Performance optimization of water-Al2O3 nanofluid flow and heat transfer in trapezoidal cooling microchannel using constructal theory and two phase Eulerian-Lagrangian approach

doi:10.1016/j.powtec.2017.09.046

Powder Technology

Volume 323, 1 January 2018, Pages 103-114

https://doi.org/10.1016/j.powtec.2017.09.046 Get rights and content

Highlights

•
Trapezoidal cooling microchannel is optimized using constructral theory.
•
Two phase Eulerian-Lagrangian method used for modeling of nanofluid.
•
Microchannel with side angle 75 has the maximum overall conductivity.
•
Optimal volume fraction will be occurred in range of 0.4 ≤ η ≤ 0.5.

Abstract

In this study, the performance of micro heat sink with nanofluid of water- Al₂O₃ of 1% and the optimum geometry dimensions are evaluated in the trapezoidal microchannel by using constructal theory and the two-phase Eulerian–Lagrangian method. Also, the optimal microchannel diameter obtained with the intersection of asymptotes method, was compared with the numerical state. The results show that for a constant pressure drop, microchannel with a 70° side angle in the optimum state, has the maximum total thermal conductivity in the dimensionless state. In addition, by reducing the side angle of the trapezoidal cross-section, the total thermal conductivity would be reduced in a dimensionless state. The maximum thermal conductivity in a trapezoidal microchannel will happen in the volume fraction range of 0.4 ≤ η ≤ 0.5. The maximum and minimum error between numerical and analytical study for the optimum hydraulic diameter is 47.54% and 3.2%, respectively.

Graphical abstract

Introduction

Developing various technologies lead to production of equipment with small volume and high rate heat transfer. Performance of electrical devices is strongly influenced by the temperature of operating condition. Thus, cooling of these devices is a vital issue that should be taken into consideration. Due to the ability of heat transfer from an area with high heat flux and ease to manufacturing, Microchannels are being used in the cooling systems for electronic devices and heat exchangers [1], [3]. Finding methods with low cost and high performance is one of the challenges for modern heat transfer. Therefore, optimization of such methods has been carried out experimentally, theoretically and also numerically [4], [6].

Bejan [7] and Bejan and Lorente [8] performed comprehensive studies on the influence of constructal design on heat transfer with the focus on shape generation and structure. This viewpoint is known as constructal theory. Furthermore, they reached the optimal shape for a constant volume under convection heat transfer. Muzychka [9] studied the effect of the length ratio on the maximum heat transfer for various ducts with different shapes such as; rectangular, elliptic, circular, polygonal and triangular. He obtained solutions to optimize heat transfer per unit volume and duct dimension. Bello-Ochende [10] investigated the influence of geometry parameter on the ratio of heat transfer in rectangular microchannel heat sinks. Salimpour et al. [11] invoked the constructal theory presented by Bejan [7] to determine the optimal dimension with various geometries. He simulated heat transfer in square, triangular and circle geometry using ANSYS software. They showed that the highest heat transfer occurs in a channel with square cross-section.

In the recent years, the nanofluids are utilized to enhance the thermal efficiency. Nanofluids have higher heat transfer rate in comparison with the base fluid. Many scholars have studied nanofluids involving modeling and experimental researches. However, many studies consider nanofluids as a single-phase flow, and the accuracy of such results have been low compared to the experimental data. Therefore, many researchers apply two-phase model to investigate nanofluid in order to improve the accuracy of the results. Several numerical and experimental studies are done on the heat transfer mechanism for nanofluid in microchannel.

Abbassi et al. [12] analyzed the force convection of Al₂O₃ nanofluid in a rectangular microchannel. They showed that, the accuracy of results in two-phase model is closer to the experimental results than a single-phase model. They applied a two-phase Eulerian–Eulerian method to study the heat transfer in their paper. Fani et al. [13] showed a numerical model to model force convection of CuO nanoparticles in a trapezoidal microchannel-heat-sink which presented 15% enhancement of pressure drop with doubling of nanoparticle diameter. Kalteh et al. [14] concluded that, the decrement of nano-particle diameter has low effect on the enhancement of heat transfer particularly for lower volume concentration. Sohel et al. [15] used three types of nanofluids including CuO–water, Al₂O₃–Water and TiO₂––water to compare the thermal performance of these nanofluids in a circular microchannel heat sink. The results showed that, using CuO/water as nano- particle in a fluid has better thermal performance compared to the nano particles of Al₂O₃ or TiO₂–, injected in the base water. Rajesh Nimmagadda et al. [16] modeled the force convection of nanofluids in rectangular microchannel heat sinks. They used silver (Ag), Al₂O₃ and hybrid (Al₂O₃ + Ag) as nanoparticles. They showed that the increase in nanofluid volume fraction and Reynolds number can improve the convective heat transfer coefficient. Furthermore, they showed higher performance of hybrid nanofluid compared to Al₂O₃ or Ag-water with equal volume concentration.

Moreover, some researchers have studied optimization of microchannel structure cooled with nanofluid. Wang et al. [17] generated a numerical model to study heat transfer in nanofluid-cooled microchannel heat sink (MCHS). They showed that, their numerical results have a closer agreement with the experimental data. Also, they simultaneously optimized the geometry of micro heat sink including channel number, width ratio of channel and channel aspect ratio parameters. Two microchannel structures, double-side and double-layer with Al₂O₃ nanofluid as coolant, were optimized and compared by Sakanova et al. [18]. They stated that the double side structure with counter flow showed a decrease in the thermal resistance compared to double-side structure. Bahiraei et al. [19] numerically investigated flow and heat transfer of water-Al₂O₃ nanofluid in triangular microchannel. Applying the Eulerian–Lagrangian simulation caused to tolerably precise results with experimental data. Fani et al. [20] assessed numerically the effect of viscous dissipation and Brownian motion of aluminum oxide nanofluid in trapezoidal microchannel using two-phase Eulerian–Eulerian approach. They observed that, the enhancement in aspect ratio at constant Reynolds number, pressure drop and Nusselt number will be decreased.

In the present paper, the optimum geometry is calculated numerically for a trapezoidal microchannel with Al₂O₃ nanofluid flow. We fixed some parameter such as; total elemental volume and axial length of the microchannel heat sink. The optimal geometry and system configuration that maximize the dimensionless global thermal conductance when the pressure drop is constant in the volumetric element, are calculated. At last, the maximum overall thermal conductivity is selected among the channels and the results are compared with the approximate counterparts.

Section snippets

Model

In this article, forced convection in heat absorbent microchannel with trapezoid section area with side angle of 30, 45, 60, 75° are studied. In Fig.1, heat will be transferred by means of the heating surfaces such as; electronic chips to the underside heat absorbent and from there through a solid component made of silicon material which has high conductivity will be guided. Then, the generated heat would be transferred to the coolant passing through channels. As shown in Fig.1 due to the

Numerical method and validation

For discretization of the aforesaid nonlinear equations, the control volume method is used. To estimate the Diffusion and convection terms, the upwind scheme of second order is used and the SIMPLE algorithm is employed for coupling the velocity and pressure fields. The solution grid is set to be non-uniform in all directions. $\begin{array}{l} |ψ^{n} - ψ^{n - 1}| \leq 10^{- 6} \end{array}$ where n is the counter variable and ψ is representative of all dependent variables (u, v, w, T) in the non-linear equations of the flow. In order to ensure the

Optimization constraints and parameters

To evaluate the performance of trapezoidal microchannel heat absorbent and its cooling capacity, a series of geometric constraints applied to the channel networks are used. The unit microchannel Volume (length and cross-section) and substrate material are fixed.

The side angle of a trapezoidal heat absorbent micro channel and the ratio of the internal thicknesses are the only variable parameters. The given volumetric computational element cell constraint for microchannel with trapezoidal

Scale analysis

The approximate solution of the present section includes the analytical development of the relation between the overall thermal conductivity, C, and different geometries (D) in two limit states D → 0 and D → ∞.

Using these asymptotic lines, the optimized value of D in an approximate way is determined in a manner for which the thermal conductivity is maximum. The assumptions used during the proximate analysis the proximate analysis are as follows: The distribution of the flow is uniform (equal flow

Results and discussion

The considered heat absorbent microchannels have five degrees of freedom(t₁/t₂, t₃/t₂, β, η, L). In the current study, the three degrees of freedom (t₁/t₂, t₃/t₂, L) are assumed constant. While the other two degrees of freedom at a given pressure drop can be changed. By considering the ratios of t₃/t₂ = 1 and t₁/t₂ = 0.08, the internal structure of microchannel is considered constant. The total cell volume of microchannel is V = 0.9 mm³and the microchannel length is considered to be L = 10 mm. Heat absorbent

Conclusions

By using the analytical and numerical approaches, microchannel with the side angels of 30, 45, 60, 75 are studied. It is shown that a channel with the side angel 75 has the maximum overall non-dimensional conductivity. Also, the comparison between the optimum numerical results with the approximate solutions shows good agreement in calculation of the optimal aspects of microchannel. In optimization of trapezoidal microchannel due to the presence of walls, one can conclude the mentioned results:

References (33)

F. Hedayati et al.
Effects of nanoparticle migration and asymmetric heating on mixed convection of TiO₂ − water nanofluid inside a vertical microchannel
Powder Technol.
(2015)
F. Hedayati et al.
Fully developed forced convection of alumina/water nanofluid inside microchannels with asymmetric heating
Powder Technol.
(2015)
J. Rostami et al.
Optimization of conjugate heat transfer in wavy walls microchannels
Appl. Therm. Eng.
(2015)
A.S. Navaei et al.
Heat transfer enhancement of turbulent nanofluid flow over various types of internally corrugated channels
Powder Technol.
(2015)
Y.S. Muzychka
Constructal design of forced convection cooled microchannel heat sinks and heat exchangers
Int. J. Heat Mass Transf.
(2005)
T. Bello-Ochende et al.
Constructal cooling channels for microchannel heat sinks
Int. J. Heat Mass Transf.
(2007)
M.R. Salimpour et al.
Constructal optimization of the geometry of an array of microchannel
Int. Commun. Heat Mass Transfer
(2011)
M. Kalteh et al.
Experimental and numerical investigation of nanofluid forced convection inside a wide microchannel heat sink
Appl. Therm. Eng.
(2012)
B. Fani et al.
Effect of nano-particles size on thermal performance of nanofluid in a trapezoidal microchannel-heat-sink
Int. Commun. Heat Mass Transfer
(2013)
M. Kalteh et al.
Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel
Int. J. Heat Fluid Flow
(2011)

M.R. Sohel et al.

Investigating the heat transfer performance and thermophysical properties of nanofluids in a circular microchannel

Int. Commun. Heat Mass Transfer

(2013)

R. Nimmagadda et al.

Conjugate heat transfer analysis of microchannel using novel hybrid nanofluids (Al₂O₃ + Ag ⁄ Water)

Eur. J. Mech. B. Fluids

(2015)

X.D. Wang et al.

Optimal geometric structure for nanofluid-cooled microchannel heat sink under various constraint conditions

Energy Convers. Manag.

(2013)

A. Sakanova et al.

Optimization and comparison of double-layer and double-side microchannel heat sinks with nanofluid for power electronics cooling

Appl. Therm. Eng.

(2014)

M. Bahiraei et al.

Prediction of entropy generation for nanofluid flow through a triangular minichannel using neural network

Adv. Powder Technol.

(2016)

B. Fani et al.

Investigating the effect of Brownian motion and viscous dissipation on the nanofluid heat transfer in a trapezoidal microchannel heat sink

Adv. Powder Technol.

(2015)

Cited by (38)

An overview of heat transfer enhancement methods in microchannel heat sinks
2023, Chemical Engineering Science
With the high miniaturization and integration of micro-electro-mechanical systems, micro-satellite, lasers, and high-voltage electrical appliances, the heat transfer of electronic equipment is facing severe challenges. The microchannel heat sink is widely used as an effective heat transfer method, which can achieve large heat flux cooling. However, conventional microchannel heat sinks have disadvantages, such as large wall superheat, low boiling critical heat flux, large pressure drop, and poor temperature uniformity. In view of the above problems, people have devoted themselves to designing and improving microchannel heat sinks to improve their comprehensive heat transfer performance, in recent years. In this paper, the latest research achievements and trends of microchannel heat sinks are systematically reviewed and summarized from four aspects: microchannel structure, internal reinforcement structure, surface treatment, and material types, which are beneficial to promote the practical application and commercialization of microchannel heat sinks. To the best of the authors' knowledge, this is the first time to summarize the research progress of enhancing the heat transfer performance of microchannel heat sinks from the perspective of surface treatment and material types. Then, the heat transfer performance and fabrication technology of diamond microchannel heat sink with great heat transfer potential are mainly studied. Based on the reviewed studies, although the combination of various enhanced heat transfer methods can improve heat transfer, the key issue is how to balance the heat transfer efficiency and the pressure drop penalty. Finally, the important research progress of enhanced microchannel heat sinks is objectively expounded, and the rationalized suggestions for the future research direction and research ideas of microchannel heat sinks are presented.
State-of-the-art review of nanofluids in solar collectors: A review based on the type of the dispersed nanoparticles
2021, Journal of Cleaner Production
Nanofluids as a new generation of fluids have attracted a lot of research works. There is growing evidence that the nanofluids are more suitable for various heat transfer applications than the conventional fluids. One of the most important parameters in the thermal behavior of such fluids is the type of nanoparticles dispersed in the base fluid. The present review paper is devoted to provide an overview on the distinct types of particles used in nanofluid research with emphasis on their application in solar collectors. The impact of nanofluids on heat transfer under different dispersive particles is explained for both numerical and experimental researches. Works concerning the application of nanofluids in solar collectors are singled out and analyzed. The nanoparticles are classified into metallic and non-metallic and the various configurations of solar collectors are considered. The review indicates that the flat plate solar collectors are the most investigated among the considered configurations. It is also shown that Al₂O₃-based nanofluids have been widely considered in these collectors compared to other nanofluids. In addition, the non-metallic based nanofluids can be more useful for the efficiency enhancement of solar collectors compared to metal based nanofluids. Some negative aspects related to nanofluids are also pointed out such as the thermo-physical instability and the reduced efficiency at high nanoparticle volume fraction. Finally, the general conclusions are drawn and future directions for research are proposed. It is noted that the present review concerns the nanofluids based on a single nanoparticle type. Hybrid nanofluids are subject to a future review.
Influence of non-uniform asymmetric heating on conjugate heat transfer in a rectangular minichannel using nanofluid by two-phase Eulerian-Lagrangian method
2021, Powder Technology
Citation Excerpt :
Although, discrete phase model (DPM) is computationally expensive, it can predict results to a closer agreement with experimental ones and provides scope of accounting for the effect of Brownian motion, thermophoretic force, drag force and lift force [4], thus increasing the implementation of DPM in theoretical studies concerning nanofluid flow in recent times. A careful review shows that a handful of literatures [4–11] are available applying the two-phase model for investigating the convective heat transfer using nanofluids. Mirmasoumi and Behzadmehr [8] and Akbarinia and Laur [9] investigated the effect of nanoparticle size using the two-phase mixture model on the mixed convection heat transfer.
A numerical analysis is conducted to examine the effects of non-uniform and asymmetric heating on the conjugate thermal transport characteristics for laminar forced convective flow of nanofluid through a rectangular minichannel. The Eulerian-Lagrangian formulation.is employed to model the nanofluid as one single fluid with two phases. The exteriors of both the walls are subjected to a sinusoidal heat flux profile with a phase difference. The theoretical model under negligible wall thickness condition always underestimates the overall rate of heat transfer. There exists an intricate interplay between the non-uniform asymmetric heat flux profiles imposed on the walls and the physico-thermal properties of the fluid and walls to characterize the thermal transport dynamics. The average heat transfer rate is higher for the non-uniform asymmetric heating as compared to uniform heating and moreover, the impact of asymmetric non-uniform heating is higher than the effect of non-uniform heating alone.
Analysis of entropy generation of ferrofluid flow in the microchannel with twisted porous ribs: The two-phase investigation with various porous layers
2021, Powder Technology
Citation Excerpt :
They showed that their results of properties with temperature dependency were almost equal to those of properties with temperature independency. Khodabandeh and Abbassi [2] optimized the thermal and hydrodynamic performance of microchannel coolant contain nanofluid using the Eulerian-Lagrangian method. They indicated that the trapezoidal microchannel with the side angle of 70 degrees had the maximum thermal conductivity.
Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels, due to their increased surface and better thermal performance than that of normal heat sinks were used in electronic cooling devices. In this numerical investigation, the first and second laws of the thermodynamic impact of twisted porous ribs on the microchannel were studied. The effects of the Reynolds number and volume fraction of nanoparticles were investigated. The range of Reynolds number was 250 to 1000. All types of the microchannel in this study consisted of a clear microchannel, a twisted porous ribbed microchannel with two and three layers of twisted porous ribs. The results show that by inserting porous ribs, the local cross-section decreases, and the local Reynolds number increases. Also, twisted porous ribs are the cause of nanofluid flow circulation and make the heat transfer coefficient greater. Increasing the porous layer from one layer to three layers has an increasing effect on the heat transfer coefficient, and the friction factor and increasing the φ is the reason for increasing the friction factor. Finally, the microchannel with triple layers of twisted porous ribs has better performance in total entropy generation, and by inserting twisted porous ribs, the entropy generation decreases.
The effect of magnetic field on the twisted porous ribs with various porous layers and pitches: The first and second laws of thermodynamics study with two-phase approach
2021, Powder Technology
Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels are utilized in electronic cooling devices owing to their increased surface and better thermal performance than that of normal heat sinks. In this numerical investigation, the first and second laws of thermodynamics impact of twisted porous ribs on the microchannel are studied. The effects of the Reynolds number, the Hartman number, and the volume fraction of nanoparticles are investigated. The range of the dimensionless number for the Hartmann number and the Reynolds number is 0 to 20 and 250 to 1000, respectively. All types of microchannel in this study consist of clear microchannels in two groups; group one (No. 1, 2 and 3) and group two (No. 4, 5, and 6). The obtained results show that at the end of each porous rib, the reported parameters depict a decrease. Twisted porous ribs cause a significant decrease in the expanding thermal boundary layer. Also, the microchannel with triple-layer porous ribs (No. 3) exhibits considerable performance in the entropy generation. Finally, since group one has a double pitch, it has the better thermal performance and increasing the Hartmann number is one of the reasons for the increasing velocity gradient near the microchannel wall and friction factor.
Analysis of heat transfer characteristics through an rectangular enclosure
2021, Materials Today: Proceedings
The aim of this present work is to investigate the characteristics of laminar airflow and heat transfer phenomena in a two-dimensional rectangular enclosure with isothermally heated baffles and adiabatic walls. Using the Boussinesq approximation and negligible viscous dissipation effect, the governing equations are solved using the finite volume method and fluent software is used to visualize the simulation results. Different forms of the baffles (trapezoidal, plane, and isosceles shapes) have been examined for several values of Reynolds number (Re) and Richardson number (Ri). In the form of isotherms, streamlines, heating efficiency, average bulk temperature, local and average Nusselt number along the hot surface, the results have been presented. Maximum heating efficiency is found to be achieved for higher values of Reynolds number, and Richardson number. In addition, it is noted that the efficiency of heat transfer decreases with the increase of baffle length. From this study, it is ensured that heat transfer enhancement becomes maximum in presence of plane baffles as compared to the other baffles.

View all citing articles on Scopus

View full text

Performance optimization of water-Al2O3 nanofluid flow and heat transfer in trapezoidal cooling microchannel using constructal theory and two phase Eulerian-Lagrangian approach

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Model

Numerical method and validation

Optimization constraints and parameters

Scale analysis

Results and discussion

Conclusions

Powder Technol.

Powder Technol.

Appl. Therm. Eng.

Powder Technol.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. Commun. Heat Mass Transfer

Appl. Therm. Eng.

Int. Commun. Heat Mass Transfer

Int. J. Heat Fluid Flow

Int. Commun. Heat Mass Transfer

Eur. J. Mech. B. Fluids

Energy Convers. Manag.

Appl. Therm. Eng.

Adv. Powder Technol.

Adv. Powder Technol.

Performance optimization of water-Al₂O₃ nanofluid flow and heat transfer in trapezoidal cooling microchannel using constructal theory and two phase Eulerian-Lagrangian approach