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Economically optimized heat exchanger design: a synergistic approach using differential evolution and equilibrium optimizer within an evolutionary algorithm framework

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Abstract

This study introduces the CP-EODE algorithm, a novel hybrid of the Equilibrium Optimizer (EO), and the Differential Evolution (DE) algorithm. It addresses EO’s tendency toward premature convergence by enhancing its exploration capabilities. The motivation for this research stems from the need for more efficient and economically viable designs in engineering, particularly in the optimization of shell-and-tube heat exchangers (STHEs) and photovoltaic module parameters. The CP-EODE algorithm leverages DE's exploration strengths to enhance EO’s performance adopting a cooperative parallel approach that divides the population into EO and DE sub-populations for a more effective search space exploration. The validation of CP-EODE’s effectiveness commenced with its application to 29 benchmark functions, where a Friedman test yielded an \({F}_{r}\) value of 22.19, significantly surpassing the critical value of 7.81, and a Wilcoxon signed rank test confirmed statistical improvements with a z-score beyond − 1.96. Four quality metrics were discussed to provide a detailed assessment of CP-EODE’s performance highlighting its robust exploration and exploitation capabilities. In practical applications, CP-EODE demonstrated significant advancements in STHE design achieving up to 19.706% reduction in heat exchanger surface area compared to traditional and other algorithmic designs, showcasing its potential to enhance engineering design efficiency and cost-effectiveness. A critical examination of the algorithm's convergence rate revealed its swift optimization capability, with rapid attainment of optimal solutions in various test cases, further establishing CP-EODE’s advantage in handling complex optimization challenges. Through rigorous statistical analysis and performance metrics, CP-EODE emerges as a superior solution for complex optimization challenges, underscoring the value of hybrid algorithmic strategies in engineering optimizations.

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Data availability

No data was used for the research described in the article.

Abbreviations

\({a}_{1}\) :

Constant (numeric)

\({a}_{2}\) :

Constant (numeric)

\({a}_{3}\) :

Constant (numeric)

\(B\) :

Spacing between baffle (\({\text{m}}\))

\({\text{Cl}}\) :

Clearance (\({\text{m}}\))

\({C}_{p}\) :

Specific heat (\({\text{kJ}}/\mathrm{kg K}\))

\({C}_{i}\) :

Capital cost (€)

\({C}_{{\text{E}}}\) :

Cost of energy (€\(/\mathrm{kW h}\))

\({C}_{{\text{o}}}\) :

Operating cost per year (€\(/{\text{year}}\))

\({C}_{{\text{D}}}\) :

Total discounted operating cost (€)

\({C}_{{\text{tt}}}\) :

Total cost per year (€)

\(d\) :

Diameter of tube(\({\text{m}}\))

\(D\) :

Diameter of shell (\({\text{m}}\))

\(f\) :

Friction factor

\({F}_{{\text{c}}}\) :

Correction factor

\(h\) :

Heat transfer coefficient (\({\text{W}}/{\text{m}}^{2} \;{\text{K}}\))

\(H\) :

Operating time per year (\({\text{h}}/{\text{year}}\))

\(i\) :

Discount rate per year (%)

\(k\) :

Thermal conductivity (\({\text{W}}/{\text{m }}\;{\text{K}}\))

\({K}_{1}\) :

Constant (numeric)

\(L\) :

Length of tubes (\({\text{m}}\))

\(m\) :

Flow rate of mass (\({\text{kg}}/{\text{s}}\))

\(n\) :

Number of tube passages

\(n1\) :

Numerical constant

\({\text{yy}}\) :

Life of equipment \(({\text{year}})\)

\({N}_{{\text{t}}}\) :

Number of tubes

\(P\) :

Pumping power (\({\text{W}}\))

\({P}_{{\text{r}}}\) :

Prandtle number

\({P}_{{\text{t}}}\) :

Tube pitch (\({\text{m}}\))

\(Q\) :

Heat duty (\({\text{W}}\))

\({\text{Re}}\) :

Reynolds number

\({R}_{{\text{f}}}\) :

Resistance of fouling (\({\text{m}}^{{2{ }}} \;{\text{K}}/{\text{W}}\))

\(S\) :

Surface area of heat transfer \({({\text{m}}}^{2 })\)

\(T\) :

Temperature \((\mathrm{ K})\)

\(U\) :

Overall heat transfer coefficient \(\left( {{\text{W}}/{\text{m}}^{2} \;{\text{K}}} \right)\)

\(v\) :

Velocity of fluid \(({\text{m}}/{\text{s}})\)

\(\Delta P\) :

Pressure drop \(({\text{Pa}})\)

\(\Delta {T}_{{\text{LM}}}\) :

Logarithmic mean temperature difference (°C)

\({\mu }_{t}\) :

Dynamic viscosity \(\left( {{\text{Pa}}\;{\text{ s}}} \right)\)

\(\rho\) :

Density \(\left( {{\text{Kg}}/{\text{m}}^{3} } \right)\)

\(\eta\) :

Overall pumping efficiency

\({\text{i}}\) :

Inlet

\({\text{o}}\) :

Outlet

\({\text{s}}\) :

Used for shell

\({\text{t}}\) :

Used for tube

\({\text{w}}\) :

Wall of tube

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Authors and Affiliations

  1. Computers and Control Systems Engineering Department, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt

    Amal Moharam, Amira Y. Haikal & Mostafa Elhosseini

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  1. Amal Moharam
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  2. Amira Y. Haikal
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  3. Mostafa Elhosseini
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Contributions

Amal Moharam: Methodology, Investigation, Software, Writing—original draft, Amira Y. Haikal: Conceptualization, Supervision, Validation. Mostafa A. Elhosseini: Conceptualization, Writing—review & editing, Supervision.

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Correspondence to Mostafa Elhosseini.

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Moharam, A., Haikal, A.Y. & Elhosseini, M. Economically optimized heat exchanger design: a synergistic approach using differential evolution and equilibrium optimizer within an evolutionary algorithm framework. Neural Comput & Applic (2024). https://doi.org/10.1007/s00521-024-09829-1

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