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FEASIBILITY STUDY OF THE UTILIZATION OF THERMAL
DISCHARGES FOR THE REARING 0F CATFISH

mesis for the Degree of M. S.
MICHIGAN STATE UNIVERSITY
LARRY PHILLIP WALKER
1975

 

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0C C)
.52.. ' ABSTRACT

(gjx FEASIBILITY STUDY OF THE UTILIZATION OF
THERMAL DISCHARGES FOR THE
REARING OF CATFISH

BY
Larry Phillip Walker

The subject of utilization of waste heat from
electric power plants in agriculture has recently
received considerable attention. Several research groups
are investigating the economical uses of thermal dis-
charge under a variety of conditions. This study is an
investigation of the use of thermal discharge for the
production of catfish under Michigan conditions.

This study explores the economic and environ-
mental incentives for using thermal discharge for the
rearing of catfish. It examines some of the constraints
in the construction of a biological System which is
dependent on the operation of a traditional industrial
system.

A computer model for catfish growth is developed.
In addition, a turbulent mixed pond is modeled to pre-

dict ambient temperature of the catfish environment in

Larry Phillip Walker

response to Michigan meteorological conditions. The two
models are used to simulate the growth of catfish over

one growing season.

    

Approved . - C / —

Major Professor 2: é_7§"

Approved 15: {2 ma

Department Chairman

FEASIBILITY STUDY OF THE UTILIZATION OF
THERMAL DISCHARGES FOR THE

REARING OF CATFISH

BY

Larry Phillip Walker

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1975

To
Joe and Christina Fowlkes
and

Empherus Jeffery

ii

ACKNOWLEDGMENTS

Every man must seek out his own predilection in
life. In his never-ending search he will cross the path
of many individuals whose encouragement and guidance
shall enhance his perception of what lies ahead.

In my journey I was fortunate to meet Dr. F. W.
Bakker-Arkema. His wisdom, encouragement and friendship
has helped me overcome some of the obstacles on this leg
of the journey. I would also like to thank the faculty
and staff of the Agricultural Engineering Department and
countless others who have contributed to my personal and
intellectual growth. Last, but not least, I would like
to thank Consumer Power Company of Michigan and Detroit

Edison for their financial support.

iii

LIST

LIST

LIST

I.

II.

III.

IV.

V.

VI.

TABLE OF CONTENTS

OF TABLES . . . . . . . .
OF FIGURES . . . . . . . .

OF SYMBOLS . . . . . . . .

INTRODUCTION . . . . . . .
FEASIBILITY EVALUATION . . .
A. Historical Development . .
B. Incentives . . . . . .
C. System Constraints . . .
D. Growth . . . . . . .
E. Calculating Water Temperature
MATHEMATICAL MODELS . . . .

A. Growth Model . . . . .
B. Pond Model . . . . . .

RESULTS AND DISCUSSION . . .
SUMMARY AND CONCLUSIONS . . .

RECOMMENDATIONS . . . . . .

REFERENCES . . . . . . . . .

APPENDIX C O O C O O O O O 9

iv

Page

vi

viii

b

NH
OSI-‘mxlb

28
37

50
58
59

60

64

LIST OF TABLES

Table Page

1. Estimated acreage devoted to catfish
farming and value of production . . . . 5

2. Instantaneous relative growth rates and
tests for differences (Tyler, 1972) . . 20

3. Details of weight gain, food consumption,
and food conversion efficiency at .
100 days and 240 days (Tyler, 1972) . . 21

4. Water quality data during the 13-to-16 week
period of catfish production (Andrews,
1971) . . . . . . . . . . . . 25

5. Meteorological condition, equilibrium
temperature, thermal exchange coef-
ficient, and heat input needed to
maintain the pond at the specified
temperature . . . . . . . . . . 51

LIST OF FIGURES

Figure Page

1. Plot of catfish production from 1960 to
1975 in units of a million pounds . . . 6

2. Curves of average lengths of 40-day-old
guppies in l/4 strength sea water at
various temperatures (weatherley,
1972) . . . . . . . . . . . . 13

3. Gross efficiency of food conversion in
relation to temperature and ration,
drawn as isoPIeths overlying the
growth curves (Brett, 1969) . . . . . 14

4. The relationship between environmental
temperature and average percentage gain
in 12 weeks of channel catfish finger-
1ings fed at three feeding rates
(Andrews, 1972) . . . . . . . . . 16

5. The relationship between environmental
temperature and food conversion ratio
(9 feed/ 9 gain) for channel catfish
fed at three feeding rates (Andrews,
1972) . . . . . . . . . . . . l7

6. Combined effects of temperature and photo-
period on food conversion efficiency
of channel catfish (Kilambi, 1971) . . . 19

7. The relations between stocking rates and
average weight per fish for each water
turnover rate (Andrews, 1971) . . . . 22

8. The relations between stocking rates and
average biomass (grams per cubic foot)
for three water exchange rates
(Andrews, 1971) . . . . . . . . . 23

9. Relations between stocking rates and food
conversion ratios (grams of feed per
gram of gain) for three water turnover
rates (Andrews, 1971) . . . . . . . 24

vi

Figure Page
10. Catfish growth causal loop diagram . . . 31
11. Catfish growth block diagram . . . . . 32

12. Plot of growth with a growth rate that
decreases exponentially . . . . . . 33

13. Flow chart of subroutine design to solve
a system of 3 equations and
3 unknowns . . . . . . . . . . . 49

14. Graph of air temperature and deWpoint
temperature over a 12 month period . . . 52

15. Plot of the thermal exchange coefficient
over a 12 month period . . . . . . . 53

16. Heat input from power plant needed to
maintain the fish pond at the optimal
temperature for growth . . . . . . . 55

17. Growth of catfish at 4 percent feeding
rate . . . . . . . . . . . . . 56

18. Growth of catfish at 6 percent feeding
rate . . . . . . . . . . . . . 57

vii

Har

br

81'

I'd t" 73 III Cl:

06 I-3 *3

LIST OF SYMBOLS

absolute temperature, °R

constant in Bowen ratio, in.-Hg-°F-l
atmOSpheric vapor pressure, in. Hg

saturation vapor pressure of water at the
temperatures of the water surface, in. H9

a general function of wind velocity and surface
phenomenon

rate<xflong-wave atmospheric radiation
rate of conductive heat transfer

net rate of heat exchange between the air and
water surface

rate of absorbed radiation (the total net
contribution to the energy of the pond), Btu
ft'2 day"l

rate of evaporative heat transfer

rate of reflected long-wave atmospheric
radiation

rate of long-wave radiation from the water

rate of reflected radiation

2 -1

thermal exchange coefficient, Btu Day ft- °F

heat of vaporization, Btu 1b-1
p0pu1ation density
temperature of fish environment, °C

air temperature, °F

dew point temperature, °F

viii

I-J

2 CI I-i

equilibrium temperature, °F
surface temperature, °F
wind velocity, miles hr-l
weight, grams

emissivity of water

proportional rate of growth

Stefan Boltzman constant, Btu ft-

ix

2

day

-l

°R

-4

I. INTRODUCTION

Society is currently confronted with an energy
problem that is affecting all aspects of American life.
It is a problem that finds its origin in an economic
philosophy which does not recognize that resources are
limited and that there are constraints on growth.. If
society is to survive this period of time it must begin
to manage resources and wastes more effectively. There
is a need to squeeze as much energy as possible from
resources and to recycle waste.

The world electrical generating capacity for
the period 1955-1967 increased at an average rate of
about eight percent per year, and thus has a doubling
period of 8.7 years (Hubbert, 1973). In order to meet
this increasing demand for electrical power, large
quantitiescflfcoal, oil and natural gas are required.
Presently, electrical power facilities are about 40 per-
cent efficient. This means that 60 percent of the
initial heat released is dissipated to the environment.
Power plants require large volumes of condenser cooling
water to carry waste heat to the receiving waters of
the locale. A typical 40 percent efficient fossil fuel

plant requires 9,000 Btu per kilowatt-hour of electricity

and discharges 4,237 Btu of waste heat to the environ-
ment. Currently, a nuclear power plant Operating at a
33 percent efficiency with a heat rate of 10,342 Btu
per kilowatt-hour discharges 6,400 Btu of waste heat,
or nearly 50 percent more heat than a fossil-fuel plant
(Wolf, 1973).

With the awakening of the nation to conscious-
ness of the environment and the advent of the energy
crises, power companies and researchers have been
searching for beneficial uses of thermal discharges.
Boersma and Rykbost (1970) proposed an integrated system
for management of thermal discharge from a steam electric
generating station. His industrial agricultural complex
has the following components: (1) a power generating
facility, (2) a cooling cycle with a soil warming loop
and an evaporative basin loop, (3) a processing plant,
and (4) an animal rearing facility. Michigan State
University on January 1, 1974, initiated an investigation
on waste heat utilization in agriculture. The components
of the integrated system are (1) fish growth, (2) crop
growth, (3) weather, (4) soil warming, (5) water reser-
voir, (6) greenhouse, (7) warm water irrigation, and

(8) grain drying.

The purpose of this thesis is to determine the
feasibility of using thermal discharge for the rearing
of catfish. The investigation consists of two parts:
(1) an examination of incentives, system operating con-
straint, growth of fish and a study of the response of
water temperature to weather conditions, and (2) the
development of computer models to simulate growth
response of catfish to water temperature and a model to
predict the response of water temperature to meteoro-

logical conditions.

II. FEASIBILITY EVALUATION

A. Historical Development

 

Aquaculture, the growing and husbandry of fresh
water fish, is one of the oldest types of agriculture.
Its origin can be traced back to Ancient China at about
2000 B.C. Under the Chinese, aquaculture flourished
and developed into a science (Hickling, 1962). Carp
rearing dominated the earlier efforts at aquaculture.

It was adaptable to pond culture and was preferred as
a food fish (TVA, 1971).

Aquaculture was introduced into the United
States by the early immigrants from Europe. The first
hatcheries were established to supplement the produc-
tion of game fish and focused mostly on trout production.
Following World War II, the demand for minnows continued
to increase and resulted in increased farm pond and
reservoir construction. Much of these efforts at fish
farming failed because (1) producers were not experi-
enced in fish culture, (2) pond construction was poor,
or (3) fish species were improperly chosen (Bureau of
Sport Fisheries, 1970).

From 1960 to 1970, interest in high density
raceway fish production increased, with research projects
initiated in many areas of the United States (Table 1

4

TABLE 1.--Estimated acreage devoted to catfish farming
and value of production.

 

 

Year Acres Miitiggezgzgds Appsgftgate
(Million $)
1960 400 0.3 0.1
1961 500 0.4 0.2
1962 1,000 1.0 0.4
1963 2,500 2.5 1.0
.1964 4,000 4.0 1.6
1965 7,000 7.0 2.8
1966 10,000 11.0 4.4
1967 15,000 16.5 6.6
1968 30,000 33.0 13.2
1969 40,000 44.0 17.6
1970 45,000 54.0 18.9
1975 75,000 112.5 40.0

 

(TVA, 1971.)

Figure 1). One area of recent interest is the use of
thermal discharge to provide the thermal environment
for catfish. Experimentation is continuing at several
facilities, both in the United States and abroad (The
Commercial Fish Farmer, 1974). The beneficial effects
of heated surface water are based on water being too
cold for Optimum growth and food conversion rates of

fish during much of the year (Strawn, 1970).

125 N

100 ‘

50 .

Million Pounds (Undressed)

25

 

A

A l
U I f

 

1960 1965 1970 1975

Year

Figure 1. Plot of catfish production from 1960 to 1975
in units of million pounds.

B. Incentives

 

There are two primary incentives for utilization
of waste heat in the rearing of catfish: (l) dissipa-
tion of heat through convective and evaporative heat
transfer at the water surface, and (2) providing the
thermal environment for optimal growth. Several other
incentives that make catfish farming a productive
endeavor are (TVA, 1971):

l. Properly managed, farm-raised catfish has
excellent flavor. It is a nutritious food, high in
vitamins, minerals and proteins.

2. The supply and quality of intensive farm
culture catfish offer better opportunities to keep pro-
duction and market opportunities in phase than the
unpredictable commercial catch of wild fish.

3. Current and future demand prosPects for
catfish appear strong. The number of consumers and
consumer incomes are increasing.

4. The catch of wild catfish in the United
States is expected to remain at about its present level
or to decline.

5. The sport fishing aspect of catfish produc-
tion--fish-out pounds--may become even more significant
when the general public recognizes what these businesses

have to offer.

6. At the present stage of development, catfish
compares quite favorably with broilers under high-level
management at the rate of about 1.5 lbs. of feed/lb. of
fish vs. broilers at 2.3 lbs. of feed/lb. of meat.

At a price of $160/ton for catfish feed and $100/ton
for broiler feed, this gives a feed cost of 12¢ for a
pound of catfish and 11.5¢ for a pound of broiler.

Though catfish are important to sport and com-
mercial fisheries as far north as Iowa, and markets for
catfish exist in all major northern cities, the southern
states will probably continue to dominate catfish cul-
ture in the United States due to the longer growing
season in that part of the country (Bardach, 1973).
However, if this investigation proves successful, cat-
fish rearing in Michigan could have an impact on the
local market. One factor which may help in the devel-
0pment of local markets is advertisement. In certain
parts of the country, advertising has improved the
image of catfish. It can be beneficial in influencing
people who are repelled by the "whiskey" appearance of
catfish or who consider this species a scavenger and

thus unfit for human consumption (Bardach, 1973).

C. System Constraints
The interfacing of a biological system with a
traditional industrial system requires a careful examina-

tion of the plant operating charateristics and biological

constraints. This is particularly true when the
operating characteristic of one system cannot be changed
to favor the other system or where the adaptability of
one of the two is marginal. In the proposed system the
operating characteristics<xfthe power plant will not

be changed in favor of the aquaculture system.

Power plants and industrial systems are forced
to shut down for equipment failure and maintenance dur-
ing certain days of the year. Some of the maintenance
and repair work will be scheduled. However, equipment
failure can occur unexpectedly during a period when
the aquaculture system is dependent on the operation of
the power plant. Mayo (1974) investigated the possi-
bility of using thermal discharge for commercial fish-
eries and developed the following list of scheduled
shutdown and Operating constraints:

1. Twice each year the power plant shuts

down for three days, around January 1
and July 1.

2. Once each year the plant can be expected
to shut down for a week with only a
brief (30 minute) forewarning.

3. Once in 10 years it will shut down for
a month with only a brief (30 minute)
forewarning.

4. The owner of the aquaculture system can-

not expect the power company to change

the Operating conditions to favor the
system.

10

To prevent major fish losses due to plant shutdown, it
is suggested that auxiliary heat be built into the pro-
posed system and be readily available.

Chlorination of condenser water to control pH
and biological growth is another operating constraint.
Chlorine is added intermittently to the circulating
water to control biological growth that may foul the
heat transfer surfaces in the condenser. An estimated
780,000 pounds of chlorine per year is added for slime
and for biological growth control in a 1160 megawatt
plant (Detroit Edison, 1973). The tolerance of fish
to chemical treatment of the intake water and the
uptake of radionuclides by cultured fish species
impose other constraints on the production and mar-
keting of fish (Coutant, 1970).

The temperature and chemistry of the water
supply is crucial to the successful Operation of an
aquaculture system. Channel catfish suffer no ill
effects in the pH range from 5 to 8.5 and the range of
6.3 to 7.5 is considered Optimal; a pH over 9.5 is
likely to be lethal (Bardach et al., 1973) . The complex
relationship between temperature, food utilization,
growth, metabolic rates and food waste production
imposes biological constraints on the system. Con-
centration of waste product increases directly with

population densities and can be a particular problem

11

in a high density system. Associated with the waste
production is the problem of oxygen depletion. Both
problems can be alleviated by increasing the exchange
rate. The oxygen depletion problem can further be
compensated by employing a sprayer system to capture
oxygen from the air and which has the added feature of

enhancing the heat dissipation of the pond.

D. Growth

 

One of the earliest comprehensive studies of
the phenomenon of growth was done by Minot (1908). His
study on growth was based on observaton and empirical
data. The general equation describing growth of an
organism is an exponential of the form (Medawar, 1945):

w = w0 erIt) (1)

aloge

‘3?"' W

Kf(t) (2)

or

where Kf(t) is a positive quantity such that f(t)
decreases with t, and af(t)/3t increases with t toward
a zero bound. Equation (2) is based on,a set of five
laws derived from experimental observation. Medawar
(1945) developed a set of axioms to explain mammalian
growth:

1. Size is an increasing function of
age.

12
2. The product of biological growth is
itself, typically, capable of growing.

3. In a constant environment, growth pro-
ceeds with uniform velocity.

4. The specific acceleration is always
negative. (The Specific growth rate
always falls.)

5. The specific growth rate declines more
slowly as the organism increases in age.

Brown (1957) carried out an intensive investiga-
tion of Medawar's axioms and their application to the
growth response of fish. Axioms 1, 2, and 3 were in
agreement with experimental observation. However, the
fourth and fifth axioms should be applied to fish growth
with considerable qualification. Most species of fish
display cyclical changes in growth, having periods of
rapid and slow growth (Brown, 1957). However, if
growth rates are calculated in the same cycle, both laws
4 and 5 are in agreement with experimental data.

If growth is unrestrained and exponential, the
instantaneous specific rate of growth would be constant.
Thus,

Limit 1 w _
[st->0 [w [—11] — K (a constant) (3)

Observation and empirical data indicate that K is not
a constant but decreases exponentially with age.
Temperature strongly influences the growth rate

of fish (Figures 2 and 3). The growth rate as a

lENGTH (mm)

I3

—I
N

d
d

5

13

SEA WATER

 

 

1 ‘ 1 1 L 4 J

20 22 21 2o 28 30 32
tween/nuns PC)

Figure 2. Curves of average lengths of 40-
day-old guppies in 1/4 strength sea water
at various temperatures. (Weatherley,1972)

SPECIFIC GROWTH RATE - ‘l. WEIGHT IOoy

l4

 

 

1
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LETML TEMPERATURE

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TEMPERATURE - C

Figure 3. Gross efficiency of food conversion
in relation to temperature and ration, drawn

as isopleths overlying the growth curves
(Brett et al., 1969).

15

function of temperature follows a parabolic-shape
curve, which rises to an optimal temperature'and then
begins to fall off. In Figure 3, each of the curves
represents growth rate as a function of temperature

at a different feeding rate. As mentioned earlier, the
growth rate decreases with time resulting in a cor-
responding flattening of the growth rate curves and
approaching the minimum growth rate for aged fish
(Brett et al., 1969).

Several studies have been conducted on growth,
digestion, and metabolism in channel catfish, but few
quantitative data are available on the interaction between
feeding rates, temperature, growth, food conversion and
body composition (Andrews and Stickney, 1972). An
examination of Figure 4 indicates that optimal growth
of channel catfish occurs in the interval of 26-34°C.
The maximum growth is achieved at a temperature of 30°C
and a feeding rate of six percent. In Figure 5, the food
conversion ratio is plotted against temperature. Again,
the optimum ratio is obtained in the interval between 22
and 30°C. Swift (1964) and Brett et a1. (1969) observed
similar growth response to temperature for the Windermen
char and sockeye salmon.

Kilambi et a1. (1971) investigated the influence
of temperature and photOperiod on growth, food consumption,

and conversion efficiency. It was observed that the

16

 

 

L FEEDING RATES
800 ‘ A 6 percent
0 4 percent
-h
. 2 percent
600 ..
2:
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n. 400
SI
13
4
200 "
II
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l 1 l J l
r I U I I
18 22 26 30 34

TEMPERATURE (°C)

Figure 4. - The relationship between environmental temperature and
average percentage gain in 12 weeks of channel catfish fingerlinga
fed at three feeding rates. Each point represents average values

from duplicate aquaria each containing twenty fish. (Andrews, 1972)

FOOD CONVERSION RATIO

12

10

17

FEEDING RATES

.I_ ; 6 percent
. 4 percent

0 2 percent

 

 

L
I

I.
c:

n
I l

18 22 26 30 34

TEMPERATURE

Figure 5. The relationship between environmental temper-
ature and food conversion ratio (9 feed/ 9 gain) for
channel catfish fed at three feeding rates. Each point
represents combined data from duplicate aquaria each
containing twenty fish (Andrews et al., 1972).

18

combined effects of temperature and photoperiod on food
consumption of channel catfish varied with time (Figure
6) .

Tyler and Kilambi (1972) determined the instanta-
neous relative growth rates of catfish (Table 2, page 20)
and expressed them as regression coefficients of equation
(1). In the first year Of the study, the fish under condi-
tions 25°C—total darkness and 30°C-16 hour photoperiod had
significantly larger growth rates in comparison to the
other test groups. In the second year, the fish under
25°C-total darkness condition again showed the greatest
growth followed by those under 30°C-8 hour conditions.
The growth rates of catfish in the rest of the experi-
ments were not significantly different.

Andrews et a1. (1971) carried out a series of
experiments on stocking rate and its influence on average
weight per catfish (Figure 7, page 22), average biomass
(Figure 8, page 23), and food conversion (Figure 9,
page 24). It was found that an increased water exchange
could offset the effect of an increased stocking rate.
The high biomass and excellent survival rates show that
channel catfish is well suited for high density culture.

One problem of high population densities and
temperatures is the growth of parasites and spread of
diseases. The Tennessee Valley Authority (TVA, 1973)

has provided a set of guidelines for disease control:

ESTIMATED FOOD CONVERSION EFFICIENCY

thONb

O)

 

19

28C
32c
26C

 

280

-....._-,.,,_..,:._---_--__,. 32c
"' ' 26c

 

_-a .............. 32C
"""‘ 250

326
260

o
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-O
'0
’0
’O u
. -
fl 9
“
O
C
.'
0"
0

I20 DAYS

90 DAYS

60 DAYS

30 DAYS

 

IO HOURS I4 HOURS

LIGHT

Figure 6. Combined effects of temperature and photo-

period on food conversion efficiency of channel cat-
fish.

20

TABLE 2.--Instantaneous relative growth rates and tests
for differences (Tyler, 1972).

 

Instantaneous Relative

Experimental Condition Growth Rate

 

 

Year 1
25C-Tota1 darkness 0.08381 *
30C-16 hr. 0.06684
25C-l6 hr. 0.03445
20C-Total darkness 0.03418
30C-8 hr. 0.03949
20C-l6 hr. 0.01716
Year 2
25C-Tota1 darkness 0.02698
30C-8 hr. 0.01558
30C-Tota1 darkness 0.00724
25C—(1/2) 8 hr. 0.00640
30C-Total darkness 0.00576
25C-(1/2) 8 hr. 0.00528
25C-8 hr. 0.00495
25C-16 hr. 0.00327
25C-8 hr. 0.00143
20C-8 hr. 0.00123
20C-Tota1 darkness 0.00111
20C-16 hr. 0.00038
30C-16 hr. 0.00025
20C-8 hr. -0.00113

 

 

*The values underscored by the same line are
not significatnly different.

21

 

 

 

 

 

 

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300

200

100

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\\\\\\‘

 

 

\\\\\\\\\\\\\

 

STOCKING RATE (FISH/CUBIC FOOT)

Figure 7. - The relations between stocking rates and average
weight per fish for each water turnover rate. Each bar re-
presents the average of two replicate groups. Ckndrews

et al., 1971)

(S/Cubic foot)

AVERAGE BIOMASS

1600

1200

800

400

23

HOURS/EXCHANGE

 

. W

 

 

 

 

 

 

 

2 4 6

STOCKING RATE (FISH/CUBIC FOOT)

Figure 8. The relations between stocking rates and average
biomass (grams per cubic fOot) for three water exchange
rates. Each bar represents the average values for two
groups (Andrews et al., 1971).

FOOD CONVERSION

3.0

2.5

2.0

24

WATER TURNOVER

A 2.5 hours/Iurnovor
. 8 hours/Iurnovor

 

 

 

 

.I 0 I2 hours/turnover
“——l
A :-
-I W'-
2 4 6

FISH / CUBIC FOOT

Figure 9. Relations between stocking rates
and food conversion ratios (grams of feed
per gram gain) for three water turnover
ratios. Each point represents the average
of two replicate groups (Andrews et al.,
1971).

25

.x0000 050800 :000xo u 000«

 

 

0.0 0 0.5 0.0 5.0 0.0 0.000
0.0 0 0.5 0.0 5.0 0.0 0.000

0.0 0 0.0 0.0 0.5 0.0 5.00

0.5 000 0.5 0.0 0.0 0 0.000

0.0 000 0.5 5.0 0.0 0 5.00

0.0 00 0.5 0.0 0.5 0 0.00

0.0 500 0.5 0.0 0.0 00 0.00

0.5 00 0.5 0.0 0.0 00 5.00

0.0 00 5.5 0.0 0.5 00 0.00

A5000 00>00 A0\0fiv A8000 0O>00 A5000 0O>00 A00>00050\mn5onv A000

O00x000 000000 h.000 000 0000EE¢ 0000xo 0509 0000£Oxm mm0EO0m
00000>¢ 00000>< 000HO>¢ 00000>¢ 0000300000 00000>¢

 

.x0nm0 ..00 pm mzmanmv

0000050000 0000000 00 000000 0003 00:00:00 000 000050 0000 0000050 0000311.0 00005

26

l. The major responsibility for disease
prevention and control will fall on the
facility operator.

2. A disease specialist should be available
in case a problem arises when the
facility operator needs assistance in
handling.

3. A prestocking check of external para-
sites at the site of the fingerling
vendor should be conducted.

4. The facility operator must keep a day-

to-day watch on the general condition of
the fish.

E. Calculating Water Temperature

 

The literature on the response of water pond
temperatures to meteorological and hydrodynamic influ-
ences is extensive. Several models have been examined
(Edinger et al., 1968; Linstrom and Boersma, 1973; Ding—
man, 1972; Goodman and Tucker, 1970) to determine which
one would be most apprOpriate for the present study to
predict the temperature in a body of water. The various
meteorological and hydrodynamic factors have to be exam-
ined to determine which factors should be considered and
which can be dropped, thereby simplifying substantially
the complexity of the model.

Hydrodynamic factors entering into the model
can be quite complex, requiring specification of inlet
and outlet geometry, water condition, geometry of the
pond, and wind direction. In addition, the conserva-

tion of mass and energy equations and the equation of

27

motion have to be solved in order to determine pre-
cisely how the warm water travels through the pond, how
it mixes and how much it is cooled in the process
(Littleton, 1970).

The flow in the pond can be assumed to be either
turbulently mixed or slug flow without turbulent mixing.
Slug flow is strongly influenced by the hydrodynamic
behavior of the pond. Because the surface temperature
is higher for the slug flow the cooling capacity is
greater. This is due to the fact that evaporation,
conduction and back radiation are greater at higher
temperatures. In a turbulently mixed pond, the tempera-
ture of the water is assumed to be approximately con-
stant in a horizontal plane as a result of horizontal

flow and mixing.

II I . MATHEMATICAL MODELS

A. Growth Model

 

In the feasiability evaluation it was stated
that the growth of catfish is not constant, but
decreases exponentially with time. Exponential growth
damped at an exponentially decreasing rate is charac-

terized by a set of differential equations (Laird et al.,

1965):
33.9 = —ow (4)
aw(t) _
—3:E— - 3W(t) (5)

where a is a constant and y is the proportional rate of

growth (a function of t). The initial conditions are

W(t) = W
and
Y = A
at t = 0. The solutions of the differential equation
become:
“Y t

I 3% = I -03t (6)
A 0

28

29

 

 

 

 

ln [%} = —0t (7)
Y = A Exp I-at] (8)
agét) = yW(t) = W(t) A Exp [-at] (9)
and
W(t) t
I 33%;; = I A Exp [-at]3t (10)
W0 0
1 W(t) _ A t
n W — - 5 Exp [-at] (11)
0 0
W(t) = W0 Exp [2’ I1 - Exp (-ont) I] (12)

The growth rate can be derived by substituting equation

(12) into equation (9):

aw t A
Bé ) = W0 A Exp {-at] Exp [5 Il ' EXP (”at)I]

 

W0 A Exp [Ak]
(l3)

Explat + g-Exp (-at)]

 

Equations (12) and (13) are in agreement with
Medawar's (1945) laws of growth discussed in the section
on feasibility evaluation. However, the effects of
temperature T and population density P are not incor-

porated into the model. As stated earlier, growth is

30

strongly influenced by temperature. Also, the effect
of pOpulation density cannot be neglected. Figure 10
is a causal loop diagram of the variables considered to
be significant for adequately modeling the growth of
fish. Figure 11 is a block diagram of catfish growth,
with the arrows representing the exogenous variable,
temperature, the endogenous variable, pOpulation
density and the desired output of growth rate K and
growth W. Figures 10 and 11 are based on the experi-
mental results of Andrews et a1. (1971), Kilambi et a1.
(1971) and Tyler and Kilambi (1972).

From the above results it can be concluded that
the proportional rate of growth y is dependent on time

t, population density P and temperature T:
Y = Y(t. T. P) (14)

The most practical approach to this problem would be
to employ a nonlinear least-squares program using eqn
(12) and fitting growth data at various times, pOpulation
densities and temperature to this equation. Unfortu-
nately, the necessary experimental data is not available.
Therefore, the above technique cannot be employed, Fig-
ure 12 is a graphical representation of equation (11).
Another approach to the problem would be to

assume that equation (4) represents the change of the

31

 

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34

proportional rate of growth Y with time at constant

temperature and population density:
<11] _ -a
— Y (15)
at T P

Applying the chain rule the following partial differen-

tial equation is generated to replace eqn (4):
.91. - .31.
at (tITlP) '-

The main obstacle preventing the utilization of eqn (16)
are the terms

LY

”LA:

and

Most fish biologists use a general exponential equation

of the form:

W(t) = w0 ekt (17)

to determine the specific growth k at different tempera-
tures. Also, BT/at is difficult to calculate and would
require a complicated pond model and growth model for

simulation on an hourly basis. This would be costly in

computer time and storage. If it is assumed that aT/at

35

is zero because waste heat is being utilized to keep
the pond at constant Optimal temperature, then the
temperature influence on growth disappears and the
remaining term is an incomplete model of growth. The
term 8P/3t can be derived from some of the present
available mathematical models observing that P is
coupled in a feedback loop. However, the term 3Y/3P)t,T
is impossible to obtain because of the lack of data.

The lack of appropriate data severely hampered
the development of a soPhisticated model for catfish
growth. It is desirable to have growth rate data over
a larger range of temperature to adequately assess the
value of waste heat in catfish production. Data on
population density would be beneficial in an effort to
obtain more accuracy in the simulation of catfish
growth. However, this endeavor is hampered by insuffi-
cient data. It can also be argued that the effects of
increased population can be offset by an increase in
the water exchange rate. The dependence of the growth
rate on time cannot be adequately explored because of
lack of data. For this investigation a constant growth
rate will be assumed, since the purpose is to assess
the value of increasing the ambient temperature of the
rearing pond.

The final alternative is to employ a linear

approximation of the growth rate at different

36

temperatures. Andrews and Stickney (1972) determined the
average percent gain over a 12 week growing period, at
five different temperatures:

W(t) - W(t - Dt)

Wo

 

= percent gain. (18)

Equation (18) is divided by the growing period (12 weeks

or 84 days) to determine the average percent gain per

 

 

day,
_ Percent gain _ W(t) - W(t - At)
k ‘ 84* ' wO At (19)
where
At = 1 day.

Rewriting equation (19), the following expression for

growth is derived:

W(t) = W(t - At) + W k At (20)

O

The next step was to approximate percentage
gain per day k as a function of temperature using an

interpolating polynomial of the form:

— n n-l O O .
P(X) — an+1x + anX + + aZX + a1 (21)
such that
P(Xi) = f(Xi) for i = 0, l, 2, ..., n (22)

37
For this investigation,

Tn + anTn-l + ~-- + a T + a

k(T) = P(T) = a. 2 l

n+1
(23)
The above polynomial with the desired property is the
LaGrange interpolation polynomial. Appendix 2 contains
a Fortran prOgram for growth employing the above method.
Equation (20) is a rough approximation of growth, yet
it makes it possible to assess the impact of waste heat

on catfish production.

B. Pond Model

 

There is more agreement on the optimum depth of
the catfish rearing pond than there is on surface area
among catfish producers. The recommended depth in the
South is 0.9 to 1.81nand 1.8 to 3.0 m in the North (Bar-
dach et al., 1972). Shallow ponds are desirable for cat-
fish growth because it poses no problem for maintaining
the oxygen requirement. With deep ponds there is the
problem of an anaerobic environment at the bottom.

When a shallow natural pond (that is, one which
does not display a vertical temperature gradient) is
subject to a constant climatic condition, the water
will approach a steady state value known as the

equilibrium temperature, T (Littleton, 1970). The

E

equilibrium temperature is the temperature that a body

38

of water reaches when the heat input and output to the
pond are balanced.

In searching the literature, several mathemati-
cal models were encountered which predict the response
of water temperature to meteorological conditions.
Boersma and Rykbost (1973) developed a mathematical model
of a system of open water basin which allows beneficial
use of heated discharge from the thermal power station.
Their model was based on the premise that the heat lossjj;
controlled by the rate of heat loss at the air-water
interface which varies as a function of windspeed and
relative humidity. The main difficulty with this ana-
lytical model is finding and implementing a solution to
a nonlinear hyperbolic differential equation.

Dingman (1972), using a set of equations to
describe the heat exchange processes at the surface,
produced curves of heat exchange rate versus (Tw - Ta),
where Ta is the air temperature. These curves can be
approximated by linear functions of wind speed, humidity,
cloud covering, etc. The problem with this approach
is that it requires vast amounts of data to obtain an
accurate linear least—square regression approximation.
The same problem is encountered with Sefchovich's (1970)
model.

Most of these models use an energy balance simi-
lar to the one used by Edinger (1968) containing the

following terms:

:1:

ar

Hbr

Hsr

If

39

rate of long-wave atmospheric radiation;
rate of conductive heat transfer;
rate of evaporative heat transfer;

net rate of heat exchange between the
air and water surface;

rate of absorbed radiation (the total net
contribution to the energy of the pond);

rate of reflected long-wave atmospheric
radiation;

rate of long-wave radiation from the water;

rate of reflected radiation.

the equilibrium temperature can be derived

from the heat contributions, then the water surface

temperature can be calculated from the following equa-

tion (Edinger, 1968):

where

K(TS - Te) (24)

thermal exchange coefficient,

surface temperature,

equilibrium temperature, and

net rate of heat exchange surface (heat

loss at the surface).

For the purpose of this investigation, it will

be assumed that HD is equal to the heat input from the

power plant needed to elevate the temperature of the

pond for optimal temperature for growth. Edinger (1968)

40

derived the following expression for the equilibrium

temperature (Te):

 

660(AT)2T: + KTe = Hr - €0(AT)4 + K;g:°iA§;3 (clTa+er)
(25)
where
K = thermal exchange coefficients,
units Btu-day-l - ft_2 - "F‘-1
e = emissivity of water
0 = Stefan-Boltzman constant,
Btu ft-z day-1 "R"4
AT = absolute temperature, -°R
C1 = constant in Bowen ratio, -:h1.Hg °F-1
Ta = air temperature, °F
Td = dew point temperature, °F
Hr = absorbed radiation, Btu - ft.2 - day-l.
The thermal exchange coefficient K has the following
form (Edinger, 1968):
K = 4eo(AT)3 + Lp(cl+s)f(u,¢) (26)
where
L = heat of vaporization of water, Btu/lb
f(U,w) = a general function of wind velocity and

surface phenomenon.

B = (eS - ea)/(Te - Td) (27)

41

where

atmospheric vapor pressure, in. Hg;

saturation vapor pressure of water at

(‘D
II

(D
II

the temperature of the water surface,

in. H .
9

Wend and Wend (1973) derived the following expression for

the general function of wind velocity and surface phenomenon:

.00682 + .00682 - U (28)

f(U: T)
where

U = wind velocity, miles per hour.

To simplify equations (27) and (26) the following con-

stants are defined:

02 = 6 so (AT)2
_ 4
C3 — 80 (AT)
3
C4 = 4 60 (AT)

Placing the above constants into equations (25) and (26)

 

 

yields
c T 2 + KT = H - c + [K‘4EG‘AT’3 (c T +BT ) (29)
2 e e r 3 (C1 + B) 1 a d
and
K = C4 + Lp(cl + B) (30)

The coefficients C1 and B are strongly dependent

on the local meteorological condition. Michigan in

42

comparison to other states receives the smallest amount
of the net radiation and has higher humidity. Edinger et
a1. (1968) were able to approximate B, K, and Te from data
they gathered from a previous investigation. In this
investigation the lack of data requires an iteration scheme
to compute three dependent variables. The problem is to
solve a system of three equations [equations (29), (30)
and (28)] and three unknowns. Newton's iteration scheme
for a system of equations (Henrici, 1964) was employed to
determine the equilibrium temperature and the thermal
exchange coefficient.

The first step in the Newton algorithm is to put

equations (27), (29), and (30) in the following form:

P(Te. B. K) = o (31)
G(Ter BI K) = 0 (32)
H(Tel B! K) = 0 (33)
Thus,
— 2 -

P(Te, B, K) - CZTe + KTe Hr + C3

K - C4

(C—l+—B—)— (ClTa + BTd) = 0 (34)
G(Te’ B. K) = c4 + Lo<cl + B)f(U. w) - K (35)

and

43

(e -e)
Te a

(Te - T

 

H(Tel 8: K) = d)

(36)

The next step is to check to see if the first and second

derivations of F, G and H are continuous and to deter-

mine the cubic range R of the (Te, 8, K) element for

which the derivatives are continuous. The derivations

of F, G and H have the following form:

2C

(Te,B,K) 2Te + K

II
n)
0

—'§ (TeIBIK)
e

 

ll
5-3
I

ll
O

— (TeIBIK)

(K - C4) (ClTa + BTd)

 

(T :B:K)
53 e (C1 + B)2

K - C
+ 4 T
(C1 + B) d

2(K - C4)(C1Ta + 8T

d)

 

— (T IBIK) = -
382 9 (c1 + e)3

(37)

(38)

(39)

(40)

(41)

o:
In
(D

C)

0)

SI:

(DN

KIT

02
:l:

J

o:
N

(Te,s,K)

(Te,e,K)

(Te,B.K)

(Te,B.K)

— (TeIBIK)

(Te.B.K)

— (TeIBIK)

(Te,B.K)

(Te’B’K)

(Te,B.K)

 

Lof(U.w)

 

 

(42)

(43)

(44)

(45)

(46)

(47)

(48)

(49)

(50)

(51)

(52)

45

SH _ _

E (TeIBIK) - l (53)
2

ii; (Te,s,K> = o (54)
as

Equations (49) and (50) indicate that there is a dis-
continuity at Te = Td. This problem can be eliminated
by decreasing the increment as the equilibrium tempera-
ture approaches the dew point temperature.

Newton's method for solving a system of equa-

tions is derived from the following equations:

P(Te+6, 8+5, K+y) = 0 (55)
G(Te+6, 8+6, K+Y) = 0 (56)
H(Te+6, 8+8, K+y) = O (57)

Using Taylor series expansion, equations (55), (56) and

(57) become:

P(Te+6, 8+3, K+y) F(Te,B,K) + FT (Te.B,K)6+FB(Te,B,K)e

e

+ FK(Te.B,K)Y = 0 (58)

G(Te+5, 8+6, K+Y) G(Te,B,K) + GT (Te,8,K)6-+G (Te,B,K)€

e

+ GK(Te,B,K)Y = 0 (59)

46

H(Te+6, 8+8, K+Y) = H(Te,B,K) + HT (Te,B,K)6 + HB(Te,B,K)e

e

+ HK(T ,B,K)Y = 0 (60)
e

or

-F(Te,B,K) FT (Te,B,K)5 + FB(Te,B,K)€ + FK(Te.B.K)Y (61)

e

-G(Te,B,K) = FTe(Te,B,K)6 + FB(Te,B,K)€ + FK(Te,B,K)Y (62)

-H(Te.B.K) HT (Te.B.K)6 + HB(Te’B’K)€ + HK(Te,8.K)Y (63)

e

This yields a system of three simultaneous linear equa-
tions with three equations with three unknowns. Applying

Cramer's rule the following solutions are generated.

 

 

 

-F FB FK
-G GB GK
6 = -H HB HK (64)
FTe FB FK
GTe GB GK
HTe HB HK

 

 

47

 

 

 

 

 

 

 

 

FT -F FK
e
G -G G
Te K
HTe -H HK
s = (65)
F F F
Te 8 K
G G G
Te 8 K
H H H
Te 8 K
F F -F
Te
GT G -G
e
HTe H -H
Y = (66)
F F F
Te K
GT G GK
e
H H H
Te K
or
= [-F(GBHK-GKHB) - FB(-GHK+GKH) + FK(-GHB+G8H)] (67)
D
t... - -
[FT ( GHK+HGK) + F(GT HK HT GK) + FK( GT H+GHT )]
€= e e e e e
D

(68)

[F (-HG +GH

48

- F (-GT H+GHT ) + FK(-G H +G H )1

 

)
Y = Te 8 B B e e Te 8 8 Te
D
(69)
where
D = F (G H -G H ) - F (G -G H ) + F (G H -G H )
Te 8 K K B 8 Te K Te K Te 8 8 Te
(70)
The final results are
T8 = Te + (71)
B = B + e (72)
K = K + y (73)

Figure 14 is a flow chart of this iteration. The time

required for the convergence of the problem is 12 sec.

on the MSU CDC 6500.

49

 

   
 

Guess-T

 

 

v

Calculate

F,G,H, ETC.

 

 

 

Calculate

 

 

5: EsY

 

    
 

No

 

Conver-

Calculate

 

 

Heat Load

 

STOP

 

Figure 13. Flow chart of subroutine design to solve a
system of 3 equations and _3 unknowns.

IV. RESULTS AND DISCUSSION

The results of the water basin simulation are
tabulated in Table 5. The simulation was implemented
using average monthly weather conditions for Michigan
(Table 5, columns 1 through 3). Columns 4 and 5 con-
tain the equilibrium temperature and the thermal exchange
coefficients. In the last three columns the heat input
from the power plant needed to elevate the pond to the
desired temperature TS is tabulated. The Optimal
temperature is 86.0°F. It would have been desirable
to simulate the response of the pond to heat input on
a daily basis. However, this was hampered by insuffi-
cient weather information. The three different surfaces
were chosen to assess the heat load necessary to main-
tain the pond at an optimal temperature for catfish
production of 86.0°F.

Figure 14 (page 52) is a plot of the air tem-
perature and the calculated equilbrium temperature
over the lZ-month period. The differences between the
two range from 3.2°F in month 1 (January) to 9.6°F in
month 7 (July). Figure 15 (page 53) is a plot of the
thermal exchange coefficient K over a 12-month period.

The values for K range from a minimum of 373.7 to

50

51

 

 

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TEMPERATURE 0F

75

65

55

45

35

25

15

52

A Air Temperature 0F

U Equilbrium Temperature 0F

 

MONTH

Figure 14. Graph of air temperature and dewpoint temperature over

a 12 month period.

10

11

12

THERMAL EXCHANGE COEFFICIENT - Btu-Day_1-ft-2-0F-1 x 10

6O

55

50

45

40

35

 

53

 

I I I I I I I I I I 1
1 2 3 4 5 6 7 8 9 10 11 12
MONTH

Figure 15. Plot of the thermal exchange coefficient over a 12 month
period.

54

2 1

570.8 Btu-day—l-ft— -°F- . The tabulated values for the
thermal exchange coefficients are well within the bounds
established by Edinger et a1. (1968) and Dingman (1972).
Figure 16 is a graph of the heat input from the power
plant needed to maintain the optimal temperature for
growth. Table 5 and Figure 16 indicate that the maximum
heat input needed to achieve the optimal temperature

for the growth of catfish is 26,058 Btu-day-l-ft-2 or

1085 Btu-hr-l-ft-z. For a hundred acre pond this is

9 1

approximately 4.72 x 10 Btu-hr- . A 700 megawatt

power plant produces thermal discharges of approxi-

9 Btu-hr-l.

mately 4.72 x 10
The temperature generated by the pond model

(Appendix 1) was used as input into the catfish growth
model (Appendix 2) to assess the impact of waste heat

on catfish production. Figures 17 and 18 are plots of
the data generated by the linear catfish model (Appendix
2). Though this is a rough approximation of growth it
can be seen that the use of waste heat does signifi-
cantly enhance the growth of catfish. If the weight

gain under the two different systems (with and without

waste heat) is compared, the ratio is 7.35 to 1.

55

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V. SUMMARY AND CONCLUSIONS

The following conclusions can be drawn from
this investigation.

1. The heat required to maintain a catfish
pond are well within the bounds of a power plant.

2. High population densities can be maintained
by using a high water exchange rate.

3. A heat exchanger should be used instead of
directly pumping the thermal discharge into the fish
pond. This is necessary to prevent biological waste
from entering the power plant cooling water and to
eliminate the risk of marketing fish that have been
exposed to biocides and other chemical agents added to
the condenser water.

4. The system is capable of utilizing a sig-
nificant portion of the thermal discharge during most

of the year.

58

VI. RECOMMENDATIONS

1. Further experimental work needs to be done
on the effects of time, temperature, food conversion
efficiency and pOpulation densities of catfish. The
experiment should be carried out by holding three of
the variables constant and allowing the remaining
parameters to vary. The data should be obtained in a
format that makes it suitable for system analysis.

2. Additional experimental data on the
response of the water to meteorological conditions is
needed to validate the model.

3. This investigation was hampered because of
insufficient weather information. In an effort to
completely assess the value of waste heat the model
should be simulated with daily and hourly temperatures,
wind speeds and humidity in order to determine the
sensitivity of the system to environmental perturba-
tions.

4. There is a need for government guidelines
on the use of agricultural and aquacultural products

from the prOposed system.

59

REFERENCES

60

REFERENCES

Andrews, J. W.; Knight, L. H.; Page, J. W.; Matsuda, Y.;
and Brown, E. E. (1971). Interaction of
stocking density and water turnover on growth
and food conversion of channel catfish reared in
intensively stocked tanks. 33:4.

Andrews, J. W. and Stickney, R. R. (1972). Interaction
of feeding rates and environmental temperature on
growth, food, and body composition of channel
catfish. Trans. American Fish Soc., 101(1):94.

Bardach, J. E.; Ryther, J. H.; and McLarney, W. O. (1972).
Aquaculture--The Farming and Husbandry of Fresh-
water and Marine Organisms. Wiley, Inc., New
York. 868 pp.

 

Boersma, L. and Rykbost, K. A. (1970). Integrated system
for utilizing waste heat from steam electric
plants. Tech. paper #3256, Ag. Exp. Sta., O.S.U.
Paper presented Aug. 1971 (N.Y., N.Y.), at the
Symposium on Beneficial Uses for Thermal Dis-
charge.

Boersma, L. and Rykbost, K. A. (1973). Integrated system
for utilizing waste heat from steam electric
plants. J. Environ. Quality, 2(2):179-187.

Brett, J. R.; Shelbourn, J. E.; and Shoop, C. F. (1969).
Growth rate and body composition of fingerling
sockeye salmon, Oncorhynchus nerka, in relation
to temperature and ration size. Fish. Res. Bd.
Canada, 26, 2363-2394.

Brown, M. E. (1957). The Physiology of Fishes. Academic
Press, Inc., New York.

Bureau of Sport Fishery and Wildlife (1970). Report to
the fish farmers. Resouce Publication 83.

Commercial Fish Farmer (1974). Power plant fish produc-

tion. The Commercial Fish Farmer and Aquaculture
News, l(l):10-13.

61

62

Coutant, C. C. (1970). Biological limitations on the use
of waste heat in aquaculture. Proc. Conf. Bene-
ficial Uses of Thermal Discharge, New York State
Dept. of Environmental Conservation.

Detroit Edison (1973). Applicant's Environmental Report
Construction Permit Stage, Greenwood Energy
Center Units 2 and 3, Vol. 2. Detroit.

 

Dingman, S. L. (1972). Equilibrium temperature and solar
radiation. Water Resource Res., 8(7):42-49.

Edinger, J. E.; Duttweiler, D. W.; and Geyer, J. C.
(1968). The re5ponse of water temperature to
meteorological conditions. Water Resource Res.,
14(5):1137-1144.

Goodman, A. S. and Tucker, R. J. (1971). Time varying
mathematical model for water quality. Water
Research, 5:227-241.

Henrici, P. (1964). Elements of Numerical Analysis.
Wiley, Inc., New York.

Hickling, C. F. (1962). Fish Culture. Faber and Faber,
1962.

 

Hubbert, M. K. (1973). Energy resource for power produc-
tion: Energy Needs and the Environment. Ed.
Seal, R. L., and Sierka, R. A. University of
Arizona Press, Tucson.

Kilambi, R. V.; Noble, J.; and Hoffman, C. E. (1970).
Influence of temperature and photoperiod on growth,
food consumption and food conversion efficiency
of channel catfish. Proc. of 24th Ann. Conf.
Southeast. Assoc. Game and Fish Commis.

Laird, A. K.; Sylvanus, A. F.; and Barton, A. D. (1965).
Dynamics of normal growth. Growth, 29:233-248.

Linstrom, F. F. and Boersma, L. (1973). Heat budget of
cooling basins. J. Environ. Quality, 2(2):
197-203.

Littleton Research and Engineering Corp. (1970). An
engineering economic study of cooling pond
performance. Water Pollution Control Research
Series, E.P.A., 16130 DFX.

63

Mayo, R. D. (1974). A format for planning a commercial
model aquaculture facility. Kramer, Chin &
Mayo, Inc., Tech. Reprint 30.

Medawar, P. B. (1945). Size, shape, and age. Growth
and Form. Ed. Thompason, D'Arcy, Clarendon
Press, London.

Minot, C. S. (1908) The Problem of Age, Growth, and
Death. Putnam's Sons, New York.

Sefchovich, E. (1970). The preliminary thermal analysis
of a body of water in power plant siting. Envi-
ronmental effect of thermal discharges, A.S.M.E.
Conf.

Straun, K. (1970). Beneficial uses of warm water dis-
charges in surface water. Electric Power and
Thermal Discharges. Ed. Eisenbud and Gleason.
Gordon and Breach Pub., New York.

Swift, D. R. (1964). The effects of temperature and
oxygen on the growth rate of the windermere
char (Salvelinus Alpinus Willughbie). Comp.
Biochem. Physiol., 12:179-183.

T.V.A. (1971). Producing and marketing catfish in the
Tennessee Valley. Conf. Proc. Tenn. Valley
Author.

T.V.A. (1973). Utilization of waste heat from power
plants for aquaculture. Gallatin Catfish Project,
Tenn. Valley Author.

Tyler, R. E., and Kilambi R. V. (1972). Temperature-
Light effects on growth, food consumption, food
conversion efficiency and behavior of blue cat-
fish. Proc. Southeast. Assoc. of Game and Fish
Commission.

Weatherly, A. H. (1972). Growth and Ecology of Fish
P0pglation. Academic Press, New Yofk.

 

 

Wend, F. H. and Bird, A. R. (1973). Cooling Pond Thermal
Performance Summary Report, Midland Plant Units
1 and 2. Hydro and Community Facility Division,
Bechtel Corporation, San Francisco.

WOlf, W. H. (1973). Water quality criteria: Energy
Needs and the Environment. Ed. Seale, R. L., and
Sierka, R. A. University of Arizona Press,
Tucson.

APPENDIX

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