Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Three-dimensional laminar slip-flow and heat transfer in rectangular microchannels having constant temperature walls are studied numerically using the finite-volume method for thermally and simultaneously developing flows. The Navier–Stokes and energy equations are solved with velocity slip and temperature jump at the wall. A modified convection–diffusion coefficient at the wall–fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is established and the effect of rarefaction on hydrodynamicaly developing flow field, pressure gradient and entrance length is analyzed. A correlation for the fully developed friction factor is presented as a function of Knudsen number (Kn) and aspect ratio (α). The influence of rarefaction on the Nusselt (Nu) number is investigated for thermally and simultaneously developing flows. The effect of velocity slip is found to increase the Nu number, while the temperature-jump tends to decrease it, and the combined effect could result in an increase or a decrease in the Nu number. In the fully developed region, there could be high as 15% increase or low as 50% decrease in Nu number is plausible for the range of parameters considered in this work.     

Thermally developing flow and heat transfer in rectangular microchannels of different aspect ratios

Laminar convective heat transfer in the entrance region of microchannels of rectangular cross-section is investigated under circumferentially uniform wall temperature and axially uniform wall heat flux thermal boundary conditions. Three-dimensional numerical simulations were performed for laminar thermally developing flow in microchannels of different aspect ratios. Based on the temperature and heat flux distributions obtained, both the local and average Nusselt numbers are presented graphically as a function of the dimensionless axial distance and channel aspect ratio. Generalized correlations, useful for the design and optimization of microchannel heat sinks and other microfluidic devices, are proposed for predicting Nusselt numbers. The proposed correlations are compared with other conventional correlations and with available experimental data, and show very good agreement.     

Numerical simulation of roughness effects on flow and heat transfer in microchannels at slip flow regime

A numerical simulation for studying fluid flow and heat transfer characteristics in microchannels at slip flow regime with consideration of slip and temperature jump is studied. The wall roughness is simulated in two cases with periodically distributed triangular microelements and random shaped micro peaks distributed on the wall surfaces. Various Knudsen numbers have used to investigate the effects of rarefaction. The numerical results have also checked with available theoretical and experimental relations and good agreements has achieved. It has been found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. The negative influence of roughness on fluid flow and heat transfer found to be the friction factor increment and Nusselt number reduction. In addition high influence of roughness distribution and shape has been shown by a comparison of Poiseuille and Nusselt numbers for tow different cases.     

Evolution of Microchannel Flow Passages--Thermohydraulic Performance and Fabrication Technology

This paper provides a roadmap of development in the thermal and fabrication aspects of microchannels as applied in microelectronics and other high heat-flux cooling applications. Microchannels are defined as flow passages that have hydraulic diameters in the range of 10 to 200 micrometers. The impetus for microchannel research was provided by the pioneering work of Tuckerman and Pease [1] at Stanford University in the early eighties. Since that time, this technology has received considerable attention in microelectronics and other major application areas, such as fuel cell systems and advanced heat sink designs. After reviewing the advancement in heat transfer technology from a historical perspective, the advantages of using microchannels in high heat flux cooling applications is discussed, and research done on various aspects of microchannel heat exchanger performance is reviewed. Single-phase performance for liquids is still expected to be describable by conventional equations; however, the gas flow may be influenced by rarefaction effects. Two-phase flow is another topic that is still under active research. The evolution of research in microchannel flow passages has paralleled the advancements made in fabrication technology. The earliest microchannels were built in silicon wafers by anisotropic wet chemical etching and sawing. While these methods have been exploited successfully, they impose a number of significant restrictions on channel geometry. A variety of advanced micromachining techniques have been developed since this early work. The current state of fabrication technology is reviewed, taxonomically organized, and found to offer many new possibilities for building microchannels. In particular anisotropic dry etching and other high aspect ratio techniques have removed many of the process-induced constraints on microchannel design. Other technologies such as surface micromachining, microstamping, hybridization, and system-on-chip integration will enable increasingly complex, highly functional heat transfer devices for the foreseeable future. It is also found that the formation of flow passages with hydraulic diameters below the microchannel regime will be readily possible with current fabrication techniques.     

Effects of entrance region transport processes on free convection slip flow in vertical microchannels with isothermally heated walls

Natural convection gaseous slip flows in vertical microchannels with isothermal wall conditions are numerically investigated, in order to analyze the influence of the entrance (developing) region on the overall heat transfer characteristics. A long channel aspect ratio is considered, so as to achieve both hydrodynamically and thermally fully developed conditions at the channel exit. In other words, the flow-field within the microchannel consists of both developing and fully developed regimes. A wide range of Rayleigh number is covered, so that the cases of very short and relatively large entrance lengths can be analyzed in the same unified mathematical framework. With first order velocity and temperature jump conditions at the microchannel walls, local and average Nusselt number values are computed, by invoking the Navier Stokes equation and the energy conservation equation. It is recognized that the micro-scale effects, being associated with the velocity slip and temperature jump conditions, exhibit enhancements in the rate of heat transfer, as compared to the similar macro-scale geometries. The relative enhancements in the average Nusselt number become more prominent for higher values of Knudsen number, whereas this augmentation effect is found to be somewhat arrested at higher values of Rayleigh number. Contrasting features in the heat transfer rate predictions with and without the considerations of the entrance region effects are also carefully noted.     

First and second law analysis of fully developed gaseous slip flow in trapezoidal silicon microchannels considering viscous dissipation effect

Fully developed gaseous slip flow in trapezoidal silicon microchannels is studied. Friction factor, Nusselt number and entropy generation in the microchannel is obtained, effect of rarefaction, aspect ratio and viscous dissipation is explored and, the range of Brinkman number in which viscous dissipation effect is important and cannot be neglected is specified. The continuum approach with the velocity slip and temperature jump condition at the solid walls is applied to develop the mathematical model of problem in the trapezoidal microchannel. Transformation of trapezoidal geometry to a square provided ease of application of finite difference method in solution of the mathematical model. The effect of viscous dissipation is quantified by Brinkman number. The calculated Brinkman number for common engineering applications even with limiting operational and geometric conditions is found less than 0.005. It is observed that viscous effect for applications with Brinkman number less than 0.005 can be neglected. The region in which viscous dissipation effect cannot be neglected is specified as Br > 0.005. Decreasing effect of rarefaction and increasing effect of Brinkman number on irreversibility due to all sources, excluded axial conduction, is established. The dominant source of irreversibility in total irreversibility is specified as a function of Brinkman number.     

Three-dimensional numerical simulation of heat and fluid flow in noncircular microchannel heat sinks

A three-dimensional model of heat transfer and fluid flow in noncircular microchannel heat sinks is developed and analyzed numerically. It is found that Nusselt number has a much higher value at the inlet region, but quickly approaches the constant fully developed value. The temperature in both solid and fluid increases along the flow direction. In addition, the comparison of thermal efficiencies is conducted among triangular, rectangular and trapezoidal microchannels. The result indicates that the triangular microchannel has the highest thermal efficiency.     

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.     

Determination of annular condensation heat transfer coefficient of steam in microchannels with trapezoidal cross sections

Experiments have been carried out to determine annular condensation heat transfer coefficient of steam in two silicon microchannels having trapezoidal cross sections with the same aspect ratio of 3.15 at 54 < G < 559 kg/m² s under 3-side cooling conditions. A semi-analytical method, based on turbulent flow boundary layer theory of liquid film with correlations of pressure drop and void fraction valid for microchannels, is used to derive the annular local condensation heat transfer coefficients. The predicted values based on the semi-analytical model are found within ±20% of 423 data points. It is shown that the annular condensation heat transfer coefficient in a microchannel increases with mass flux and quality and decreases with the hydraulic diameter.     

Natural convection in a rectangular cavity with partially active side walls

A numerical study is performed to investigate the effect of aspect ratio on the natural convection of a fluid contained in a rectangular cavity with partially thermally active side walls. The active part of the left side wall is at a higher temperature than that of the right side wall. The top and bottom of the cavity and inactive part of the side walls are thermally insulated. Nine different relative positions of the active zones are considered. The equations are discretized by the control volume method with power law scheme and are solved numerically by iterative method together with a successive over relaxation (SOR) technique. The results are obtained for Grashof numbers between 10³ and 10⁵ and the effects of the aspect ratio on the flow and temperature fields and the rate of heat transfer from the walls of the enclosure are presented. The heat transfer rate is high for the bottom–top thermally active location while the heat transfer rate is poor in the top–bottom thermally active location. The heat transfer rate is found to increase with an increase in the aspect ratio.     

Friction factors in smooth trapezoidal silicon microchannels with different aspect ratios

An experiment has been conducted to measure the friction factor of laminar flow of deionized water in smooth silicon microchannels of trapezoidal cross-section with hydraulic diameters in the range of 25.9-291.0 μm. It is shown that the friction constant of these microchannels is greatly influenced by the cross-sectional aspect ratio, W_b/W_t. Based on the 334 data points, a correlation equation for the friction constant of a fully developed laminar flow of water in these microchannels is obtained in terms of the cross-sectional aspect ratio. The experimental data is found to be in good agreement with an existing analytical solution for an incompressible, fully developed, laminar flow under no-slip boundary condition. It is confirmed that the Navier-Stokes equations are still valid for the laminar flow of deionized water in smooth silicon microchannels having hydraulic diameter as small as 25.9 μm. For smooth channels with larger hydraulic diameters of 103.4-291.0 μm, transition from laminar to turbulent flow is found at Re=1500-2000.     

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.     

Three-dimensional numerical simulation of the slip flow through triangular microchannels

Three-dimensional numerical analysis for fully developed incompressible fluid flow and heat transfer through triangular microchannels over the slip flow regime is simulated in this paper. In order to study the flow through the channel, the Navier–Stokes equations are solved in conjunction with slip/jump boundary conditions. The influences of Knudsen number (0.001 < Kn < 0.1), aspect ratio (0.2 < A < 4.5), and Reynolds number (1 < Re < 15) on the fluid flow and heat transfer characteristics are extensively investigated in the paper. The numerical results reveal that the rarefaction decreases the Poiseuille number, while its effect on the Nusselt number completely depends on the interaction between velocity slip and temperature jump. It is also found that the aspect ratio has an important role in the analysis, but the variation of Reynolds number is less remarkable.     

Heat transfer in trapezoidal microchannels of various aspect ratios

Heat transfer in the thermal entrance region of trapezoidal microchannels is investigated for hydrodynamically fully developed, single-phase, laminar flow with no-slip conditions. Three-dimensional numerical simulations were performed using a finite-volume approach for trapezoidal channels with a wide range of aspect ratios. The sidewall angles of 54.7° and 45° are chosen to correspond to etch-resistant planes in the crystal structure of silicon. Local and average Nusselt numbers are reported as a function of dimensionless length and aspect ratio. The effect of Prandtl number upon the thermal entrance condition is explored. The fully developed friction factors are computed and correlated as a function of channel aspect ratio. Correlations are also developed for the local and average Nusselt numbers in the thermal entrance region as a function of a dimensionless axial length variable.     

The effect of geometrical parameters on heat transfer characteristics of microchannels heat sink with different shapes

The effect of geometrical parameters on water flow and heat transfer characteristics in microchannels is numerically investigated for Reynolds number range of 100–1000. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using finite volume method. The computational domain is taken as the entire heat sink including the inlet/outlet ports, wall plenums, and microchannels. Three different shapes of microchannel heat sinks are investigated in this study which are rectangular, trapezoidal, and triangular. The water flow field and heat transfer phenomena inside each shape of heated microchannels are examined with three different geometrical dimensions. Using the averaged fluid temperature and heat transfer coefficient in each shape of the heat sink to quantify the fluid flow and temperature distributions, it is found that better uniformities in heat transfer coefficient and temperature can be obtained in heat sinks having the smallest hydraulic diameter. It is also inferred that the heat sink having the smallest hydraulic diameter has better performance in terms of pressure drop and friction factor among other heat sinks studied.     

The heat transfer characteristics of liquid cooling heatsink containing microchannels

This paper numerically and experimentally investigates the heat transfer performance and characteristics of liquid cooling heatsink containing microchannels. The effects of channel geometry and pressure drop between the entrance and exit of heatsink on the heat transfer performance are studied. The geometrical parameters include aspect ratio and cross-sectional porosity of the channels. The height of the microchannels is considered constant. The aspect ratio is set from 1.67 to 14.29 and the porosity is from 25% to 85%. The imposed pressure drop ranges between 490 and 2940 Pa. It is found that the aspect ratio corresponding to the lowest effective thermal resistance is changed with respect to the pressure drop. It is also noticed that the value of effective thermal resistance is almost a constant for cross-sectional porosity in the range of 53%–75%. The effective thermal resistance is increased when cross-sectional porosity is deviated from this range. In addition, the increasing of pressure drop enhances heat transfer performance for channels of high aspect ratio more than those of low aspect ratio.     

Study of heat transfer enhancement in a nanofluid-cooled miniature heat sink

This paper reports numerical solution for thermally developing temperature profile and analytical solution for fully developed velocity profile in a miniature plate fin heat sink with SiO₂–water nanofluid as coolant. The flow regime is laminar and Reynolds number varies between 0 and 800. The heat sink is modeled using porous medium approach. Modified Darcy equation for fluid flow and the two-equation model for heat transfer between the solid and fluid phases are employed to predict the local heat transfer coefficient in heat sink. Results show that the nanofluid-cooled heat sink outperforms the water-cooled one, having a considerable higher heat transfer coefficient. The effects of channel aspect ratio and porosity on heat transfer coefficient of the heat sink are studied in detail. Based on the results of our analysis, it is found that an increase in the aspect ratio or the porosity of the plate fin heat sink enhances the heat transfer coefficient.     

Comparative Study of Thermal Performance of Parallel Plate and Rectangular Microchannel Counter Flow Heat Exchangers

This paper is aimed at comprehensive investigations of the thermal performance of parallel plate and rectangular microchannel counter flow heat exchangers based on axial conduction, number of transfer units, and non-dimensional power density. The geometrical parameters of the two configurations are optimized for a given heat transfer rate, effectiveness, and pressure drop. A reduced order model of rectangular micro channel counter flow heat exchanger is developed in which it is transformed into a hydrodynamically and thermally equivalent parallel plate micro heat exchanger. To improve the accuracy of the model, correction factors obtained from detailed computational fluid dynamics model are introduced. Various factors affecting the dimensionless power density of both the counter flow micro heat exchangers are studied. It is found that the axial conduction plays an important role on the performance of rectangular channel counter flow micro heat exchanger. In the limiting case where the channel aspect ratio tends to zero, the dimensionless power density of rectangular channel is found to approach that of a parallel plate counter flow micro heat exchanger.     

Single-Phase Laminar Forced Convection in Microchannels With Rounded Corners

This work investigates the frictional and heat transfer behavior of laminar, fully developed flow in microchannels with trapezoidal and rectangular cross-section and rounded corners under boundary conditions of uniform heat flux along the channel length and perimeter and uniform temperature on the heated perimeter of each cross section. The equations of momentum and energy are solved numerically using the least square method, and the results are validated with analytical data, when available. The runs have been carried out for different aspect ratios and nondimensional radii of curvature, with either all sides or three sides heated, one short side adiabatic for rectangular geometries and three sides heated, the longest one adiabatic for trapezoidal geometries. The Poiseuille and Nusselt numbers are reported and show, for the rectangular cross-section heated on all sides, a maximum increase for the highest value of the aspect ratio with increments in the Poiseuille and Nusselt numbers of about 11% and 16%, respectively, for values of the nondimensional radius of curvature of 0.5, increasing as the geometry approaches the circular duct (12.5% and 21%). The increase is less pronounced as the aspect ratio decreases and also when only three sides are heated (maximum increase of the Nusselt number around 10% for the latter); in the case of trapezoidal geometry the effects of rounding the corners are almost negligible (a maximum increase in the Nusselt number of around 2%).     

Prediction of temperature distribution and Nusselt number in rectangular microchannels at wall slip condition for all versions of constant wall temperature

Slip flow in rectangular microchannels heated at constant and uniform wall temperature (H1 boundary condition) is studied. The study is extended to the eight possible thermal versions that are formed of different combinations of heated and adiabatic walls. Integral transform method is applied to derive the velocity and temperature distributions and thus, the average Nusselt number for all the eight thermal versions. It is found that, for microchannels with perfect accommodation for velocity and temperature, the rarefaction has a decreasing effect on heat transfer for all the eight thermal versions. The results of the paper for the special case of non-slip flow agree exactly with the results found for macrochannels in literature.