Elliptical Microchannels Research Articles

Numerical simulation of convective heat transfer behavior of nanofluids in elliptical microchannels

This study employs a numerical simulation approach to investigate the heat transfer performance of elliptical microchannel heat sinks (MCHS) with varying aspect ratios (AR) of the elliptical cross-section. The convective heat transfer behavior of water and water-based nanofluids containing CuO nanoparticles at different volume fractions within the MCHSs is examined. The research results indicate that at Re = 600, as the AR of the elliptical cross-section increases from 1:1 to 1.75:1, the thermal performance of the MCHS improves by 5.33%. Furthermore, with an increase in the volume fraction of nanofluid from 0 to 0.75%, the convective heat transfer coefficient of the nanofluid increases by 11.87%. Compared to the circle MCHS using water as the coolant, the MCHS with an elliptical cross-section with an AR of 1.75:1 and a nanofluid volume fraction of 0.75% can reduce the maximum temperature of the chip by 9.78%.

Convective Heat Transfer and Entropy Generation Analysis in Elliptic Microchannels

Abstract In this paper, we investigate analytically the first and the second law characteristics of fully developed gaseous slip flow with the H1 boundary condition through elliptical microchannels. The closed-form solution of temperature distribution was obtained with the separation of variables method. Expressions for the Nusselt number, the nondimensional entropy generation rate, and the Bejan number were further deduced. The influences of crucial factors, including viscous dissipation, rarefaction, aspect ratio, and fluid axial heat conduction, have been carefully evaluated. The results indicated that viscous dissipation has a dramatic impact on heat transfer characteristics. But the rarefaction effect was found to significantly reduce the effect of the viscous dissipation on the Nusselt number, and the former may not deteriorate the heat transfer performance when considering the viscous dissipation. The main source of the entropy generation rate is controlled by fluid axial heat conduction when the Peclet number is less than one. The impacts of the viscous dissipation, the rarefaction, and the aspect ratio on entropy generation are magnified when fluid axial conduction dominates the irreversibility. The analytical solutions of the current study will make it possible to compare, evaluate, and optimize alternative elliptical microchannel heat exchanger design options.

Exact solution of the Graetz–Brinkman problem extended to non-Newtonian nanofluids flow in elliptical microchannels

Exact solution of the Graetz–Brinkman problem extended to non-Newtonian nanofluids flow in elliptical microchannels

Numerical Forced Convection Heat Transfer, Fluid Flow and Entropy Generation Analyses of Al2O3- Water Nanofluid in Elliptical Channels

This study investigates a three-dimensional elliptical microchannel heat sink for heat dissipation in laminar forced convection. The study seeks to improve thermal performance and overcome overheating associated with excessive temperature commonly experienced in heat-generating equipment, which is beyond the temperature usually specified by the manufacturer. The objective of the study is to evaluate the heat transfer, fluid flow, and entropy generation characteristics of Al2O3-water nanofluid in an elliptical cooling channel. The numerical analysis is investigated on the structure experiencing constant volumetric heat generation. The parameters considered are Reynolds number of 100 ≤ Re ≤ 500, nanoparticle concentration ϕ, from 0% to 4% with channel aspect ratio Ar from 1 to 3. The impacts of these parameters on the maximum temperature, heat transfer coefficient, friction factor, and volumetric entropy generation are reported. The study demonstrates that heat transfer is enhanced in the elliptical cooling channel at different aspect ratios, nanoparticle concentrations, and Reynold numbers. The results showed that as the nanoparticle concentration, channel aspect ratio, and Reynolds number (Re) increase, the maximum temperature, and total entropy generation decrease. As the channel aspect ratio increases at a specified Re = 200 and nanofluid concentration, ɸ = 3%, the maximum temperature, and total entropy generation decrease by up to 62% while the heat transfer coefficient increases by up to 78% and the friction factor increase by less than 2% with aspect ratio. However, the friction factor is not sensitive to the nanofluid concentration as a coolant.

Analytical solutions of slip flow and H1 heat transfer in elliptical microchannels

The slip flow and heat transfer problems inside a micro- or nano-channel are active research topics. Understanding the velocity and temperature distributions in these channels is essential in both theory and applications. In this paper, the analytical solutions of the fully developed slip flow and heat transfer under the H1 boundary condition in elliptical microchannels are obtained with the velocity slip and temperature jump. The separation of variables method is employed to solve the momentum and energy equations, and the coefficient of the velocity profile is calculated using the binomial series twice. Based on the result of the velocity profile, the analytical solution of the temperature profile is also derived. A new model is deduced to predict the Poiseuille number in elliptical microchannels. The close-form solution of the Nusselt number is first obtained and can serve as a benchmark for other approaches.

Combined Pressure-Driven and Electroosmotic Slip Flow through Elliptic Cylindrical Microchannels: The Effect of the Eccentricity of the Channel Cross-Section

Electroosmotic force has been used extensively to manipulate fluid flow in a microfluidic system with various channel shapes, especially an elliptic cylinder. However, developing a computational domain and simulating fluid flow for a system involving an elliptic channel consumes a large amount of time. Moreover, the mathematical expression for the fluid velocity of electroosmotic flow in an elliptic channel may be given in the form of the Mathieu functions that have difficulty in achieving the numerical result. In addition, there is clear scientific evidence that confirms the slippage of fluid at the solid-fluid interface in a microscale system. In this study, we present the mathematical model of combined pressure-driven and electroosmotic flow through elliptic microchannels under the slip-fluid condition. From the practical point of view in fluidics, the effect of the eccentricity of the channel cross-section is investigated on the volumetric flow rate to overcome the difficulty. The results show that the substitution of the equivalent circular channel for an elliptic channel provides a valid flow rate under the situation that the areas of both channel cross-sections are equal and the eccentricity of the elliptic cross-section is less than 0.5. Additionally, the flow rate obtained from the substitution is more accurate when the slip length increases or the pressure-gradient-to-external-electric-field ratio decreases.

Laminar Forced Convective Heat Transfer Performance Analysis of Elliptical and Semicircular Microchannels

In this paper, a single-phase fluid flow, and heat transfer characteristics of elliptical and semicircular microchannels using air as a working fluid are analyzed for a range of Reynolds number (). Experiments are performed on aluminum alloy (AlSi10Mg) microchannels, including inlet and outlet manifolds fabricated using three-dimensional printing technology. A numerical model is developed and validated with the experimental results to study the effect of operating and geometrical parameters on the heat transfer performance of the microchannels. It is found that the temperature difference, Poiseuille number, and average Nusselt number in the elliptical microchannel are higher for all the Reynolds numbers. The axial wall conduction significantly affects the temperature distribution in the fluid and wall of the microchannels. The effect of axial conduction weakens with the increase in the Reynolds number. The numerical average Nusselt number increases with Reynolds number for and is higher than the average Nusselt number predicted from the correlation.

Effect of Cross-Sectional Geometry on Hydrothermal Behavior of Microchannel Heat Sink

Abstract The aim of this paper is to numerically analyze the hydrothermal behavior of different cross-sectional geometries of microchannel heat sinks (MCHSs) and conduct a comparative analysis of traditional and non-traditional designs using ANSYS Fluent. It is expected that the proposed design discussed in this paper will improve the performance of MCHSs by maximizing the cooling capability and minimizing the thermal resistance and entropy generation rate, thus leading to better energy efficiency. The channel designs include a rectangular microchannel (RMC), a circular microchannel (CMC), an elliptical microchannel (EMC), a trapezoidal microchannel (TMC), a hexagonal microchannel (HMC), and a new microchannel (NMC) which has a plus-like shape. The discussed geometry of the NMC is designed in such a way that it maximizes the cross-sectional area and the wetted perimeter of the channel, keeping the hydraulic diameter constant ( D h = 412 {D_{h}}=412 µm). The performance of various channels is compared on the basis of pressure drop, wall temperature, thermal enhancement factor, thermal resistance, thermal transport efficiency, and entropy generation rates. It has been observed that the NMC is capable of cooling effectively and it can achieve a minimum wall temperature of 305 K, thus offering the lowest thermal resistance ( R th {R_{\mathrm{th}}} ), irreversible heat loss, and entropy generation rate. Moreover, the NMC has achieved the highest value of the thermal enhancement factor, i. e., 1.13, at Re = 1 , 000 \mathrm{Re}=1,000 . Similarly, it has the highest thermal transport efficiency of almost 97 % at Re = 1 , 000 \mathrm{Re}=1,000 , followed by the TMC and the RMC. Overall, the NMC has achieved the best performance in all aspects, followed by the RMC and TMC. The performance of the EMC, the CMC, and the HMC was found to be the worst in this study.

Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Approximations for Steady Unidirectional Slip Flows in Elliptic Microchannels

Abstract Consider steady flows in a channel whose cross section Ω is an ellipse, flows with the Navier slip boundary condition. Denote the volume flow rate by Q. We apply to elliptic cross section a recent simple approximation, a rigorous lower bound R on Q, requiring, along with the channel's area and perimeter, the calculation of just the torsional rigidity and two other domain functionals. This avoids the need for solving the partial differential equation repeatedly for differing values of the slip parameter.

Oscillating pressure-driven slip flow and heat transfer through an elliptical microchannel

This paper studies the transient slip flow and heat transfer of a fluid driven by the oscillatory pressure gradient in a microchannel of elliptic cross section. The boundary value problem for the thermal-slip flow is formulated based on the assumption that the fluid flow is fully developed. The semi-analytical solutions of velocity and temperature fields are then determined by the Ritz method. These solutions include some existing known examples as special cases. The effects of the slip length and the ratio of minor to major axis of the elliptic cross section on the velocity and temperature distribution in the microchannel are investigated.

Thermodynamic optimisation of rectangular and elliptical microchannels with nanofluids

The thermodynamic optimisation of laminar flow in rectangular and elliptical microchannels subjected to low or high heat flux is analytically studied. Two mathematical models are developed, by incorporating the aspect ratio term, to evaluate entropy generation numbers. Two relations for calculating the conductivity and the viscosity of CuO-water nanofluids, based on experimental data from literature, are proposed. An entropy generation analysis is proposed to optimise the geometry of the microchannel and the working fluid for each heat flux condition. It has been revealed that at low heat flux, using water in microchannels with aspect ratio e = 1 is more efficient. However, at high heat flux, it is more advisable to use microchannels with the smallest possible aspect ratio containing CuO-water nanofluids with higher conductivity and higher nanoparticles concentration. For the two cases, the rectangular microchannel reaches the minimum value of total entropy generation number compared to the elliptical microchannel.

Thermodynamic optimisation of rectangular and elliptical microchannels with nanofluids

Thermodynamic optimisation of rectangular and elliptical microchannels with nanofluids

Size dependences of hydraulic resistance and heat transfer of fluid flow in elliptical microchannel heat sinks with boundary slip

As a well-accepted interfacial property, boundary slip condition is believed to affect hydraulic and thermal performances of various micro/nanofluidic applications. By considering the boundary slip for water flow through a microchannel heat sink, size dependences of hydraulic resistance and heat transfer of the water flow in a group of elliptical microchannel heat sinks with the same channel cross-sectional area but different length ratios of semi-major and minor axes are re-examined. The present work finds that hydraulic resistance and heat transfer of water flow in a microchannel are strongly dependent on the geometric parameters of the channel and the boundary slip condition. Both the hydraulic resistance and the convective heat transfer coefficient of the water flow in the elliptical shaped microchannel decrease with the increasing hydraulic diameter of the channel. An elliptical shaped microchannel having the largest hydraulic diameter, namely a microtube with the minimum length ratio of semi-major and minor axes being equal to one, has the smallest hydraulic resistance and the smallest heat transfer coefficient. Boundary slip at the solid-liquid interface can attenuate the hydraulic resistance and enhance the heat transfer capacity of the water flow in a microchannel, and these effects of slip on the mass and heat transfer are size-dependent. For the microchannel with a smaller hydraulic diameter, slip has a more significant attenuation effect on the hydraulic resistance and a more significant enhancement effect on the heat transfer. Geometric size optimization combined with the effective regulation of boundary slip can be a potential method to improve the mass and heat transfer of fluid flow over the micro/nanoscale.

Shear work contribution to convective heat transfer of dilute gases in slip flow regime

In the literature some researchers highlighted that for a dilute gas in slip flow regime and in presence of a non negligible viscous heating, the analysis of the gas micro-convection has to be tackled by modifying the thermal boundary conditions to account for the shear work due to the slip at the wall. Although in the recent past a specific modified boundary condition has been proposed, theoretically justified and applied to investigate the effect of the shear work on the convective heat transfer in presence of dilute gases, in this paper is demonstrated that there is not a need of a modified boundary condition in order to take into account the effect of the shear work in the analysis of forced convection. In the present work by means of a comprehensive theoretical analysis is demonstrated that the modified boundary condition is useless for the analysis of the effect of shear work on the evaluation of the convective heat transfer coefficients in presence of a dilute gas with non-negligible viscous dissipation.Moreover, to evaluate the inaccuracy of the results obtained by using the modified boundary conditions the difference, in terms of Nusselt number, between the exact and the approximate solution has been numerically estimated for elliptical microchannels. The numerical outcomes point out that the adoption of the modified boundary condition leads to an underestimation or an overestimation of the Nusselt numbers depending on the values of Brinkman number and on the channel cross section geometry.

Electroosmotic flow of a power law fluid in an elliptic microchannel

Abstract In this paper the two dimensional electroosmotic flow of a non-Newtonian fluid governed by the power law model is studied for circular and elliptic microchannels. The electric potential and the velocity distribution inside the microchannel are solved without invoking the Debye–Huckel linear approximation. The solutions are sought for different aspect ratio (E), power law index (n), Debye–Huckel parameter (K) and the wall zeta potential (ζ). The effect of these parameters is studied on the ratio of flow rates Q/Qcir and friction parameter. The comparison of a circular geometry (E = 1) and an elliptical geometry (E ≠ 1) is made on an equal cross sectional area basis. Elliptic microchannels always reduce the flow rate when compared to circular microchannels. This reduction is much more significant at lower values of K and ζ. Shear thickening fluids affect the reduction in flow rates much more when compared to shear thinning ones. This reduction in flow rates becomes larger as the aspect ratio increases. The frictional parameter increases with K and ζ for all E. Shear thickening fluids have larger frictional parameter values compared to shear thinning fluids.

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

Flow and Thermal Performance of a Water-Cooled Periodic Transversal Elliptical Microchannel Heat Sink for Chip Cooling.

Flow and thermal performance of transversal elliptical microchannels were investigated as a passive scheme to enhance the heat transfer performance of laminar fluid flow. The periodic transversal elliptical micro-channel is designed and its pressure drop and heat transfer characteristics in laminar flow are numerically investigated. Based on the comparison with a conventional straight micro- channel having rectangular cross section, it is found that periodic transversal elliptical microchannel not only has great potential to reduce pressure drop but also dramatically enhances heat transfer performance. In addition, when the Reynolds number equals to 192, the pressure drop of the transversal elliptical channel is 36.5% lower than that of the straight channel, while the average Nusselt number is 72.8% higher; this indicates that the overall thermal performance of the periodic transversal elliptical microchannel is superior to the conventional straight microchannel. It is suggested that such transversal elliptical microchannel are attractive candidates for cooling future electronic chips effectively with much lower pressure drop.

Numerical Investigation of Viscous Dissipation in Elliptic Microducts

In this work a numerical analysis of heat transfer in elliptical microchannels heated at constant and uniform heat flux is presented. A gaseous flow has been considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effects. The velocity and temperature distributions have been determined in the elliptic cross section, for different values of aspect ratio, Knudsen number and Brinkman number, solving the Navier-Stokes and energy equations within the Comsol Multiphysics® environment. The numerical procedure has been validated resorting to data available in literature for slip flow in elliptic cross sections with Br =0 and for slip flow in circular ducts with Br > 0. The comparison between numerical results and data available in literature shows a perfect agreement. The velocity and temperature distributions thus found have been used to calculate the average Nusselt number in the cross section. The numerical results for Nusselt number are presented in terms of rarefaction degree (Knudsen number), of viscous dissipation (Brinkman number), and of the aspect ratio. The results point out that the thermal fluid behavior is significantly affected by the viscous dissipation for low rarefaction degrees and for aspect ratios of the elliptic cross-section higher than 0.2.

Dilute gas flows through elliptic microchannels under H2 boundary conditions

This work presents a numerical investigation of slip flow inside microchannels characterized by an elliptic cross-section. A gaseous flow is considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effect. The momentum and energy equations are solved resorting to the finite element method; the numerical results are compared with analytical values available in the literature for slip flow in elliptic cross sections and in circular ducts, to validate the numerical procedure. The temperature field is determined by considering the H2 boundary condition for different combinations of heated walls among the four branches constituting the elliptic perimeter. Nusselt numbers and normalized wall temperatures in the case of two or four heated sides are presented and discussed.The influence of the cross section aspect ratio and of the rarefaction effects on the fluid behavior are investigated. The numerical results point out that the Nusselt number decreases with the Knudsen number, and increases with the aspect ratio of the elliptical channel.To evaluate the Nusselt numbers for different values of aspect ratio and Knudsen number (in all analyzed cases) a simple polynomial correlation is proposed.Finally a comparison between rectangular and elliptic microchannels has been performed, when the whole perimeter of the cross-section is heated, showing that for values of the aspect ratio greater than 0.33 the elliptic microducts are characterized by better thermal performances.