Page 204 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 193

between the capabilities of nonlinear programming methods for optimiza-
tion and the computational nature of the heat exchanger analysis. Hence, a
package approach consisting of various nonlinear programming methods
and heat exchanger analysis is recommended, as no single optimization
method is going to work for all heat exchanger problems.
In a heat exchanger optimization methodology, each possible surface
geometry and construction type can be considered to be an alternative
design. In order to make a legitimate comparison of these alternatives, each
design must be optimized for the specified application. Thus, there may be
several independent optimized solutions satisfying the problem require-
ments. Engineering judgment, comparison of objective function values,
and other evaluation criteria are then applied to select a final optimum
solution for implementation.
In the design optimization, the constraints of the problem such as the
customer’s specified explicit constraints (e.g., the fixed frontal area and
the ranges of heat exchanger dimensions) and implicit constraints (e.g.,
required minimum heat transfer and allowable maximum pressure drop)
shall be formulated. Once the basic surface geometry for an alternative
design is selected, some additional constraints such as the ranges of fin param-
eters, tube diameter and length, flow length, number of flow passes, and flow
rates are required. The design parameters including the variables appearing
in the constraints will be selected as the design variables to be optimized.
To optimize a heat exchanger, the designer starts with one set of heat
exchanger surface geometrical dimensions and operating conditions while
may not even satisfy all or some imposed constraints. Subsequently, the
various geometrical properties (such as heat transfer area, free flow area,
and hydraulic diameter) and thermal properties are evaluated. The heat
transfer rate and pressure drop are then evaluated using either the
ε-NTU method or the logarithmic temperature difference method. Next,
the output from heat exchanger calculations is fed to the optimization
computer program package where the constraints and the objective func-
tion are evaluated. New values for the design variables are subsequently
generated, and heat exchanger calculations are repeated. The iterations
are continued until the objective function is optimized with the accuracy
specified, and all the constraints are satisfied. In some situations, it may not
be possible to satisfy all the constraints for exterior penalty methods, an
optimization with essentially result in coming as close as possible to the
constraints. Engineering judgment will be needed to find out whether
or not the optimum design is satisfactory.