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Optimal Design of a Dry-Type Natural-Draft Cooling Tower by Geometric Programming

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Advances in Geometric Programming

Part of the book series: Mathematical Concepts and Methods in Science and Engineering ((MCSENG,volume 21))

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Abstract

In this paper, the optimal design of dry-type natural-draft cooling towers is investigated. Using physical laws and engineering design relations that govern the system, a rather detailed optimization model is developed. This model is then reformulated as a geometric programming problem. A primary consideration in this reformulation is how certain polynomial equations may be effectively replaced by inequalities. A numerical example follows.

This research was supported in part by the National Science Foundation, Grant No. MPS75-09443, and by the NATO Postdoctoral Fellowship Program in Science.

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Abbreviations

A Fi :

total fin surface, sq ft

A i :

total inside tube surface, sq ft

A o :

total outside tube surface, sq ft

\( \overline{A} \) o :

total outside bare tube surface (finned tubes), sq ft

A To :

tot surface area of tower shell, sq ft

a s :

free flow area, sq ft

b :

fin thickness, ft

C F,Fi :

fixed charges on air cooler fins, $/yr

C F,To :

fixed charges on tower shell, $/yr

C F,Tu :

fixed charges on air cooler tubes, $/yr

C O,P :

operating cost of air cooler pump, $/yr

c :

distance between two adjacent fins, ft

c p,a :

cP a specific heat of air, Btu/lb °F

D e :

equivalent diameter, ft

D i :

inside tube diameter, ft

D o :

outside tube diameter, ft

D To :

tower diameter, ft

D v :

equivalent volumetric diameter, ft

d :

distance between centerlines of two adjacent banks of tubes in air cooler, ft

e :

gap between fins of two adjacent banks of tubes, ft

F:

cross-flow-temperature-difference correction factor

f :

frictional surface, sq ft

G :

greater terminal temperature difference, °F

H To :

tower height above air entrance, ft

h :

fin height, ft

h i :

inside film coefficient, Btu/(sq ft) hr °F

h o :

outside film coefficient, Btu/(sq ft) hr °F

L :

tube length, ft

l :

tube wall thickness, ft

N :

number of tubes in bank of air cooler

\( \overline{N} \) :

number of vertical banks in air cooler

n :

number of fins per ft. of tube length

q :

rate of heat transfer, Btu/hr

S l :

center-to-center distance to the nearest tube in the next bank, ft

S t :

pitch in a bank, ft

t To :

tower shell thickness, ft

T :

temperature, °R

U :

lesser terminal temperature difference, °F

W :

flow rate, lb/hr

ΔP f :

tower friction loss, psi

ΔP l :

tower leaving loss, psi

ΔP o :

pressure drop across air cooler coils, psi

ΔP t :

theoretical tower draft, psi

ΔT a :

change in air temperature, °F

ΔT m :

overall mean temperature drop between hot and cold fluid, °F

ΔT mi :

mean temperature drop through inside tube film, °F

ΔT mo :

mean temperature through outside tube film, °F

Ω:

fin efficiency

a :

air

w :

water

c :

cold

h :

hot

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Author information

Authors and Affiliations

  1. Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain, Belgium

    J. G. Ecker (Associate Professor)

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York, USA

    J. G. Ecker (Associate Professor)

  3. Unternehmensberatung Schumann GmbH, Cologne, West Germany

    R. D. Wiebking (Engineering Consultant)

Authors
  1. J. G. Ecker
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  2. R. D. Wiebking
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Editor information

Editors and Affiliations

  1. Technion-Israel Institute of Technology, Haifa, Israel

    Mordecai Avriel

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© 1980 Plenum Press, New York

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Ecker, J.G., Wiebking, R.D. (1980). Optimal Design of a Dry-Type Natural-Draft Cooling Tower by Geometric Programming. In: Avriel, M. (eds) Advances in Geometric Programming. Mathematical Concepts and Methods in Science and Engineering, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8285-4_22

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  • DOI: https://doi.org/10.1007/978-1-4615-8285-4_22

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-8287-8

  • Online ISBN: 978-1-4615-8285-4

  • eBook Packages: Springer Book Archive

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