# Design of spiral heat exchanger from economic and thermal point of view using a tuned wind-driven optimizer

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## Abstract

This paper presents an optimization of spiral heat exchangers by wind-driven optimization and a novel variant of this algorithm by the insertion of a statistic distribution to self-adapting of the evolution parameters of the algorithm. Spiral heat exchangers are the ideal type for cooling slurries and fluids that presents high viscosity and is very common in food and petrochemical industries. The variables used for the optimization were the spacing channels for hot and cold streams, the length, the width and the thickness of the heat exchanger. Two case studies were presented where the minimization of the cost and the maximization of the overall heat transfer coefficient were implemented. Reductions about 4.46 and 23% were obtained for the cost and increases about 18.8 and 16.4% were reached for the overall heat transfer coefficient for each case study in comparison to previous works. The proposed technique reached better results in all the simulations, in some cases with GA, but performed better accuracy among all the simulations.

## Keywords

Spiral heat exchanger Wind-driven optimization Minimization of total cost Maximization of overall heat transfer coefficient Optimization## Abbreviations

## List of symbols

- \(a_{1}\)
Numerical constant (€)

- \(a_{2}\)
Numerical constant (€ m

^{−2})- \(A\)
Heat exchanger surface area (m

^{2})*B*Width of spiral heat exchanger (m)

- \(C\)
Core diameter (m)

- \(C_{\text{e}}\)
Energy cost (€ W

^{−1}h^{−1})- \(C_{\text{i}}\)
Capital investment (€)

- \(C_{\text{o}}\)
Annual operating cost (€ year

^{−1})- \(C_{\text{od}}\)
Total discounted operating cost (€)

- \({\text{cp}}\)
Specific heat (J kg

^{−1}K^{−1})- \(C_{\text{tot}}\)
Total cost (€)

- \({\text{Dh}}\)
Hydraulic diameter (m)

- \(D_{\text{s}}\)
Spiral outer diameter (m)

- \(H_{\text{w}}\)
Amount of hours of work (h year

^{−1})- \(h\)
Convective coefficient (W m

^{−2}K^{−1})- \(i\)
Annual discount rate (%)

- \(k\)
Thermal conductivity (W m

^{−1}K^{−1})- \(k_{\text{p}}\)
Thermal conductivity of the wall (W m

^{−1}K^{−1})- \(L\)
Tube of spiral heat exchanger (m)

- \(\Delta T_{\text{LM}}\)
Logarithmic mean temperature difference (K)

- \(\dot{m}\)
Mass flow rate (kg s

^{−1})- \(Nu\)
Nusselt number

- \({\text{ny}}\)
Equipment life (yr)

- \(P_{r}\)
Prandtl number

- \(Q\)
Heat duty (W)

- \(R_{\text{m}}\)
Spiral mean diameter (m)

- \(R_{ \hbox{min} }\)
Spiral minimum diameter (m)

- \(R_{ \hbox{max} }\)
Spiral maximum diameter (m)

- \(Re\)
Reynolds number

- \({\text{Rf}}\)
Fouling resistance (m

^{2}K W^{−1})- \(S\)
Channel spacing (m)

- \(T\)
Temperature (K)

- \(U\)
Overall heat transfer coefficient (W m

^{−2}K^{−1})- \(v\)
Fluid velocity (m s

^{−1})- \(\Delta P\)
Pressure drop (kPa)

- \(\Delta P_{ \hbox{max} }\)
Maximum pressure drop (kPa)

## Greek letters

- \(\alpha_{1,2}\)
Numerical constants

- \(\mu\)
Viscosity (Pa s)

- \(\mu_{\text{c}}\)
Consistency viscosity (cP)

- \(\tau_{0}\)
Yield stress (Pa)

- \(\rho\)
Density (kg m

^{−3})- \(\eta\)
Pumping efficiency

## Subscripts

- \(c\)
Cold stream

- \(h\)
Hot stream

*i*Inlet

*o*Outlet

## Notes

### Acknowledgements

The authors would like to thank the National Council of Scientific and Technologic Development of Brazil-CNPq (projects: 303906/2015-4-PQ and 303908/2015-7-PQ) and Paraná Association of Culture-APC for the scholarship financial support of this work.

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