LBM modeling and analysis on microchannel slip flow and heat transfer under different heating conditions

Abstract

This article aims to explore the effects of buoyancy force and thermal boundary condition on the mixed convection heat transfer performance of air in a horizontal microchannel. Three different heat flux models, including bottom wall heated, top wall heated (single wall heating – a novel heating approach compared to recent studies) and both walls heated, are analyzed at four different values of the Grashof number (Gr?=?0, 100, 300, 600) using a lattice Boltzmann method (LBM). The slip velocity boundary condition is also applied to the bottom and top walls. It can be found that the buoyancy force changes the velocity distribution structure near the bottom wall and top wall, particularly at the inlet regions in all models, and a negative slip velocity is generated due to the backflow formed at a relatively large Grashof number and it strictly determines the local wall friction coefficient. Either the bottom wall or the top wall is heated. A vortex is found close to the top wall because the mixing position of the hot and cold fluids is in the vicinity of the top wall. This feature facilitates the heat transfer near the top wall and core flow zone. The thermal performance is most positive for the case when the top wall is heated due to the generation of an induced vortex and no influence of the vortex near the bottom wall.     

微通道内流动沸腾特性研究

对国内外微通道流动和换热的研究实验作了总结,阐述了影响微通道换热系数的因素,如热流密度、过热度和干度等.对去离子水在内径为0.65 mm、长为102 mm的圆形管道内流动沸腾换热进行了实验研究,得到了局部换热系数随干度的变化关系,进而根据换热系数的变化趋势讨论了饱和流动沸腾区微通道内主导的换热机制.结果表明:从换热系数随干度的变化关系很难判定主导的换热机制;将实验数据与已发表的预测关联式进行了比较,发现大多关联式都失效,说明基于常规理论的模型不再适用于微通道.     

Effect of non-uniform heating on the performance of the microchannel heat sinks

The present study experimentally investigates the performance of a 2-pass microchannel heat sink subject to non-uniform heating. The size of the microchannel heat sink is 132 mm × 82 mm × 6 mm with a rectangular channel of 1 mm × 1 mm. Three independent heaters having identical size (96 mm × 38.5 mm × 1 mm) is placed consecutively below the microchannel heat sink. Two kinds of manifolds are used for testing of the microchannel, one with a side entrance (type A) and the other with a front entrance (type B). Test results show that both maximum temperature and average temperature rise with the total input power, and this is applicable for both manifolds. For uniform heating condition, the maximum temperature for type B manifold is much lower than that for type A manifold due to a better flow distribution and heat transfer performance. The pressure drop is slightly reduced with the rise of supplied power. For non-uniform heating, the maximum temperature and the average temperature depend on the location of heaters. For the same supplied power with non-uniform heating, it is found that heater being placed at the inlet of the microchannel will give rise to a higher maximum temperature than that being placed at the rear of the heat sink. This phenomenon is especially pronounced when the inlet flowrate is comparatively small and becomes less noted as the inlet flowrate is increased to 0.7 L/min.     

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.     

Convective heat transfer in a composite trapezoidal microchannel during magnetic heating

The analysis of conjugate heat transfer in a composite channel of trapezoidal cross-section is presented. The channel is formed by etching a silicon < 100> wafer and bonding that with a slab of gadolinium. Gadolinium is a magnetic material that exhibits high temperature rise during adiabatic magnetization around its transition temperature of 295 K. Heat is generated in the substrate by the application of a magnetic field. A thorough investigation of heat transfer coefficient at the solid–fluid interface is performed by varying the channel aspect ratio, the thickness of gadolinium slab, spacing between channels in the heat exchanger, Reynolds number, and the magnetic field strength. The results are validated by comparing with existing results for single material channels.     

矩形微通道中流体流动阻力和换热特性实验研究

以去离子水为流体工质,对其在矩形微尺度通道中的流动阻力和传热特性进行了实验研究。通过测量流量、进出口压力和温度等参数,获得了流体流过微通道时的摩擦阻力系数、对流换热过程中的热流通量和N u等。微尺度通道中流体流动的摩擦阻力系数较常规尺度通道中的摩擦阻力系数小,仅是常规尺度通道中摩擦阻力系数的20%~30%;且流动状态由层流向湍流转捩的临界R e也远小于常规尺度通道的。微尺度通道中对流换热的N u与常规尺度通道的显著不同。流量较小时,N u较常规尺度通道中充分发展段的小;随着水流量的增加,微通道的N u迅速增加,并很快超过常规尺度通道的N u,表现出微尺度效应。热流通量对微尺度通道中对流换热N u存在影响,其影响规律在不同流速条件下呈不同趋势,流速较小时,N u基本保持不变;而在流速较大时,N u随热流通量增加而呈增加趋势。     

Natural convection slip flow in a vertical microchannel heated at uniform heat flux

Numerical solutions for steady state developing natural convection flow in air, in vertical parallel-plate microchannels are accomplished. An asymmetric heating is considered and the walls are assumed to be at uniform heat flux. A first-order model is used for slip and jump boundary conditions and an analytical solution for the fully developed flow is also given. Results are performed for air, for the heat flux ratio in the 0.0–1.0 range, for Rayleigh, Ra, and Knudsen, Kn, numbers from 10^?1 to 8 × 10³ and from 0.0 to 0.10, respectively. The maximum mass flow rate is always obtained for the highest considered Kn value, whereas the average Nusselt number, Nu, increases for lower Ra (<10) and decreases for Ra > 100. Wall temperature profiles have the lowest values for highest considered Kn value at lower Ra, whereas for the developing flow, they present opposite trends. For developing flow, velocity profiles for asymmetric and symmetric heating are completely different. In developing flow velocity profiles along the wall present the highest increases for asymmetric heating and the highest considered Kn value.     

滑移区气体-颗粒流动与传热特性研究

针对气体-颗粒微尺度流动与传热过程开展数值模拟研究,所构建模型中气体处理为可压缩、变物性流体,并在颗粒表面采用速度滑移和温度跳跃边界条件以考虑气体稀薄效应。在数值模拟基础上,研究分析稀薄效应对颗粒与其周围气体流动与换热的影响程度,并进一步提出新的阻力系数与传热努谢尔特数关联式。研究结果表明,气体稀薄效应将减小颗粒阻力系数,同时抑制颗粒与其周围气体的传热过程。     

Effect of substrate thickness and material on heat transfer in microchannel heat sinks

Heat and fluid flow in microchannels of size (200μm × 200 μm, 5 cm long) of different substrate thicknesses (t = 100 μm–1000 μm) and different MEMS (Microelectromechanical Systems) materials (Polyimide, Silica Glass, Quartz, Steel, Silicon, Copper) was studied to observe the effects of thermal conductivity and substrate thickness on convective heat transfer in laminar internal flows.The results of the model were first validated by the theoretical results recommended by standard forced convection problem with H1 (Constant heat flux boundary condition) condition before the results from the actual microchannel configurations were obtained. Thereafter, general Nusselt number results were obtained from the models of many microchannel configurations based on the commercial package COMSOL MULTIPHYSICS^® 3.4 and were discussed on both local and average basis.A general Nusselt number correlation for fully developed laminar flow was developed as a function of two dimensionless parameters, namely Bi, Biot number and relative conductivity k¹, to take the conduction effects of the solid substrate on heat transfer into account. It was also demonstrated when the commonly used assumption of constant heat flux boundary (H1) condition is applicable in heat and fluid flow analysis in microfluidic systems. For this, a new dimensionless parameter was employed. A value of 1.651 for this suggested dimensionless parameter (Bi^0.04k^1?0.24) corresponds to 95% of the Nusselt number associated with the constant heat flux boundary condition so that it could be set as a boundary for the applicability of constant heat flux boundary (H1) condition in microfluidic systems involving heat transfer.     

Effect of geometric configuration on the laminar flow and heat transfer in microchannel heat sinks with cavities and fins

A numerical simulation is performed to investigate the characteristics of flow and heat transfer in microchannels with cavities and fins. Nine microchannels with various shaped cavities and fins are presented and compared to the smooth microchannel. The effect of cavity and fin shapes on the flow field and temperature field is analyzed. Results show that the presence of cavity and fin can increase the heat transfer area, intensify mainstream disturbance, and induce chaotic advection, which result in obvious heat transfer enhancement. The shape of cavity or fin has a great influence on the hydrodynamic and thermal performance for such micro heat sinks. Based on the performance evaluation criterion (PEC), the overall performance of the microchannel is evaluated. The combination of cavities and fins leads to lower bottom temperature, lower net temperature gradient of fluid, and better heat transfer performance, which has the potential to meet the increased heat removal requirement.     

The performance evaluation of Al2O3/water nanofluid flow and heat transfer in microchannel heat sink

The numerical modeling of the conjugate heat transfer and fluid flow of Al₂O₃/water nanofluid through the microchannel heat sink is presented in the paper. The laminar flow regime was considered along with viscous dissipation effect. The microchannel heat sink with square microchannels and D_h = 50 μm is considered. The heat flux was fixed to q = 35 W/m² with heating and cooling cases. The water based Al₂O₃ nanofluid was encountered with various volume concentrations of Al₂O₃ particles $?=1''–''9\%$ and three diameters of the particle d_p = 13, 28 and 47 nm. The analysis is performed on the results obtained for the local heat transfer coefficients based on a fixed pumping power. The results reveal a different local heat transfer behavior compared to the analysis made on a basis of the constant Re.     

Heat transfer of a parallel flow two-layered microchannel heat sink

A numerical study is conducted to predict the thermal performance of a parallel flow two-layered microchannel heat sink on heat transfer and compared to the case of counterflow for various channel aspect ratios. Findings reveal that the parallel flow configuration leads to a better heat transfer performance except for high Reynolds number and high channel aspect ratio. Further study on the horizontal rib thickness shows that lower thermal resistance can be achieved in a parallel flow two-layered microchannel heat sink with smaller thickness of middle rib.     

Influence of nanofluids on parallel flow square microchannel heat exchanger performance

The effects of using various types of nanofluids and Reynolds numbers on heat transfer and fluid flow characteristics in a square shaped microchannel heat exchanger (MCHE) is numerically investigated in this study. The performance of an aluminum MCHE with four different types of nanofluids (aluminum oxide (Al₂O₃), silicon dioxide (SiO₂), silver (Ag), and titanium dioxide (TiO₂)), with three different nanoparticle volume fractions of 2%, 5% and 10% using water as base fluid is comprehensively analyzed. The three-dimensional steady, laminar developing flow and conjugate heat transfer governing equations of a balanced MCHE are solved using the finite volume method. The MCHE performance is evaluated in terms of temperature profile, heat transfer rate, heat transfer coefficient, pressure drop, wall shear stress pumping power, effectiveness, and overall performance index. The results reveal that nanofluids can enhance the thermal properties and performance of the heat exchanger while having a slight increase in pressure drop. It was also found that increasing the Reynolds number causes the pumping power to increase and the effectiveness to decrease.     

Channel cross section effect on heat transfer performance of oblique finned microchannel heat sink

In the present work, the effect of channel cross section on the heat transfer performance of an oblique finned micro-channel heat sink was investigated. Water and Al₂O₃/water nanofluid of volume fraction 0.25% were used as a coolant. The oblique finned microchannels are designed with three channel cross-sections namely square, semicircle and trapezoidal. The primary work of this paper is to study the heat transfer and hydrodynamic characteristics in the oblique finned microchannel. The experimental setup and procedure are validated using water as coolant in a micro-channel heat sink. Heat transfer and flow characteristics are examined for three cross-sections of varying mass flux. The trapezoidal channel cross-section increases the considerable heat transfer rate improvement for both water and nanofluid by 3.133% and 5.878% compared to square and semicircle cross section. Also, the pressure drop is higher in the trapezoidal cross-section over the square and semicircle cross section. This is due to increase in friction loss of trapezoidal cross section. The results indicate that trapezoidal cross-section oblique finned micro-channel is more suitable for heat transfer in the electronic cooling application.     

The effect of axial conduction on heat transfer in a liquid microchannel flow

Analysis is presented for conjugate heat transfer in a parallel-plate microchannel. Axial conduction in the fluid and in the adjacent wall are included. The fluid is a constant property liquid with a fully-developed velocity distribution. The microchannel is heated by a uniform heat flux applied to the outside of the channel wall. The analytic solution is given in the form of integrals by the method of Green’s functions. Quadrature is used to obtain numerical results for the local and average Nusselt number for various flow velocities, heating lengths, wall thicknesses, and wall conductivities. These results have application in the optimal design of small-scale heat transfer devices in areas such as biomedical devices, electronic cooling, and advanced fuel cells.     

Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel

Numerical analysis of fully developed laminar slip flow and heat transfer in trapezoidal micro-channels has been studied with uniform wall heat flux boundary conditions. Through coordinate transformation, the governing equations are transformed from physical plane to computational domain, and the resulting equations are solved by a finite-difference scheme. The influences of velocity slip and temperature jump on friction coefficient and Nusselt number are investigated in detail. The calculation also shows that the aspect ratio and base angle have significant effect on flow and heat transfer in trapezoidal micro-channel.     

The heat transfer and fluid flow of a partially heated microchannel heat sink

Numerical modeling of the conjugate heat transfer in microchannel heat sink is presented. As the most of the cooling applications deals with the partial heated sections, the influence of the heating position on the thermal and hydrodynamic behavior is analyzed. The laminar fluid flow regime and the water as a working fluid are considered. It is observed that partial heating together with variable viscosity has a strong influence on thermal and hydrodynamic characteristics of the micro-heat sink.     

Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks

Three-dimensional conjugate numerical simulations using the inlet, average and variable thermal properties respectively were performed for the laminar water flow and heat transfer in rectangular microchannels with D_h of 0.333 mm at Re of 101–1775. Both average and variable properties are adopted in data reduction. The calculated local and average characteristics of flow and heat transfer are compared among different methods, and with the experiments, correlations and simplified theoretical solution data from published literatures. Compared with the inlet property method, both average and variable property methods have significantly lower f_app, but higher convective heat transfer coefficient h_z and Nu_z. Compared with the average property method, the variable property method has higher f_appRe_ave and lower h_z at the beginning, but lower f_appRe_ave and higher h_z at the later section of the channel. The calculated Nu_ave agree well with the Sieder-Tate correlation and the recently reported experiment, validating the traditional macroscale theory in predicting the flow and heat transfer characteristics in the dimension and Re range of the present work.     

MHD convective flow of a viscous heat generating fluid in slip flow regime with hall currents

This paper is concerned with the steady magnetohydrodynamical free convective flow through a porous medium of a viscous heat-generating rarefied gas past a vertical plate when a strong magnetic field is imposed in a plane which makes an angle α normal to the plate. Expressions for the velocity and temperature fields are obtained, and the effect of Hall currents on the flow is studied for various values of α (angle) and δ (heat source).