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Parametric study and optimization of pillow-plate heat exchanger using multi-objective genetic algorithm and entropy generation minimization approaches

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Abstract

The pillow-plate heat exchanger (PPHE) is a kind of heat exchanger constructed by a set of wavy surfaces like a pillow. In this study, the influence of pillow-plate geometrical parameters (including dimensionless channel height, dimensionless plate width, and pillow plates number) and flow specification (including Reynolds and Prandtl numbers) in terms of derived dimensionless parameters on their thermo-hydraulic performance is evaluated through a comprehensive parametric investigation. The fully developed regime in PPHE channel is assumed and fluid flow, heat transfer, and thermodynamics principles are combined in terms of the entropy generation minimization (EGM) approach. Afterwards, a multi-objective optimization method is applied by using the non-dominated sorting genetic algorithm (NSGA-II) to find the optimal design of PPHE. In this way, the maximization of performance evaluation criterion (PEC) against the minimum total entropy generation for PPHE is eventuated. The behavior of PPHE’s important evaluation criteria are illustrated for different Reynolds numbers from 1000 to 6000 by varying Prandtl number and the proposed dimensionless geometry parameters. Also, contrariness between two parts of non-dimensional entropy generation (NDEG), i.e., thermal and frictional, is concluded from the result for Pareto-optimal front. It indicates there is an optimum Re number that minimizes (NDEG)tot at any geometrical parameters. On the other hand, multi-objective optimization results show the conflict between two main objective functions namely PEC and (NDEG)tot that reveals any geometrical change to increase in the PEC of heat exchanger leads rising in total entropy generation and vice versa. The final optimum values of the objective functions are PECopt = 1.3712 and (NDEG)tot,opt = 0.0145 which occurs at Re = 3265.

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Abbreviations

A :

Heat transfer area, m2

C p :

Specific heat capacity of the fluid, J/(kg.K)

d :

Diameter, m

e i :

Inner channel height, m

e :

Outer channel height, m

f :

Friction factor, -

G :

Mass flux, kg/(m2.s)

h :

Heat transfer coefficient, W/(m2.K)

k :

Thermal conductivity, W/(m.K)

L :

Height of the pillow plate, m

\(\dot{m}\) :

Mass flow rate, kg/s

N :

Number of plates row, -

Nu:

Nusselt number, -

PEC :

Performance evaluation criteria, -

Pr:

Prandtl number, -

NDEG:

Non-dimensional Entropy generation, -

t w :

Wall thickness, m

Re:

Reynolds number, -

R f :

Thermal resistance of fouling, (m2.K)/W

S T :

Transversal distance between welding spots, m

S gen :

Entropy generation, W/(m.K)

S L :

Longitudinal distance between welding spots, m

ΔP :

Pressure drop, kPa

ΔT :

Temperature difference, K

U :

Overall heat transfer coefficient, W/(m2.K)

V :

Channel flow velocity, m/s

w :

Dimensionless plate width, -

W e :

Width of edges of the pillow plate, m

Q :

Heat load, kW

hyd :

Hydraulic

sp :

Spot welding point

p :

Pillow plate

ΔT :

Thermal

ΔP :

Frictional

tot :

Total

\(\mu\) :

Fluid dynamic viscosity, Pa·s

\(\rho\) :

Density, kg/m3

\(\eta\) :

Efficiency

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Mohsen Tavallaei & Ali Jabari Moghadam

  2. Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Mahmood Farzaneh-Gord

  3. Mechanical Engineering Department, Faculty of Engineering, Quchan University of Technology, Quchan, Iran

    Amir Ebrahimi-Moghadam

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  1. Mohsen Tavallaei
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Appendix

Appendix

This appendix deals with the general comparison of PPHE and conventional FPHE modeling result. In this way, the FPHE model with similar dimensions of PPHE has been developed using particular hydraulic diameter and correlations of f and Nu as follows [59]:

$$d_{hyd} = 2e_{i}$$
(A1)
$$f = 3.44\,{\text{Re}}^{ - 0.225}$$
(A2)
$${\text{Nu}} = 0.143\,{\text{Re}}^{0.71} \Pr{^{0.3}}$$
(A3)

Based on the above equations, to observe the f and Nu trends as the evaluating parameters by varying Re, results of the developing numerical code for the FPHE are compared with the PPHE. This comparison is depicted in Fig. 13.

Fig. 13 
figure 13

Comparison of PPHE and FPHE at different Re numbers, a changing friction factor and Nu, b changing (NDEG)tot, (NDEG)ΔT and (NDEG)Δp

Full size image

It could be seen in Fig. 13(a) that friction factor and heat transfer of PPHE are lower and higher than FPHE, respectively. By attention to the structure of PPHE and consequent redirected flow around the welding spots inside the channel, formation of boundary layer leads to improve the heat transfer comparison to FPHE. However, this could slightly increase the pressure drop in PPHE channel depending on welding points pattern and theirs distances. Fig. 13(b) illustrates variation of main EGM assessment parameters i.e. (NDEG)tot, (NDEG)ΔT and (NDEG)Δp in different Re numbers for both PPHE and FPHE. As expected, because of some PPHE structural features against the FPHE which have been led to improve heat transfer and totally reduction in pressure drop, the derived thermal, frictional and total form of non-dimensional entropy generation in PPHE are lower than FPHE.

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Tavallaei, M., Farzaneh-Gord, M., Moghadam, A.J. et al. Parametric study and optimization of pillow-plate heat exchanger using multi-objective genetic algorithm and entropy generation minimization approaches. Heat Mass Transfer 59, 1687–1706 (2023). https://doi.org/10.1007/s00231-023-03363-x

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