Stack Of Parallel Plates Research Articles

Quantum field theory at finite temperature for 3D periodic backgrounds

The one-loop quantum corrections to the internal energy of some lattices due to the quantum fluctuations of the scalar field of phonons are studied. The band spectrum of the lattice is characterised in terms of the scattering data, allowing to compute the quantum vacuum interaction energy between nodes at zero temperature, as well as the total Helmholtz free energy, the entropy, and the Casimir pressure between nodes at finite non-zero temperature. Some examples of periodic potentials built from the repetition in one of the three spatial dimensions of the same punctual or compact supported potential are addressed: a stack of parallel plates constructed by positioning δδ′ -functions at the lattice nodes, and an ‘upside-down tiled roof’ of parallel two-dimensional Pöschl–Teller wells centred at the nodes. They will be called generalised Dirac comb and Pöschl–Teller comb, respectively. Positive one-loop quantum corrections to the entropy appear for both combs at non-zero temperatures. Moreover, the Casimir force between the lattice nodes is always repulsive for both chains when non-trivial temperatures are considered, implying that the primitive cell increases its size due to the quantum interaction of the phonon field.

Full-scale numerical simulations of standing-wave thermoacoustic engines with circular-pore and pin-array stacks

Thermoacoustic engines (TAEs) can convert thermal energy into acoustic energy with no moving parts. Previous numerical studies normally focused on the TAEs with a parallel-plate stack due to their simple structures and used two-dimensional (2-D) computational fluid dynamics (CFD) models to save computational costs. In this study, we conduct full-scale three-dimensional (3-D) CFD simulations on the standing-wave TAEs with more complicated circular-pore and pin-array stacks. Firstly, the dynamic behavior of the standing-wave TAEs in the start-up process is investigated. It is found that the optimal ratios of hydraulic radius rh to thermal penetration depth δk for the TAEs with circular-pore and pin-array stacks are 2 and 3.2, respectively. Secondly, the acoustic, hydrodynamic, and thermodynamic characteristics of the standing-wave TAEs in the steady-state process are explored. We find that when operating at optimal rh/δk, the TAE with a pin-array stack generates much larger acoustic power than that with a circular-pore stack. Examination of the vortex shedding at the stack ends indicates that the pin arrays exhibit less flow resistance than circular pores. At optimal rh/δk, the time-averaged transversal heat flux at the pin array ends is calculated to be around 1.2 × 105 W/m2, which is larger than 7.5 × 104 W/m2 of circular pores, corresponding to a better thermodynamic performance. The 3-D numerical investigations in this work give deeper insights into the performances of TAEs with circular-pore and pin-array stacks which were investigated in experiments, providing useful guidance for the future design and development of more sophisticated thermoacoustic devices for low-grade heat recovery.

Analysis of non-linear losses in a parallel plate thermoacoustic stack

PurposeThis study aims to analyse the non-linear losses of a porous media (stack) composed by parallel plates and inserted in a resonator tube in oscillatory flows by proposing numerical correlations between pressure gradient and velocity.Design/methodology/approachThe numerical correlations origin from computational fluid dynamics simulations, conducted at the microscopic scale, in which three fluid channels representing the porous media are taken into account. More specifically, for a specific frequency and stack porosity, the oscillating pressure input is varied, and the velocity and the pressure-drop are post-processed in the frequency domain (Fast Fourier Transform analysis).FindingsIt emerges that the viscous component of pressure drop follows a quadratic trend with respect to velocity inside the stack, while the inertial component is linear also at high-velocity regimes. Furthermore, the non-linear coefficient b of the correlation ax + bx2 (related to the Forchheimer coefficient) is discovered to be dependent on frequency. The largest value of the b is found at low frequencies as the fluid particle displacement is comparable to the stack length. Furthermore, the lower the porosity the higher the Forchheimer term because the velocity gradients at the stack geometrical discontinuities are more pronounced.Originality/valueThe main novelty of this work is that, for the first time, non-linear losses of a parallel plate stack are investigated from a macroscopic point of view and summarised into a non-linear correlation, similar to the steady-state and well-known Darcy–Forchheimer law. The main difference is that it considers the frequency dependence of both Darcy and Forchheimer terms. The results can be used to enhance the analysis and design of thermoacoustic devices, which use the kind of stacks studied in the present work.

Numerical study on thermal behaviors of parallel plate systems for sensible thermal energy storage with heat loss

A numerical study on thermal energy storage systems with parallel plates to collect sensible heat is conducted with porous and direct model approaches. The simulations in a two-dimensional domain are performed with COMSOL Multiphysics commercial software. For the equivalent porous medium, the permeability and effective thermal conductivity as well as the specific area, and interfacial convective coefficient are numerically evaluated, considering a thermally and hydrodynamically fully developed flow. A stack of parallel plates is the system with assigned length and height, and the external heat losses effect is considered. The analysis allows to evaluate an optimized configuration as Channels Per Length (CPL) by means of a balance in the channels between pressure drop and heat transfer. Moreover, the effect of CPL values and heat loss from the parallel plate system is estimated in terms of charging time and heating capacity. The results exhibit that as the CPL increases, the time required for the charging process decreases while heat accumulation inside the system increases significantly. In fact, at the highest CPL, charging time is 2.7 times faster and the amount of heat accumulation is approximately 20% higher in adiabatic case. It is illustrated that the amount of heat accumulation inside the system varies considerably for different heat loss values. Ultimately, this study shows that porous model is more practical and accurate to be used for higher CPL cases.

Design optimization and CFD analysis of the dynamic behavior of a standing wave thermoacoustic engine with various geometry parameters and boundary conditions

Thermoacoustic devices are converters of thermal energy into acoustic energy and vice versa. Although these machines contain simple components, the design of these machines is very challenging. In order to predict the behavior and optimize the efficiency of a standing-wave thermoacoustic engine designed to drive a thermally driven thermoacoustic refrigerator, considering changes in geometrical parameters and operating conditions, two analogies have been presented in this paper. The first analogy is based on a CFD simulation carried out to investigate the influence of stack parameters, working gas and boundary conditions on the thermoacoustic process. The second analogy is performed by the use of an optimization algorithm based on the simplified linear thermoacoustic theory to design and optimize the parameters investigated by the CFD study. Stack of parallel plates of normalized stack center positions of 0.007 to 0.26, normalized stack lengths of 0.018 to 0.11, and several gaps and thicknesses of plates and working gases are used. The results from the algorithm give the ability to design any thermoacoustic engine with high efficiency by picking the appropriate parameters. Simulation results show that decreasing thickness and position of the plates gives a significant efficiency. However, there are optimum values for length of the stack and the gap between two plates. The material chosen for the construction of plates should have a low thermal conductivity and gases with higher ratios of specific heats and lower Prandtl numbers are well suitable for thermoacoustic systems.

Numerical analysis of thermoacoustically driven thermoacoustic refrigerator with a stack of parallel plates having corrugated surfaces

Most numerical research on thermoacoustic devices with a stack made of parallel plates has considered a rectangular form for the plate. However, a variety of plate shapes can improve the heat transfer and performance of the stack. In this paper, a 2D numerical model based on computational fluid dynamics (CFD) analysis is used to examine the efficiency of thermoacoustic couples using a diversity of plate surfaces. For this investigation, flat plates and others profiles with corrugated surfaces (rounded and triangular surfaces) were tested to compare their performances and the effect of plate form on thermoacoustic systems. The efficiency of the thermoacoustic engine (TAE) is measured in terms of the generated acoustic pressure and the performance of the thermoacoustic refrigerator (TAR) is considered in terms of the temperature gradient along the refrigeration stack. The results showed that plates profile with irregular surfaces improves the generated acoustic pressure due to the increase of the stack porosity known as the blockage ratio (BR). The triangular shape performed better with a 10% gain than using a flat plate, followed by rounded ripples with a 5.2% increase in pressure amplitude compared to flat surfaces. Unlike in TAR, it was revealed that the stack made of flatform could produce a higher temperature difference (∆T) among the refrigeration stack extremities. By using rounded ripples, ∆T undergoes a reduction up to 52%, and 65% if using triangular ripples compared to flatform. From this investigation, it is observed that the stack with corrugated plates is the most suitable for TAE; however, the flat plates generate a higher temperature difference in TAR.

Performance Analysis of Thermoacoustic Refrigerator of 10 W Cooling Power made up of Poly-Vinyl-Chloride for Different Parallel Plate Stacks by using Helium as a Working Fluid

Refrigerants are usually provided in the conventional refrigeration system although the refrigerants produce Chlorofluorocarbons (CFCs) and Hydro-chlorofluorocarbons (HCFCs), which are hazardous to the environment. However, these disadvantages can be overcome by using air or inert gas in the thermoacoustic refrigeration system. In the present experimental work, helium is used as a working gas with an operating pressure range of 0.2 MPa to 1.0 MPa in order to study the performance of thermoacoustic refrigerator (TAR) which is fabricated using Poly-Vinyl-Chloride (PVC). The parallel plate stacks with different porosity ratios have been considered to study the performance of TAR. The temperature difference between the hot and cold heat exchanger and acoustic dynamic pressure were recorded by using Bruel and Kjaer data acquisition system under different operating conditions. The effect of different operating parameters such as operating frequency (200 Hz to 600 Hz), cooling load (2 W to 10 W) and drive ratio (0.6% to 1.6%) have also been considered to study the performance of TAR. The TAR also modeled in DeltaEC software and the results are compared with the experimental outcomes and found to be in good agreement. The experimental results show that −2.1°C is the lowest temperature measured at cold heat exchanger by achieving the highest temperature difference of about 32.9°C. An improvement is around 36% as compared to that of previous experiments that used aluminium TAR. The highest Coefficient of Performance (COP) and the Relative Coefficient of Performance (COPR) are found to be 2.024 and 0.217 respectively.

Fluid dynamics of oscillatory flow across parallel-plates in standing-wave thermoacoustic system with two different operation frequencies

Thermoacoustic system is one of the alternative technologies that provides green working principles but the lack of understanding of the complex fluid flow and energy transfer interactions within structures inside the system is leading to difficulty in accurate analysis related to the system. This study presents fluid dynamic investigation of vortex shedding and velocity profile of an oscillatory flow across a parallel-plate structure inside a standing-wave thermoacoustic system by using a two-dimensional ANSYS FLUENT CFD (computational fluid dynamics) of SST k-ω turbulence model. The model was validated using experimental data and theoretical solution. Two different operating frequencies of 14.2 Hz and 23.6 Hz were investigated with drive ratios (defined as maximum pressure amplitude to mean pressure) from 0.3% up to 3%. The results revealed that velocity profiles and boundary layers within the area of parallel-plate stack changes with time and the changes followed the cyclic travel of vortex across the structure. Two layers of vortex formed near the surface of the solid structure. These layers, known as the main and secondary vortex layers, change with the cyclic flow, and are affecting the shape of velocity profiles within the channel. The appearance of an ‘m’ shape, a ‘slug’ shape and a ‘parabolic’ shape velocity profiles are also depending on the flow amplitude (drive ratio) and flow frequency. The ‘parabolic’ velocity profile is only found for a certain moment of flow with thick boundary layer. The results indicated that fully developed flow may not be likely for cases presented in this paper. Hence care should be exercised in the use of equations during the analysis of thermoacoustic system. As the parallel-plate structure is usually an important structure of the system, a proper understanding of the dynamics of flow within this structure is crucial. These findings are expected to give better insight for future design of thermoacoustic system.

Effect of parallel plate stack spacing on the performance of thermoacoustic refrigerator in terms of temperature difference using air as a working fluid

The existing conventional refrigerators are operated by using hazardous refrigerants, which produces CFCs and HCFCs resulting in the depletion of the ozone layer. However, these disadvantages can be overcome using inert gases in the thermoacoustic refrigeration system. The present research involves the effect of the spacing of a parallel plate stack on the performance of the thermoacoustic refrigerator (TAR). TAR is fabricated by using Poly-Vinyl-Chloride (PVC), which is designed for 10W cooling power. Three parallel plate stacks have been used to study the performance of TAR considering different porosity ratios by varying the gap between the parallel plates (0.28 mm, 0.33 mm and 0.38 mm). The parallel plate stacks are fabricated by using aluminium and mylar sheet material, and the working fluid used for the experimental study is zero air. The experiments have been carried out with different drive ratios ranging from 0.6% to 1.6%, with operating frequencies of 200 – 600 Hz. Also, the mean operating pressure used for the experiment is 2 to 10 bar, and the cooling load of 2 to 10W is considered. The temperature difference (ΔT) between the hot heat exchanger and cold heat exchanger is recorded using RTDs and Bruel and Kjaer data acquisition system. Experimental results show that the lowest temperature measured at cold heat exchanger is 1.23 °C by maintaining the hot heat exchanger temperature at about 32 °C. The maximum ΔT of 30.77 °C is achieved.

Experimental Performance Evaluation of Thermoacoustic Refrigerator made up of Poly-Vinyl-Chloride for different Parallel Plate Stacks using Air as a working medium

Abstract Most of the experimental work carried out by fabricating Aluminium and other metallic resonator system in order to evaluate the performance of thermoacoustic refrigerator. In this experimental work, poly-vinyl-chloride has been used to fabricate all the structural parts including the resonator system to study the performance of thermoacoustic refrigerator for different operating conditions. Three parallel plate stacks are fabricated by using Aluminum and the Mylar sheet material of 0.12 mm thickness by considering three different porosity ratios. In this research work, only pure air is used as a working fluid. The experiments are conducted for the drive ratios ranging from 0.6% to 1.6% with an operating frequency varies from 200Hz to 600Hz with a step of 100 Hz. Also, the mean operating pressure and cooling load varies from 2 to 10 bar and 2 to 10 W respectively. In this work, Bruel and Kjaer data acquisition system and RTDs are used to measure and record the temperature difference between two heat exchangers. The effect of different parameters such as operating pressure, operating frequency, cooling load and drive ratios on the performance of thermoacoustic refrigerator in terms of temperature difference and coefficient of performance (COP) are studied.It is observed from experimental results that 1.23 oC is the lowest measured temperature at the cold heat exchanger by maintaining 32 oC at the hot heat exchanger. It is important to note that 30.77 oC is the highest value of temperature difference measured between two sides of stack, which is about 41% improvement in the temperature difference as compared to previous findings

Experimental Study of Condensation in a Thermoacoustic Cooler With Various 3D-Printed Regenerators Using Water Vapor as the Working Fluid

Abstract Thermoacoustics (TA) deals with the conversion of heat into sound and vice versa. The device that transfers energy from a low-temperature reservoir to a high-temperature one by utilizing acoustic work is called TA cooler (TAC). The main components of a typical TAC are a resonator, a porous regenerator (e.g., stack of parallel plates), and two heat exchangers. The thermoacoustic phenomenon takes place in the regenerator where a nonzero temperature gradient is imposed and interacts with the sound wave. The low temperature at the cold end of TAC can be used to condense water from the humid air and also reduce the moisture. In the current study, the sound wave with high intensity was produced to drive a TAC to produce cooling power at a cold temperature around 18 °C, using saturated water vapor as the working fluid. The drainage of condensate in the regenerator is the key to the system’s performance. This work is dedicated to investigate the effect from temperature gradient created in TAC on the condensation enhancement, by adopting three different designs of regenerators. A 3D printer was used to design and fabricate different structures of regenerator, and then, the systematic cooling capacity was tested and compared with different regenerators. This work can be extended to evaluate how the TA effect can be affected by the condensation if humid air is directly used as the working fluid. The potential application of this investigation can be an autonomous TAC system for water harvesting in arid areas.

Influence of Parallel Plate Stack Spacing on the Temperature Difference of Thermoacoustic Refrigerator by using Helium as a Working Medium

The refrigerants are usually provided in the conventional refrigeration system despite the fact that, they produce CFCs and HCFCs, which are hazardous to the environment. However, these disadvantages can be overcome using air or inert gas in the thermoacoustic refrigeration system. The present research involves the effect of spacing of parallel plate stack on the performance of thermoacoustic refrigerator (TAR) in terms of temperature difference (ΔT). The entire resonator system as well as other structural parts of the refrigerator are fabricated by using PVC to reduce conduction heat loss. Three parallel plate stacks have been used to study the performance of TAR considering different porosity ratios by varying the gap between the parallel plates (0.28 mm, 0.33 mm and 0.38 mm). The parallel plate stacks are fabricated by using aluminium and mylar sheet material and the working fluid used for the experimental study is helium. The experiments have been carried out with different drive ratios ranging from 0.6% to 1.6% with operating frequencies of 200 – 600 Hz. Also the mean operating pressure used for the experiment is 2 to 10 bar and cooling load of 2 to 10W are considered. The ΔT between the hot heat exchanger and cold heat exchanger is recorded using RTDs and Bruel and Kjaer data acquisition system. Experimental results shows that the lowest temperature measured at cold heat exchanger is -2.1 oC by maintaining the hot heat exchanger temperature at about 32 oC. The maximum temperature difference of 32.90 oC is achieved.

Design and Development of High Current Pulse Shaping Inductor Based on Bitter Magnet Configuration for Electro Magnetic Launcher

A unique pulse shaping inductor was designed and developed using a modified Bitter magnet configuration, to operate at peak current of 150 kA for duration of 5-10 ms in a Pulse Forming Network (PFN). The inductor was designed with a stack of parallel copper plates in the form of circular discs with a central hole, with GRP insulation plates in between. The design is optimized by electromagnetic finite element techniques for inductance and structural stability. The conducting discs and insulators are clamped together with tie rods between two endplates to provide adequate contact pressure and sufficient mechanical support. The conducting, inter connecting and insulating components were modeled and optimised parametrically for the desired performance and structural integrity. The device was fabricated, assembled and tested with 24 bitter plates for 28 μH inductance. The inductor was integrated with 400 kJ capacitor bank module and tested under static and dynamic condition. Current pulse of peak above 100 kA was generated, with consistent arc-free performance, high reliability and structural stability.

Experimental study of thermoacoustic cooling with parallel-plate stack in different distances

Thermo-acoustic is one of Non-Vapor compression cooling technologies also environmentally friendly technology developed rapidly to the present time due to its only use the sound wave to get the magnitude of cooling temperature with the oscillatory motion of the working gas pass through the stack inside a resonator is made in such manner, not use moving part such as the compressor. No lubrication system, low electricity consumption, and without the use of any chemical refrigerants so that the constructions, it will be more simplified and cheaper. The Stack is considered as the heart of the thermo-acoustic system which is the important heat transfer processes will be occur in this area. The variation of the shape, stack distances, kind of material stack applied on the system will be influenced the output of temperature as well. The writer will build a thermo-acoustic refrigerator with the parallel plate stack that is made from PVC Rigid sheets. This study will be done to see how the stack performance with temperature different aspect that would be achieved in the stack, the expectation on this experiment that the performance will have optimum result. The Writer also tried to conduct simulation with the DeltaEC’s Software.

The Influence of Stack Position and Acoustic Frequency on the Performance of Thermoacoustic Refrigerator with the Standing Wave

Abstract Thermoacoustic refrigerator uses acoustic power to transport heat from a low-temperature source to a high-temperature source. The increasing interest in thermoacoustic technology is caused due to its simplicity, reliability as well as application of environmentally friendly working fluids. A typical thermoacoustic refrigerator consists of a resonator, a stack of parallel plates, two heat exchangers and a source of acoustic wave. The article presents the influence of the stack position in the resonance tube and the acoustic frequency on the performance of thermoacoustic refrigerator with a standing wave driven by a loudspeaker, which is measured in terms of the temperature difference between the stack edges. The results from experiments, conducted for the stack with the plate spacing 0.3 mm and the length 50 mm, acoustic frequencies varying between 100 and 400 Hz and air as a working fluid are consistent with the theory presented in this paper. The experiments confirmed that the temperature difference for the stack with determined plate spacing depends on the acoustic frequency and the stack position. The maximum values were achieved for resonance frequencies and the stack position between the pressure and velocity node.

Multi-Objective Optimization of Force Convective Heat Transfer in a Stack of Horizontal Channels Using CFD and Genetic Algorithms: a Comparison with Asymptotic Method Results

In this paper, by combining the computational fluid dynamics (CFD) and NSGA II algorithm, the forced convective heat transfer flow in a stack of horizontal parallel plates has been multi-objectively optimized. In the optimization process, the distance between the plates in the set of parallel channels has been changed so as to simultaneously optimize the amount of heat transfer between the plates and fluid and the pressure drop of the fluid (maximization of heat transfer and minimization of pressure drop). The Pareto front, which illustrate the changes of the heat transfer from the plates and the pressure drop of fluid simultaneously, have been presented in the results section. This result contains important information regarding the thermal designing of stack of channels subjected to forced convective heat transfer. The Pareto front have been obtained for four different fluids that have different Prandtl (Pr) numbers (mercury, air, water and oil), and the results related to each fluid have been discussed. Finally, the multi-objective optimization results obtained in this paper have been compared with the results of the asymptotic analysis method (which is a single-objective method aimed at increasing the amount of heat transfer from plates) for internal fluid flows; and useful information has been obtained.

Influence of stack geometry on the performance of thermoacoustic refrigerator

The work reported in this paper is focused on the performance of a thermoacoustic refrigerator under various operating conditions. The experiments were conducted with various stack geometries fabricated with epoxy glass and Mylar material. Four stacks with different pore sizes are used to evaluate the performance of the refrigerator. Stack 1 has parallel plates of Mylar material 0.12 mm thick spaced 0.36 mm apart. Stacks 2, 3 and 4 are made of epoxy glass with pores of circular cross-section having 1, 2 and 3 mm diameter, respectively. The entire resonator system was constructed from aluminium material coated with polyurethane material from inside to reduce conduction heat losses. Helium gas was used as a working fluid. The experiments were conducted with different drive ratios ranging from 1.6% to 2% with varying cooling load from 2 to 10 W. For the experiments, operating frequencies from 200 to 600 Hz with mean pressure varying from 2 to 10 bar in steps of 2 bar each were considered. The temperatures of the hot end and cold end of the heat exchangers were recorded using RTDs and a data acquisition system under various operating conditions. The coefficient of performance (COP) and relative COP (COPR) are evaluated. Results show that COP of the refrigerator rises with increase of cooling load and decreases at higher drive ratio. It was also observed that the temperature difference between the hot end and cold end of the stack is higher at 2 W cooling load for 400 Hz operating frequency. The temperature difference between the hot end and cold end of the stack was observed to be 19.4, 17.2, 14 and 12.4°C for stacks 1, 2, 3 and 4, respectively, for 10 bar mean pressure and 2 W cooling load. The temperature difference and COP of the parallel plate stack are better compared with other stack geometries.

Casimir energies of self-similar plate configurations

We construct various self-similar configurations using parallel $\delta$-function plates and show that it is possible to evaluate the Casimir interaction energy of these configurations using the idea of self-similarity alone. We restrict our analysis to interactions mediated by a scalar field, but the extension to electromagnetic field is immediate. Our work unveils an easy and powerful method that can be easily employed to calculate the Casimir energies of a class of self-similar configurations. As a highlight, in an example, we determine the Casimir interaction energy of a stack of parallel plates constructed by positioning $\delta$-function plates at the points constituting the Cantor set, a prototype of a fractal. This, to our knowledge, is the first time that the Casimir energy of a fractal configuration has been reported. Remarkably, the Casimir energy of some of the configurations we consider turn out to be positive, and a few even have zero Casimir energy. For the case of positive Casimir energy that is monotonically decreasing as the stacking parameter increases the interpretation is that the pressure of vacuum tends to inflate the infinite stack of plates. We further support our results, derived using the idea of self-similarity alone, by rederiving them using the Green's function formalism. These expositions gives us insight into the connections between the regularization methods used in quantum field theories and regularized sums of divergent series in number theory.

Numerical Study of Entropy Generation Within Thermoacoustic Heat Exchangers with Plane Fins

In this paper a simplified two-dimensional computational model for studying the entropy generation characteristics of thermoacoustic heat exchangers with plane fins is presented. The model integrates the equations of the standard linear thermoacoustic theory into an energy balance-based numerical calculus scheme. Relevant computation results are the spatial distribution of the time-averaged temperature, heat fluxes and entropy generation rates within a channel of a parallel-plate stack and adjoining heat exchangers. For a thermoacoustic device working in the refrigeration mode, this study evidences as a target refrigeration output level can be achieved selecting simultaneously the heat exchangers fin length and fin interspacing for minimum entropy generation and that the resulting configuration is a point of maximum coefficient of performance. The proposed methodology, when extended to other configurations, could be used as a viable design tool for heat exchangers in thermoacoustic applications.

Multi-objective optimization of cooling of a stack of vertical minichannels and conventional channels subjected to natural convection

In this paper, by employing the Computational Fluid Dynamics (CFD) and applying the NSGA II algorithm, cooling of a stack of vertical parallel plates subjected to natural convective heat transfer is multi-objectively optimized. In the optimization process, the plates spacing is changed so as to simultaneously maximize the flow rate of the fluid sucked through the stack of plates (cooling flow rate) and the amount of heat transfer between the plates and ambient air. The plates spacing varies from 200 µm to 100 mm; and thus, the investigated channels can be classified between minichannels and conventional channels. In Section 3, the Pareto front, which simultaneously displays the variations of the cooling suction flow rate and the heat transfer from plates, will be presented, and it will be demonstrated that the Pareto front conveys very important results for the thermal designing of a stack of parallel channels subjected to natural convective heat transfer. At the end, the multi-objective optimization results obtained in this paper will be compared with the related results of the asymptotic method and the analytical approach, which are single-objective optimization methods and aimed at increasing the amount of heat transfer from the plates; and very useful and valuable conclusions will be obtained.