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