insulation around the k-th pipe

t|^ = thickness of the insulation around the k-th pipe

” outside surface heat transfer coefficient around the pipe (if no data

are available)

= temperature of the k-th pipe

= air temperature in the conduit

Tq = undisturbed ground temperature surrounding the conduit

K = overall heat transfer factor of the conduit calculated by

K

_1

2nkg

ko kn

iln ] + An [1 +

^ R

(18)

k0 = thermal conductivity of earth surrounding the conduit

R = outside radius of the conduit*

ky = effective thermal conductivity of the conduit wall

t = thickness of the conduit wall

d = depth of the conduit, distance between the ground surface and the

center-line of the conduit

In equation (17), the value of heat transfer coefficient of air space h^ is

not well known. For a concentric annular space, natural convection coefficient

such as determined by formula developed by Grigull and Hauf [5] may be used in

conjunction with standard radiation exchange formula. Figures 7 and 8 are obtained by such calculations.

In equations (17) and (18) the thermal resistance across the walls of the

metallic pipe and metallic conduit were neglected from the formulas. If the

metallic pipe or conduit is uninsulated, terms such as

* If the conduit is square in cross section instead of circular, equivalent

radius may be approximated by R = 0.56 W, where W is the external width of

the square conduit [ 2 ].

13
Figure 6. Pipes in a conduit.

14
18 -T

o

ocLU

U00

Q_

00

16

-3.0 Inner pipe temperature 250°F |12rC|

Outer pipe temperature 150°F (66°C|

-2.8 Emissivity of the annular surfaces 0.9

Inner pipe

diameter

-2.6 inches

14

12 -

10 -

8 -

1.5 2.0

AIR SPACE THICKNESS, cm

2-3/8”

Figure 7. Conduit air space heat transfer coefficient with respect to air

space thickness.

15
25

20

15

10

5

0

Btu/hft

Conduit air space heat transfer coefficient with respect to inner

pipe diameters.

16
Ti. , Ti kg

JL- in ( — —) or — »» (A) R-t

may be dropped for the uninsulated non-metallic pipes or conduit; the wall

thickness and its thermal conductivity value should be retained for the values

for t]^ and t, and kj^ and ky, respectively.

Solving for from equation (16) and rearranging it, the heat transfer from

k-th pipe in the conduit can be obtained as follows

Qk = 2’'ri,Uk(TFk-TA) . (W)

where

T

A

M

KTg + 2 2irrk

k=l

M

K + I Uk

k=l

(20)

If the conduit is ventilated and the ventilation mass flow rate is known to

be G, Ib/hr, equation (20) may be modified to yield

TA

M

E k=l

M

E k=l

“k + KTg

GC

2TTrkUk + -—P + K

L

where Cp = specific heat of air

Ty = the ventilation air temperature

L = total vented length of the conduit.

( 21 )

Data on ventilation rates for underground conduits are extremely scarce. Possible natural ventilation (without the wind effects) for a vented underground conduit system may be estimated as follows:

The theoretical natural draft APp, chimney effect, for an underground conduit

of d ft depth may be calculated by [6]

AP^ = 0.52 • Pg» d [1— - -i— ), inches of water

'^0 ^A

( 22 )

where

Pg = atmospheric pressure, psi

d = depth of the conduit, ft

Tq = absolute temperature of outdoor air, Rankine

= absolute temperature of conduit air, Rankine.

17
Also, the pressure drop AP^ of ventilation air flowing within an underground

conduit can be calculated by

AP. = (C. + C- + —)

• (——) (

2—) inches of water A ^ 1 o D 4005 0.075

(23)

where = entrance pressure loss coefficient

Cq = exit pressure loss coefficient

f = frictional pressure loss coefficient

L = length of the pipe between two consecutive vents along the pipe, ft

D = hydraulic diameter of the air passage within the conduit, ft

V = velocity of the air flow, ft/mln

p = density of the air within the conduit, Ib/ft^

By noting that the net ventilation flow G (Ib/hr) can be expressed by

where represents the cross sectional area for air passage within the conduit,

and by noting the fact that AP-j and AP^ should be equal, it is possible to write

For evaluation of G it is necessary to have data on Cj, Cq, and f. Moreover,

equation (21) requires calculation of the value of T^, conduit air temperature.

Thus, the process of estimating the air temperature in a vented conduit requires

iterative procedures which are cumbersome for manual calculation.

2.4 UNDERGROUND PIPE IN AN INSULATED TRENCH (figures 9 and 10)

In some installations, pipes are Installed in a trench and an insulating

material is poured over and around the pipes, as illustrated in figures 9 and

10. For the case of a single pipe system (fig. 9), a square region insulated

in the trench may be treated as an equivalent annular ring of exterior radius

0.56 W (Loudon [2]), whereby W denotes the exterior width of the insulated

region. The formulas and tables discussed in section 2.1 can then be used to

approximate the pipe heat transfer. For the case shown in figure 10, or the

multiple-pipe system, the computational method developed in section 2.2 can be

used if the insulated region is assumed to consist of two equivalent annular

zones such as shown by the dotted circles in figure 10. This assumption can be

expected to yield erroneous results if the distance(s) between the pipes is

(are) very small as compared with the total dimensions of the insulated zone. The precision can be improved, however, in the following manner. Repeat the

above calculation on the premise that uninsulated pipes are burled in soil

whose thermal properties are equal to those of the insulating material. The

actual pipe heat transfer value should lie between the two sets of values thus

calculated

.

G = 60 pVAc , (24)

G = 240300 (25)

18
GROUND SURFACE

Figure 9. Pipe in an insulated trench.

GROUND SURFACE

Figure 10. Two pipes in an insulated trench.

19
3. EARTH TEMPERATURE DATA

When evaluating underground pipe heat transfer, it is essential that the

temperature of the earth surrounding the pipe be known.

It has been customary when designing a heating pipe system to assume that the

earth temperature is equal to the well water temperature for any given region,

and that the well water temperature is close to the annual average air temperature. This concept appears reasonable as long as the annual average heat

transfer from the heat distribution system is what is desired to be estimated.

Moreover, well water temperature data, such as those compiled by Collins [7], are readily available for many localities in the United States. If, however,

the maximum heat loss or heat gain of the underground pipes is desired, the

well water temperature, which is the annual average earth temperature, is not

adequate [8]. This is because the majority of the underground pipes are installed at a depth less than 10 ft from the surface, where the seasonal

change of the ambient air temperature affects the heat transfer process.

Penrod's data [9] show, for instance, at a depth of 10 ft the temperature of

the earth at Lexington, Kentucky is at its minimum in April, approximately

50 °F, and at its maximum in October, approximately 65 °F. Thus, it is considered to be impractical to evaluate the maximum heat gain to a chilled water

pipe which was buried at a depth of 5 ft on the basis of the well water temperature, or on the annual average air temperature, which in this particular

example is 58 °F.

According to reference [8], the annual earth temperature cycle, T, of a given

thermal diffusivlty, a, may be approximated by a simple harmonic function such

as

where y

= depth

P = period of the annual cycle, 365 days

t = time in days

A = annual average earth temperature ~ well water temperature

B = amplitude of the earth surface temperature cycle

4) = phase angles of the earth temperature cycle relative to a datum

Reference [8] lists the values of A, B and (]) for various earth temperature

stations in the United States. While A and B depend on the monthly normal

temperature cycle of a given climatic region, the value of ({> is relatively

constant at 0.6 radians.

The thermal diffusivlty appearing in equation (26) is dependent upon the type

of soil and its moisture content, as shown, for example, in figure 11.

The average earth temperature, Tq, as used in previous discussions can be

evaluated by taking the integrated average of equation (26) to the depth of

cos [ (26)

point

20
THERMAL

DIFFUSIVITY

(ftVh)

Figure 11. Thermal diffusivity versus moisture content for several so

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

ils

.

21

THERMAL

DIFFUSIVITY

(mVtlay)
interest. The following equation yields an integrated value of T between

0 < y < 1

T = A - B

* ^ * cos (l!L t - 4) - (27)

P

-2x cos 3+1

232

X = e ^

l ~x*(cos 3+sln g) ~j l-x*(cos 3-sin 3)^^

Since the center-line depth for most underground pipes is at around 10 ft, the

Integrated average temperatures for A = 10 ft were obtained for many places in

the United States where the earth temperature records were maintained. The

results of this integration calculation are presented in Appendix A for

Winter (January 1), Spring (April 1), Summer (July 1) and Fall (October 1),

representing the seasonal average values. Reference [8] shows that the majority of the thermal diffusivity values deduced from the measured earth temperatures in the United States are in the neighborhood of 0.025 ft2/hr. Appendix A

was, therefore, obtained for a *= 0.025.

4. SAMPLE PROBLEMS AND SOLUTIONS

This section presents some typical heat transfer problems and solutions to

illustrate the use of the formulas and tables developed in section 2.

Evaluate the heat gain of a double pipe system (fig 12) —one pipe is for the

supply of 42 “F chilled water and another is for the return of 57 °F water.

These two pipes are bare steel pipes of 24-in diameter, and both are installed

at the depth of 72 in from the ground surface to the center lines of the pipes

and separated by a distance of 4 ft on center. Assume that the average undisturbed earth temperature around the pipe is 68 °F and the thermal conductivity

of the earth is 5 Btu - in/hr ft2 “F.

Solution

Setting the origin of the coordinate system to be as shown in figure 3, the

constants indicated in formulas (8) and (11) can be numerically evaluated as follows

where y

= 0, a2 = 4

dl = d2 = -6

ri = r2 = 1

22
= 160

1*12 1*21 iln (1^) = 0.440

2 Zn (^) = 0.949

Ti - Tg = 42 - 66 = -34

T2 - Tg = 57 - 66 = -9

The pipe heat transfer Q]^ and Q2 can then be solved from the following

simultaneous equation (12)

0.949 Qx + 0.440 Q2 = -34

0.440 Qx + 0.949 Q2 = -9

The solutions to these equations are

Qx = -26.6 Btu/hr ft

Q2 = 2.84 Btu/hr ft.

If these two pipes are separated at a distance so that each pipe is considered

a single pipe sytem, Qx would have been -25.3 Btu/hr ft and Q 2 = -9.48 Btu/hr

ft. It is interesting to observe that the supply chilled-water pipe, 42°F,

gains more heat by being in the vicinity of the return water pipe, 57 °F, and

the return water pipe actually loses heat instead of gaining it from the

warmer earth.

The total system heat gain for the double pipe system is, however, 23.76 Btu/hr

ft, much less than 34.76 Btu/hr ft had they been separated at a distance from

each other.

Thus, there is a definite advantage by installing the chilled-water lines near each other. The advantage will be offset, however, if the two pipes are too

close together, because then the supply water would be warmed up too much before

it reaches its destination, by gaining heat from the return pipe.

Figure 12 also includes a table showing the effect of distance on heat transfer

rates between the two pipes for values of 4 ft, 5 ft, 10 ft and Infinity, and

earth thermal conductivities of 10 and 5 Btu in/hr, ft^, °F.

23
CASE a 0| ^2

1 5’1 0 - 50.79 0.565

2 oo 1 0 - 50.57 - 18.96

3

4' 10 - 53.21 5.687

4 4 5 - 26.60 2.843

5 OO 5 - 25.29 -9.48

6 10 5 - 24.37 -5.11

Figure 12. Sample double-pipe problem.

24
5 . SUMMARY

Calculation methods were developed with sample problems as well as with computer

program listings to approximate heat transfer of multiple pipe systems. Several

pipes of different temperatures, insulations, and sizes Installed in the same vicinity can be evaluated to study the heat transfer of each pipe affected by

its neighboring pipes.

Seasonal average earth temperature data (from surface to approximately 10 ft

depth) for underground piping distribution systems were developed for selected

stations in the United States and for the thermal diffusivity of earth of 0.025

ft^/hr. These data will permit the appraisal of the heat gain of chilled water

systems as well as the heat loss of the hot water or steam pipes.

6. REFERENCES

[1] Henderson, J. H., Economic Justification of Thermal Insulation of

Underground Chilled Water Piping, American Society for Heating, Refrigerating and Air Conditioning Engineers (ASHRAE), Symposium Bulletin of Chilled

Water Systems , January, 1970.

[2] Loudon, A. G., Heat Loss from Underground Heating Mains, Journal of

Institute for Heating and Ventilating Engineers (IHVE), London, November,

1957, pp. 196-203.

[3] Eckert, E. R. G., Heat and Mass Transfer , McGraw-Hill Book Company, 1959,

pp. 60-64.

[4] McAdams, W. H., Heat Transmission , McGraw-Hill Book Company, 1954, page 25.

[5] Grigull, U., and Hauf, Werner, National Convection in Horizontal

Cylindrical Annuli, Proceedings of the Third International Heat Transfer

Conference , American Institute of Chemical Engineers, 1966, pp 182-195.

[6] Handbook of Fundamentals, American Society of Heating, Refrigerating and

Air-Conditioning Engineers, 1967, page 406.

[7] Collins, W. D., Temperature of Water Available for Industrial Use in

the United States. U.S. Geological Survey, Water Supply Paper 520-F,

1925.

[8] Kusuda, T., and Achenbach, P. R. , Earth Temperature and Thermal

Diffusivity at Selected Stations in the United States. ASHRAE Transactions , Vol. 1, Part 1, 1965, and more detailed data in NBS Report 8972 of

the same title.

[9] Penrod, E. B., Variation of Soil Temperature at Lexington, Kentucky

from 1952-1956. University of Kentucky Engineering Experiment Station,

Bulletin No. 57, September 1960.

25
7. UNIT CONVERSION FACTOR

English units are used throughout the text because of the fact that this report

has been prepared for American practicing engineers and underground system

manufacturers. The conversion multipliers to SI units for the pertinent variables

are found as follows

Multiplier

thermal conductivity Btu-in/h» f t^* F to W/m»K = 0.144

pipe heat transfer factor Btu/h* f t*F to W/m»K = 1.728

heat transfer coefficient Btu/h»ft2» F to W/m2.K = 5.678

length ft to m = 0.3048

velocity f t/mln to m/ s = 0.00508

density Ib/min to kg/m^ = 16.03

pressure ln*H20 to Pa = 249

pressure psi to KPa = 6.89

temperature °F to °C = (F-32)/l

Rankine to kelvin = 0.556

thermal diffusivity ft2/h to m2 / day = 2.23

26
Table A

Illustrative Thermal Conductivities for Some Pipe Insulation Materials

Thermal Conductivity, kj

Btu/hr, ft2, °F/in

Temperature Level

Insulating Materials

50 °F 100 °F 200

Cellular Glass 0.38 0.42 0.48

Cork Board 0.27 0.29

Calcium Silicate 0.30 0.32 0.37

Expanded Polyurethane 0.16 0.18 0.21

Expanded Polystyrene 0.25 0.26

Mineral Fiber

(rock, slag, or glass)

0.22 0.24 0.29

Lightweight Concrete

(perlite, vermlculite,

etc . , 30 psf

)

0.9

Sawdust 0.48

Sand 2.1

300 °F

0.55

0.42

* Multiplier to obtain SI unit W/m»K is 0.144.

27
y
Appendix A. Earth Temperature Tables for Underground Heat-Distribution-System

Design

The following list presents the average earth temperature in deg F from 0 to

10 feet below the surface for the four seasons of the year and for the whole

year for the indicated locales. The temperatures were computed on the basis of

the method described in the 1965 ASHRAE technical paper entitled "Earth Temperature and Thermal Diffusivity at Selected Stations in the United States" by

T. Kusuda and P. R. Achenbach (in ASHRAE Transactions, Volume 71, Part I, p. 61,

1965) using the monthly average air temperatures published by the U.S. Weather

Bureau for the listed localities in the United States. Earth temperatures are expressed in Fahrenheit degrees.

Location Winter Spring Summer Autumn Annual

Alabama

Anniston AP^ 55. 58. 70. 67. 63.

Birmingham AP 54. 58. 71. 68. 63.

Mobile AP 61. 63. 74. 71. 67.

Mobile CO^ 61. 64. 75. 72. 68.

Montgomery AP 58. 61. 73. 70. 65.

Montgomery CO 59. 62. 74. 71. 66

.

Arizona

Bisbee COOP^ 55. 58. 70. 67. 62,

Flagstaff AP 35. 39. 54. 50. 45.

Ft Huachuca (proving

ground) 55. 58. 71. 68. 63.

Phoenix AP 60. 64. 79. 75. 69.

Phoenix CO 61. 65. 80. 76. 70.

Prescott AP 46. 49. 65. 61. 55.

Tucson AP 59. 62. 76. 73. 68.

Winslow AP 45. 49. 65. 61. 55.

Yuma AP 65. 69. 84. 80. 75.

Arkansas

Fort Smith AP 52. 56. 72. 68. 62.

Little Rock AP 53. 57. 72. 68. 62.

Texarkana AP 56. 60. 74. 71. 65.

California

Bakersfield AP 56. 60. 74. 70. 65.

Beaumont CO 53. 56. 67. 64. 60.

Bishop AP 47. 51. 65. 61. 56.

Blue Canyon AP 43. 46. 58 55. 50.

Burbank AP 58. 60. 68. 66

.

63.

^ AP = Airport Data

^ CO = City Office Data

^ COOP = Cooperative Weather Station

A-1
Location Winter Spring Summer Fall Annual

California

Eureka CO 50. 51. 54. 54. 52.

Fresno AP 54. 58. 68. 63.

Los Angeles AP 58. 59. 64. 63. 61.

Los Angeles CO 60. 61. 68. 66

.

64.

Mount Shasta CO 41. 44. 57. 54. 49.

Oakland AP 53. 54. 60. 59. 56.

Red Bluff AP 54. 58. 72. 69. 63.

Sacramento AP 53. 56. 67. 64. 60.

Sacramento CO 54. 57. 68. 65. 61.

Sandberg CO 47. 50. 63. 60. 55.

San Diego AP 59. 60. 66

.

65. 62.

San Francisco AP 53. 54. 59. 57. 56.

San Francisco CO 55. 55. 59. 58. 57.

San Jose COOP 55. 57. 64. 62. 59.

Santa Catalina AP 57. 58. 64. 62. 60.

Santa Maria AP 54. 55. 60. 59. 57.

Colorado

Alamosa AP 30. 35. 52. 48. 41.

Colorado Springs AP 39. 43. 59. 55. 49.

Denver AP 39. 43. 60. 56. 50.

Denver CO 41. 45. 61. 58. 51.

Grand Junction AP 39. 44. 65. 60. 52.

Pueblo AP 41. 45. 62. 58. 51.

Connecticut

Bridgeport AP 40. 44. 61. 57. 50.

Hartford AP 39. 43. 61. 57. 50.

Hartford AP (Brainer) 39. 43. 60. 56. 50.

New Haven AP 40. 44. 60. 56. 50.

Delaware

Wilmington AP 44. 48. 64. 60. 54.

Washington, D.C.

Washington AP 47. 51. 66

.

63. 56.

Washington CO 47. 51. 66. 63. 57.

Silver Hill OBS^^ 46. 50. 65. 61. 55.

Florida

Apalachicola CO 63. 65. 75. 73. 69.

Daytona Beach AP 65. 67. 75. 74. 70.

Fort Myers AP 70. 71. 78. 76. 74.

Jacksonville AP 63. 66

.

75. 73. 69.

Jacksonville CO 64. 66

.

76. 73. 70.

Key West AP 74. 75. 80. 79. 77.

Key West CO 75. 76. 81. 79. 78.

Lakeland CO 68. 69. 77. 75. 72.

A-2
Location Winter Spring Summer Fall Annual

Florida

Melbourne AP 68. 70. 77. 75. 72.

Miami AP 72. 74. 79. 78. 76.

Miami CO 72. 73. 78. 77. 75.

Miami Beach COOP 74. 75. 80. 78. 77.

Orlando AP 68. 70. 77. 75. 72.

Pensacola CO 62. 64

.

74. 72. 68.

Tallahassee AT 61. 64

.

74. 72. 68.

Tampa AP 68. 69. 77. 75. 72.

West Palm Beach 71. 73. 79. 77. 75.

Georgia

Albany AP 60. 63. 75. 72. 67.

Athens AP 54. 58. 71. 68. 63.

Atlanta AP 54. 57. 70. 67. 62.

Atlanta CO 54. 57. 70. 67. 62.

Augusta AP 56. 59. 72. 69. 64.

Columbus AP 56. 59. 72. 69. 64.

Macon AP 58. 61. 74. 71. 66.

Rome AP 53. 56. 70. 67, 61.

Savannah AP 60. 63. 74. 71. 67,

Thomasville CO 62. 64. 74. 72. 68,

Valdosta AP 61. 64. 74. 72. 68.

Idaho

Boise AP 40. 44. 62. 58. 51,

Idaho Falls 46 W 30. 35. 55. 50. 42.

Idaho Falls 42 NW 28. 33. 54. 49. 41.

Lewiston AP 42. 46. 63. 59. 52,

Pocatello AP 35. 40. 59. 55. 47,

Salmon CO 32. 37. 56. 52. 44,

Illinois

Cairo CO 49. 53. 70. 66

.

60.

Chicago AP 38. 43. 62. 57. 50.

Joliet AP 37. 42. 61. 56. 49.

Moline AP 38. 43. 62. 58. 50.

Peoria AP 39. 44. 63. 58. 51.

Springfield AP 41. 45. 64. 60. 52.

Springfield CO 43. 47. 66

.

62. 54.

Indiana

Evansville AP 47. 51. 67. 63. 57.

Fort Wayne AP 39. 43. 61. 57. 50.

Indianapolis AP 41. 46. 64. 59. 52.

Indianapolis CO 43. 48. 65. 61. 54.

South Bend AP 38. 42. 61. 56. 49.

Terre Haute AP 42. 47. 65. 60. 53.

A-3
Location Winter Spring Summer Fall Annual

Iowa

Burlington AP 39. 44. 64. 59. 51.

Charles City CO 33. 38. 60. 55. 46.

Davenport CO 39. 44. 64. 59. 51.

Des Moines AP 37. 42. 63. 58. 50.

Des Moines CO 38. 43. 64. 59. 51.

Dubuque AP 34. 39. 60. 55. 47.

Sioux City AP 35. 40. 62. 57. 49.

Waterloo AP 35. 40. 61. 56. 48.

Kansas

Concordia CO 42. 47. 67. 62. 54.

Dodge City AP 43. 48. 67. 62. 55.

Kansas

Goodland AP 38. 43. 62. 57. 50.

Topeka AP 43. 47. 66

.

62. 55.

Topeka CO 44. 49. 68. 63. 56.

Wichita AP 45. 50. 68. 64. 57.

Kentucky

Bowling Green AP 47. 51. 67. 63. 57.

Lexington AP 44. 48. 65. 61. 54.

Louisville AP 46. 50. 67. 63. 56.

Louisville CO 47. 51. 67. 64. 57.

Louisiana

Baton Rouge AP 61. 63. 74. 72. 67.

Burrwood CO 65. 67. 77. 74. 71.

Lake Charles AP 61. 64. 75. 73. 68.

New Orleans AP 63. 65. 75. 73. 69.

New Orleans CO 64. 66

.

77. 74. 70.

Shreveport AP 58. 61. 75. 72. 66.

Maine

Caribou AP 24. 29. 50. 45. 37.

Eastport CO 33. 37. 51. 48. 42.

Portland AP 33. 38. 56. 51. 44.

Maryland

Baltimore AP 45. 49. 65. 61. 55.

Baltimore CO 47. 51. 67. 63. 57.

Frederick AP 44. 48. 65. 61. 55.

Massachusetts

Boston AP 41. 44. 61. 57. 51.

Nantucket AP 41. 44. 57. 54. 49.

Pittsfield AP 34. 38. 55. 51. 44.

Worcester AP 36. 40. 58. 54. 47.

A-4
Location Winter Spring Summer Fall Annual

Michigan

Alpena CO 33. 37. 54. 50. 43.

Detroit Willow Run AP 38. 42. 60. 56. 49.

Detroit City AP 38. 43. 60. 56. 49.

Escanaba CO 30. 35. 53. 49. 42.

Michigan

Flint AP 36. 40. 58. 54. 47.

Grand Rapids AP 36. 40. 58. 54. 47.

Grand Rapids CO 38. 42. 60. 56. 49.

East Lansing CO 36. 40. 58. 54. 47.

Marquette CO 31. 35. 53. 49. 42.

Muskegon AP 36. 40. 57. 53. 47.

Sault Ste Marie AP 28. 32. 51. 47. 39.

Minnesota

Crookston COOP 25. 31. 55. 49. 40.

Duluth AP 25. 30. 52. 47. 38.

Duluth CO 26. 31. 52. 47. 39,

International Falls 22. 27. 51. 45. 36.

Minneapolis AP 32. 37. 60. 54. 46

.

Rochester AP 31. 36. 58. 53. 44.

Saint Cloud AP 28. 33. 56. 51. 42,

Saint Paul AP 32. 37. 60. 54. 46.

Mississippi

Jackson AP 57. 61. 73. 70. 65.

Meridian AP 57. 60. 72. 69. 64.

Vicksburg CO 58. 61. 74. 71. 66.

Missouri

Columbia AP 43. 48. 66. 62. 55.

Kansas City AP 44. 49. 68. 64. 56.

Saint Joseph AP 42. 47. 67. 62. 54.

Saint Louis AP 45. 49. 67. 63. 56.

Saint Louis CO 46. 50. 68. 64. 57.

Springfield AP 45. 49. 66. 62. 56.

Montana

Billings AP 35. 40. 59. 55. 47.

Butte AP 27. 31. 50. 45. 38.

Glasgow AP 27. 33. 56. 51. 42.

Glasgow CO 28. 34. 57. 52. 43.

Great Falls AP 34. 38. 56. 52. 45.

Havre CO 31. 36. 57. 52. 44.

Helena AP 31. 36. 55. 50. 43.

Helena CO 32. 36. 55. 50. 43.

Kalispell AP 32. 37. 54. 50. 43.

Miles City AP 32. 37. 59. 54. 45.

A-5
Location Winter Spring Summer Fall Annual

Montana

Missoula AP 33. 37. 56. 51. 44.

Nebraska

Grand Island AP 38. 43. 64. 59. 51.

Lincoln AP 39. 44. 64. 60. 52.

Lincoln CO University 40. 45. 65. 61. 53.

Norfolk AP 35. 40. 62. 57. 48.

North Platte AP 37. 42. 62. 57. 49.

Omaha AP 39. 44. 65. 60. 52.

Scottsbluff AP 36. 41. 60. 56. 48.

Valentine CO 35. 40. 61. 56. 48.

Nevada

Elko AP 34. 39. 57. 53. 46.

Ely AP 35. 39. 56. 52. 45.

Las Vegas AP 56. 60. 78. 74. 67.

Reno AP 40. 44. 58. 55. 49.

Tonopah 41. 45. 61. 57. 51.

Winnemucca AP 38. 42. 60. 56. 49.

New Hampshire

Concord AP 33. 38. 56. 52. 45.

Mt. Washington COOP 17. 21. 37. 33. 27.

New Jersey

Atlantic City CO 45. 49. 63. 60. 54.

Newark AP 43. 47. 63. 59. 53.

Trenton CO 43. 47. 64. 60. 53.

New Mexico

Albuquerque AP 46. 50. 67. 63. 57.

Clayton AP 43. 47. 63. 59. 53.

Raton AP 38. 42. 58. 54. 48.

Roswell AP 51. 54. 69. 66

.

60.

New York

Albany AP 36. 40. 59. 54. 47.

Albany CO 38. 43. 61. 56. 49.

Bear Mountain CO 38. 42. 59. 55. 48.

Binghamton AP 34. 38. 56. 52. 45.

Binghamton CO 38. 42. 59. 55. 48.

Buffalo AP 37. 41. 58. 54. 47.

New York AP (La Guardia) 44. 48. 64. 60. 54.

New York CO 44. 47. 63. 59. 53.

New York Central Park 44. 48. 64. 60. 54.

Oswego CO 36. 40. 58. 54. 47.

Rochester AP 37. 41. 58. 54. 47.

Schenectady COOP 35. 40. 59. 55. 47.

A-6
Location Winter Spring Summer Fall Annual

New York

Syracuse AP 38. 42. 60. 56. 49.

North Carolina

Asheville CO 48. 51. 64

.

61. 56.

Charlotte AP 52. 55. 69. 66

.

60.

Greensboro AP 49. 53. 67. 64. 58.

Hatteras CO 56. 59. 70. 68. 63.

Raleigh AP 51. 55. 69. 65. 60.

Raleigh CO 52. 56. 70. 66. 61.

Wilmington AP 56. 59. 71. 69. 64.

Winston Salem AP 50. 53. 67. 64. 58.

North Dakota

Bismarck AP 27. 33. 56. 51. 42.

Devils Lake CO 24. 29. 54. 48. 39.

Fargo AP 26. 32. 56. 50. 41.

Minot AP 25. 31. 54. 49. 39.

Williston CO 27. 33. 56. 50. 41.

Ohio

Akron-Canton AP 39. 43. 60. 56, 50.

Cincinnati AP 43. 47. 64. 60, 54.

Cincinnati CO 46. 50. 66

.

63. 56.

Cincinnati ABBE OBS 45. 49. 65. 61. 55.

Cleveland AP 40. 44. 61. 57. 51.

Cleveland CO 41. 45. 62. 58. 51.

Columbus AP 41. 46. 62. 59. 52.

Columbus CO 43. 47. 64. 60. 53.

Dayton AP 42. 46. 63. 59. 52.

Sandusky CO 41. 45. 62. 58. 51.

Toledo AP 38. 43. 60, 56. 49.

Youngstown AP 39. 43. 60. 56. 50.

Oklahoma

Oklahoma City AP 50. 54. 71. 67. 60.

Oklahoma City CO 50. 55. 71. 68. 61.

Tulsa AP 50. 54. 71. 67. 61.

Oregon

Astoria AP 47. 48. 56. 54. 51.

Baker CO 36. 40. 56. 52. 46.

Burns CO 36. 40. 58. 54. 47.

Eugene AP 46. 48. 59. 57. 52.

Meacham AP 34. 38. 52. 49. 43.

Medford AP 46. 49. 62. 59. 54,

Pendleton AP 42. 46. 63, 59. 53.

Portland AP 46. 49. 60, 57. 53.

Portland CO 48. 50. 61, 59. 55.

A-7
Location Winter Spring Summer Fall Annual

Oregon

Roseburg AP 47. 49. 60. 57. 53.

Roseburg CO 48. 51. 61. 59. 55.

Salem AP 46. 49. 60. 57. 53.

Sexton Summit 42. 44. 55. 52. 48.

Troutdale AP 45. 48. 59. 57. 52.

Pennsylvania

Allentown AP 40. 44. 62. 58, 51.

Erie AP 38. 42. 58. 55. 48.

Erie CO 40. 44. 60. 56. 50.

Harrisburg AP 43. 47. 63. 59. 53.

Park Place CO 36. 40. 57. 53. 46.

Philadelphia AP 44. 48. 64. 61. 54.

Philadelphia CO 46. 50. 66

.

62. 56.

Pittsburgh Allegheny 42. 46. 62. 58. 52.

Pittsburgh GRTR PITT 40. 44. 61. 57. 51.

Pittsburgh CO 44. 48. 64. 60. 54.

Reading CO 43. 47. 64. 60. 54.

Scranton CO 40. 44. 61. 57. 50.

Wilkes Barre-Scranton 39. 43. 60. 56. 49.

Williamsport AP 40. 44. 61. 57. 51.

Rhode Island

Block Island AP 41. 45. 59. 55. 50.

Providence AP 39. 43. 59. 56. 49.

Providence CO 41. 45. 62. 58. 51.

South Carolina

Charleston AP 58. 61. 72. 70. 65.

Charleston CO 60. 62. 74. 71. 67.

Columbia AP 56. 59. 72. 69. 64.

Columbia CO 57. 60. 72. 69. 64.

Florence AP 55. 59. 72. 69. 64.

Greenville AP 53. 56. 69. 66

.

61.

Spartanburg AP 53. 56. 70. 66

.

61.

South Dakota

Huron AP 31. 37 60. 55. 46.

Rapid City AP 34. 39. 58. 54. 46.

Sioux Falls AP 32. 37. 60. 55. 46.

Tennessee

Bristol AP 48. 51. 65. 62. 56.

Chattanooga AP 51. 55. 69. 65. 60.

Knoxville AP 50. 54. 68. 65. 59.

Memphis AP 52. 56. 71. 68. 62.

Memphis CO 53. 57. 72. 68. 62.

Nashville AP 51. 54. 69. 66

.

60.

A-8
Location Winter Spring Summer Fall Annual

Tennessee

Oak Ridge CO 49.

Oak Ridge 8 S 49.

Texas

Abilene AP 55.

Amarillo AP 47.

Austin AP 60.

Big Springs AP 56.

Brownsville AP 68.

Corpus Chrlstl AP 65.

Dallas AP 57.

Del Rio AP 62.

El Paso AP 54.

Fort Worth AP (Amon

Carter) 57.

Galveston AP 63.

Galveston CO 63.

Houston AP 62.

Houston CO 63.

Laredo AP 67.

Lubbock AP 50.

Midland AP 55.

Palestine CO 58.

Port Arthur AP 61.

Port Arthur CO 63.

San Angelo AP 58.

San Antonio AP 61.

Victoria AP 64.

Waco AP 58.

Wichita Falls AP 53.

Utah

Blandlng CO 39.

Milford AP 37.

Salt Lake City AP 40.

Salt Lake City CO 41.

Vermont

Burlington AP 32.

Virginia

Cape Henry CO 51.

Lynchburg AP 48.

Norfolk AP 51.

Norfolk CO 52.

Richmond AP 48

.

Richmond CO 50.

Roanoke AP 48

.

52. 67. 64. 58

52. 67. 64

.

58

58. 73. 70. 64

50. 67. 63. 57

63. 76. 73. 68

59. 74. 70. 65

70. 79. 77. 74

68. 78. 76. 72

61. 76. 72. 66

65. 77. 75. 70

58. 72. 69. 63

60. 75. 72. 66

66

.

77. 74. 70

66

.

77. 74. 70

65. 76. 73. 69

66. 77. 74. 70

70. 81. 79. 74

54. 69. 65. 59

59. 73. 70. 64

62. 74. 71. 66

64. 75. 72. 68

65. 76. 74. 69

61. 74. 71. 66

64. 77. 74. 69

67. 78. 76. 71

62. 76. 73. 67

57. 73. 69. 63

43. 60. 56, 50

42. 61. 56. 49

44. 63. 59. 51

46. 65. 60. 53

37. 57. 52. 44

55. 68. 65. 60

51. 66

.

62. 57

54. 68. 64. 59

56. 69. 66. 61

52. 67. 63. 58

53. 68. 64. 59

51. 66

.

62. 57

A-9
Location Spring Fall Annual

Washington

Ellensburg AP 37. 41. 59. 55. 48.

Kelso AP 45. 47. 57. 54. 51.

North Head L H RESVN 47. 49. 54. 53. 51.

Olympia AP 44. 46. 56. 54. 50.

Omak 2 mi N W 36. 40. 59. 55. 47.

Port Angeles AP 45. 46

.

53. 52. 49.

Seattle AP (Boeing Field) 46. 48. 58. 56. 52.

Seattle CO 47. 50. 59. 57. 53.

Seattle-Tacoma AP 44. 47. 57. 55. 51.

Spokane AP 37. 41. 58. 54. 47.

Stampede Pass 32. 35. 48. 45. 40.

Tacoma CO 46. 48. 58. 55. 52.

Tattosh Island CO 46. 47. 52. 51. 49.

Walla Walla CO 44. 48. 65. 61. 54.

Yakima AP 40. 44. 61. 57. 50.

West Virginia

Charleston AP 47. 50. 65. 61. 56.

Elkins AP 41. 45. 59. 56. 50.

Huntington CO 48. 52. 67. 63. 57.

Parkersburg CO 45. 49. 65. 61. 55.

Petersburg CO 44. 48. 63. 60. 54.

Wisconsin

Green Bay AP 31. 36. 56. 51. 44.

La Crosse AP 32. 38. 60. 55. 46.

Madison AP 34. 39. 59. 54. 47.

Madison CO 34. 39. 60. 55. 47.

Milwaukee AP 35. 40. 58. 54. 47.

Milwaukee CO 36. 41. 59. 55. 48.

Wyoming

Casper AP 34. 38. 57. 52. 45.

Cheyenne AP 35. 39. 55. 51. 45.

Lander AP 31. 35. 56. 51. 43.

Rock Springs AP 31. 35. 54. 50. 42.

Sheridan AP 33. 37. 56. 52. 44.

Hawaii

Hilo AP 72. 72. 74. 74. 73.

Honolulu AP 74. 75. 77. 77. 76.

Honolulu CO 74. 74. 77. 76. 75.

Lihue AP 72. 73. 76. 75. 74.

Alaska

Anchorage AP 25. 29. 46. 42. 35.

Annette AP 40. 42. 51. 49. 46.

Barrow AP 4. 7. 16. 14. 10.

A-10
ocation Spring Summer Fall Annual

Alaska

Bethel AP 18.

Cold Bay AP 33.

Cordova AP 32.

Fairbanks AP 14.

Galena AP 13.

Gambell AP 15.

Juneau AP 34.

Juneau CO 36.

King Salmon AP 25.

Kotzebue AP 10.

McGrath AP 14.

Nome AP 16.

Northway AP 12.

Saint Paul Island AP 31.

Yakutat AP 33

.

West Indies

Ponce Santa Isabel AP 75.

San Juan AP 77.

San Juan CO 77

.

Swan Island 80.

Virgin Islands

St. Croix, V.I. AP 78.

Pacific Islands

Canton Island AP 83.

Koror 81.

Ponape Island AP 81.

Truk Moen Island 81.

Wake Island AP 79.

Yap 81.

23. 41. 37. 30

35. 43. 41. 38

35. 45. 43, 39

19. 38. 34. 26

18. 37. 33. 25

19. 34. 30. 24

36. 47. 45. 41

39. 49. 46

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42

28. 44. 40. 34

14. 31. 27. 21

18. 37. 33. 25

20. 37. 33. 26

16. 32. 29. 22

32. 40. 38. 35

36. 45. 43. 39

76. 78. 78. 77

77. 79. 79. 78

77. 79. 79. 78

80. 82. 81. 81

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00 81. 80. 79

84. 84. 84. 84

81. 81. 81. 81

81. 81. 81. 81

81. 81. 81. 81

79. 81. 81. 80

81. 82. 82. 82

A-11

Appendix B. Computer Program Listing for Multiple Pipe Heat Transfer and

Economic Analysis

The attached computer program calculates pipe heat loss (heat gain) for an underground heat distribution system, for which up to fifteen different pipes

are buried. Each of the pipes covered in turn contains up to five inner pipes.

All the pipes could be either insulated or uninsulated. The uninsulated pipes

are considered to be insulated by material having the same thermal conductivity

as that of the surrounding soil. The economic analysis requires the energy cost

per million Btu's and capital cost in terms of dollar per linear foot of the

installed system. The life-cycle-cost calculation includes the effect of the

given discount rate and cost escalation rate. The program allows the determination of minimum life cycle cost with respect to the variation of insulation

thickness of one pipe, which may be the subject of major importance.

The following input data will have to be read on the interactive console in

response to the questions. The input data will be displayed on the console

for validation and correction (if necessary). The sequence of this interactive

operation is illustrated at the end of the program listing.

M; number of pipes in the trench

A: horizontal distance of each pipe from a reference pipe, inches

D; depth of each pipe, inches

R: external radius of the pipe (inclusive of insulation and air space if

applicable) , inches

KS: thermal conductivity of soil, Btu-in/hr.ft^ .°F

TG: ground temperature, °F

TPF: pipe fluid temperature, ®F

For each pipe the layer-by-layer data on

TH; thickness, inches

KI: thermal conducltivty , Btu-in/hr . f t^. °F

are required in the sequence of carrier pipe wall, insulation, air space, and

conduit wall.

The program would output at this point

C: thermal conductance of each pipe, Btu/hr.ft. F

TP; pipe/soil interface temperature, °F

Q: heat loss/gain from each pipe, Btu/hr, ft

QP: heat loss/gain from each pipe when all the pipes are completely insolated

from each other, Btu/hr, ft.

If the cost calculation is required, the following input must be provided:

B-1
pipe cost in terms of $/ft installed

cost of heat in terms of $/million Btu

total pipe length, ft

annual interest rate, %

price escalation rate, %

the terms of payment in years.

The program would output the percent-worth factor, pipe cost, heat cost and

total cost.

If the optimization analysis is required for the insulation thickness for one

of the pipes, that particular pipe should be identified. Five steps of insulation thickness, thermal conductivity, and corresponding incremented cost

(installed cost) are then inputted to observe the total cost profile, which

will in turn provide the optimum insulation thickness.

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.-20
NBS«n4A (REV. 2<-60) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. PubI ication Date

NBSIR 81 2378 November 1981

4. TITLE AND SUBTITLE

HEAT TRANSFER ANALYSIS OF UNDERGROUND HEAT AND CHILLED-WATER DISTRIBUTION SYSTEMS

AUTHOR(S)

T . Kusuda

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESSrStreeL City, Stotf, ZIP) _ _

fj’-j- j^_g 0j-Yic 6 S I Naval Facllitlss Engrg. Council, USN, wasnington, DC ZUiyo

Directorate of Civil Engrg., USAF, Washington, DC 20330

Office of Chief of Engrs., U.S. Army, Washington, DC 20304

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here) Simplified calculation procedures for determining heat exchange between the earth

and a multiplicity of buried pipes having different temperature and thermal insulation

are presented. The procedures deal with cases where pipes are buried side by side, as well as those when several pipes are bundled in a conduit. The effects of seasonal

variation of earth temperature are treated in a quasi-steady-state equation that

includes the soil thermal properties, depth of burial, pipe sizes, and relative

locations of pipes. Sample calculations are included, together with the Fortran

program listing and thermal properties of earth to be used for the calculations.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

computer program; earth temperature; heat transfer; pipes; thermal insulation;

thermal properties; underground systems.

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

Uni imited

1 1 For Official Distribution. Do Not Release to NTIS 62

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. 15. Price

Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $8.00

USCOMM-DC 6043-P80
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