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    cost of the exchanger. The total cost consists of five components:
    the capital cost of the exchanger, the capital costs for two pumps,
    and the operating (power) costs of the pumps. The expression for
    the total annual cost is of the form
    TAC ¼ Af ðCexc þ Cpump;T þ Cpump;SÞþ Cpow
    HY
    g
    _ mtDPT
    qt
    þ
    _ msDPS
    qs
    
    ð12Þ
    where Cexc, Cpump,T and Cpump,S are the capital cost for the exchanger,
    tube-side and shell-side pumps, respectively. The capital costs for
    the pumps are given by the following equations:
    Cpump;T ¼ Ce þ Cf
    _ mtDPT
    qt
    e
    ð13Þ
    Cpump;S ¼ Ce þ Cf
    _ mSDPS
    qs
    e
    ð14Þ
    The capital cost for the heat exchanger is typically calculated by an
    equation of the form
    Cexc ¼ Ca þ C0
    bAc
    ð15Þ
    Alternatively, one can incorporate a more detailed estimation by
    splitting the capital cost into the cost of component parts and man-
    ufacturing costs. Purohit [11] suggested the following expression
    for that purpose:
    Cexc ¼ Cts þ Csh þ Cb þ Ctd þ Ctb þ Cba ð16Þ
    where Cts is the tube-sheet cost based on weight, including cutting
    but not drilling; Csh is the shell cost including fabrication, based on
    weight; Cb is the baffle cost assuming 1/2-in thickness, based on
    weight; Ctd is the tube-sheet, baffle drilling and bundle tubing cost,
    based on number of tubes; Ctb is the cost of tubes, based on outside
    heat transfer surface; and Cba is the base cost to cover overhead and
    labor costs, which is independent on the type of material.
    2.4. Search variables
    A vector x of search variables was manipulated as part of the
    optimization algorithm. The vector contains 10 components,
    according to the degrees of freedom of the problem; the definition
    of variables is given in Table 1. Once the search vector is defined,
    the algorithm by Serna and Jimenez [10] is used to obtain the de-
    sign of the exchanger. It should be clear that a major difficulty is
    the selection of design values that satisfy all of the geometric
    and operational constraints.
    3. Optimization model using genetic algorithms
    To generate an efficient optimization method, genetic algo-
    rithms are used. Genetic algorithms search for an optimum solu-
    tion based on the mechanics of natural selection and genetic
    [12,13].
    Table 1
    Search optimization variables
    Variable Definition
    x1 Tube-side pressure drop
    x2 Shell-side pressures drop
    x3 Baffle cut (between 15% and 45%)
    x4 Number of tube passes (1, 2, 4, 6 or 8)
    x5 Standard inside, outside tube diameters and pitch (80 standard
    possible combinations given by the TEMA)
    x6 Tube pattern arrangement (triangular, square or rotated square)
    x7 Hot fluid allocation (tubes or shell)
    x8 Number of sealing strings (0, 1, 2, 3 or 4)
    x9 Tube bundle type (fixed-tube plate, packed-tube plate, floating head,
    pull-through floating head or U-tube bundle)
    x10 Ratio inlet and outlet baffle spacingwas found in 121 generations, which required the simulation of
    12,100 heat exchangers, and consumed 51 s of CPU time. One can
    notice that the design obtained with the proposed algorithm has a
    lower total annual cost than the one obtained byMizutani et al. [9].
    This observation seems to indicate that the solution obtained by
    Mizutani et al. [9] got trapped into a local optimal point within
    their search algorithm. The main difference between both results is
    in the pumping costs. Our solution shows a reduction in pumping
    costs of about 60% that, in spite of an increment in the area cost of
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