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RESEARCH PAPERS

# Application of Exergoeconomic Techniques to the Optimization of a Refrigeration Evaporator Coil With Continuous Fins

[+] Author and Article Information
Tahar Khir

Jeddah College of Technology, P.O. Box 42204, Jeddah 21 541, Kingdom of Saudi Arabiatbskhir@yahoo.com

Rahim K. Jassim

Yanbu Industrial College, Royal Commission For Jubail and Yanbu, P.O. Box 30436, Yanbu Industrial City 21 477, Kingdom of Saudi Arabiarkjassim@yahoo.com

Galal M. Zaki

King Abdulaziz University, P.O. Box 80204, Jeddah 21 587, Kingdom of Saudi Arabiagzaki@kaau.edu.sa

J. Energy Resour. Technol 129(3), 266-277 (Jul 16, 2006) (12 pages) doi:10.1115/1.2751507 History: Received December 03, 2004; Revised July 16, 2006

## Abstract

An optimization for the geometrical parameters of continuous fins on an array of tubes of a refrigeration evaporator is developed in this paper using the exergy method. The method is based on exergy, economic analysis, and optimization theory. As there are humid air and refrigerant single- and two-phase streams involved in the heat transfer process, then there are irreversibilities or exergy destruction, due to pressure losses $İΔP$, due to temperature difference $İΔT$ and due to specific humidity gradient $İΔω$. These principal components of total irreversibility are not independent, and their relative contribution to total irreversibility of a cross-flow refrigeration evaporator is investigated. A change in geometry was obtained by varying the evaporator tube diameter for a selected evaporator capacity, and hence the evaporator tube length and total heat transfer area are calculated for a fixed evaporator face length. In this way, the effect of changes in the geometry on the total number of exergy destruction units of the heat exchange process is investigated. The optimum balance between the three components of irreversibility ($İΔP,İΔT$, and $İΔω$) is also determined, thereby giving the optimum solution for the heat exchanger area. The total cost function, which provides a measure of the contribution of the evaporator to the total cost of the refrigeration system, is expressed on the basis of annual capital and electrical energy costs. The total cost function is minimized with respect to the total heat transfer area and the total number of exergy destruction units $(NI)$. The relationship between the operational variables, heat transfer area, refrigerant and air irreversibilities, and the total annual cost for this type of evaporator are developed, presented, and discussed. The pressure, temperature, and specific humidity irreversibilities are found to be 30.34%, 33.78%, and 35.88%, respectively, of the total irreversibility, which is 8.5% of the evaporator capacity.

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## Figures

Figure 1

Evaporator with continuous fins on an array of tubes and triangular pitch

Figure 2

(a) Physical model for the evaporator, (b) air temperature and entropy generation rate variation

Figure 3

Cooling and dehumidifying process on the psychrometric chart

Figure 4

Schematic presentation of temperature irreversibility rate of an evaporator

Figure 5

(a) Evaporator two-phase region pressure drop irreversibility (13), (b) evaporator superheated region pressure drop irreversibility (13)

Figure 6

(a) Dependence of irreversibilities on the ℓev,t∕(doNcol) ratio, (b) variation of total irreversibilities versus ℓev,t∕(doNcol)

Figure 7

Variation of the evaporator tube length per column, ℓt versus do

Figure 8

Variation of the evaporator dimensions versus ℓev,t∕(doNcol)

Figure 9

Variation of the number of exergy destruction units versus ℓev,t∕(doNcol)

Figure 10

Variation of the evaporator annual cost versus ℓev,t∕(doNcol)

Figure 11

Variation of the condensed vapor mass flow rate versus ℓev,t∕(doNcol)

Figure 12

Variation of the exergetic efficiency ηex versus ℓev,t∕(doNcol)

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