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.     

An evaluation of secondary effects on microchannel frictional and convective heat transfer characteristics

The frictional and convective heat transfer characteristics of rarified flows in rectangular microchannels, with either isoflux or isothermal boundary conditions, are evaluated subject to second-order slip boundary conditions, creep flow, viscous dissipation, and axial conduction effects. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with first- and second-order slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. The results, reported in the form of Poiseuille and Nusselt numbers, are found to be significant functions of aspect ratio, Knudsen number, slip model parameters, Brinkman number, and Peclet number.     

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.     

The effect of creep flow on two-dimensional isoflux microchannels

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.     

Burnett simulation of gas flow and heat transfer in micro Poiseuille flow

The Burnett equations with slip boundary conditions are used to simulate the compressible gas flow and heat transfer in micro Poiseuille flow in the slip and transition flow regime. A relaxation method on Burnett terms is proposed in the present study and the thermal creep effect is considered. Convergent results at Knudsen number up to 0.4 are achieved and the results agree very well with experimental data. It is found that with the increase of Knudsen number, the Poiseuille number decreases while Nusselt number increases. The local Poiseuille number decreases along the whole channel while the local Nusselt number decreases rapidly first and then increases slowly afterwards.     

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.     

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.     

Thermal and hydraulic characteristics of turbulent nanofluids flow in a rib–groove channel

Thermal and hydraulic characteristics of turbulent nanofluids flow in a rib–groove channel are numerically investigated. The continuity, momentum and energy equations were solved by means of a finite volume method (FVM). The top and bottom walls of the channel are heated at a constant temperature. Nine different rib–groove shapes are considered in this study, which are three different rib shapes with three different groove shapes including rectangular, triangular and trapezoidal and they are interchanged with each other. Four different types of nanoparticles Al₂O₃, CuO, SiO₂, and ZnO with different volume fractions in the range of 1% to 4% and different nanoparticle diameters in the range of 25 nm to 80 nm, are dispersed in different base fluids (water, glycerin, engine oil) are used. In this study, several parameters such as different Reynolds numbers in the range of 5000 < Re < 20000, and different rib–groove aspect ratios in the range of 0.5 ≤ AR ≤ 4 are also examined to identify their effects on the heat transfer and fluid flow characteristics. The results indicate that the rectangular rib–triangular groove has the highest Nusselt number among other rib–groove shapes. The SiO₂ nanofluid has the highest Nusselt number compared with other nanofluid types. The Nusselt number increased as the nanoparticle volume fraction, Reynolds number and aspect ratio increased; however, it decreased as the nanoparticle diameter increased. It is found that the glycerin–SiO₂ shows the best heat transfer enhancement compared with other tested base fluids.     

Entropy generation for microscale forced convection: Effects of different thermal boundary conditions,velocity slip,temperature jump,viscous dissipation,and duct geometry

This work presents closed form solutions for fully developed temperature distribution and entropy generation due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001 < Kn < 0.1. Two different cross-sections are analyzed, being microducts (composed of two parallel plates) and micropipes, with the effects of viscous dissipation being included. Invoking the temperature jump equation, two different thermal boundary conditions are investigated, being isothermal and isoflux walls. Expressions are presented for the local and bulk temperature profiles, the Nusselt number, the Bejan number, and the entropy generation rate in terms of the key parameters. Though the results are obtained for the microscale problems, they can be generalized to the macroscale counterparts by letting Kn = 0.     

Slip flow in elliptic microchannels

Microscale fluid dynamics has received intensive interest due to the emergence of Micro-Electro-Mechanical Systems (MEMS) technology. When the mean free path of the gas is comparable to the channel's characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. The elliptic cross-section is one useful channel shape that may be produced by microfabrication. The elliptic microchannels have potential practical applications in MEMS. Slip flow in elliptic microchannels has been examined and a detailed theoretical analysis has been performed. A solution is obtained using elliptic cylinder coordinates and the separation of variables method. A simple model is developed for predicting the Poiseuille number in elliptic microchannels for slip flow. The developed model may be used to predict mass flow rate and pressure distribution of slip flow in elliptic microchannels.     

Heat transfer coefficient of gas flowing in a circular tube under rarefied condition

The purpose of this paper is to present heat transfer measurements of gas in a tube under rarefied condition. The measurements are made in a circular tube of inner diameter 25 mm for approximately constant wall temperature boundary conditions, with nitrogen, oxygen, argon, and helium as the working fluids. The range of Knudsen and Reynolds numbers covered in this study are 0.0022–0.032 and 0.13–14.7, respectively. Whereas the continuum values are correctly reproduced in our setup, the measured values for Nusselt numbers are very small in the slip regime. The measured values are two-five orders of magnitude smaller than the corresponding values in the continuum regime, and suggest that the Nusselt number is a strong function of Reynolds, Knudsen and Brinkmann numbers in the slip flow regime. These are among the first heat transfer measurements in the slip flow regime and the current theoretical and simulation models are inadequate to explain such low values of Nusselt number.     

Slip-flow and heat transfer of gaseous flows in the entrance of a wavy microchannel

The present work investigates the developing fluid flow and heat transfer through a wavy microchannel with numerical methods. Governing equations including continuity, momentum and energy with the velocity slip and temperature jump conditions at the solid walls are discretized using the finite-volume method and solved by SIMPLE algorithm in curvilinear coordinate. The effects of creep flow and viscous dissipation are assumed. The numerical results are obtained for various Knudsen numbers. The results show that Knudsen number has declining effect on both the C_f.Re and Nusselt number on the undeveloped fluid flow. Significant viscous dissipation effects have been observed for large Knudsen number. Also, viscous dissipation causes a singular point in Nusselt profiles.     

Variation of Nusselt number with flow regimes behind a circular cylinder for Reynolds numbers from 70 to 30 000

The dependence of the Nusselt number in the separated flow behind a circular cylinder to the cross-flow varies greatly with Reynolds number according to the flow regimes, i.e., laminar shedding, wake transition, and shear-layer transition regimes. The Nusselt number at the rear stagnation point, Nu_r/Re^0.5, increases with Reynolds number in the laminar shedding regime (Re < 150) and the shear-layer transition regime (3000 < Re < 15 000), corresponding to the shortening of the vortex formation region. On the contrary, the Nusselt number, Nu_r/Re^0.5, decreases with Reynolds number in the regime in which the wake develops to a complex three-dimensional flow (300 < Re < 1500), corresponding to the lengthening of the vortex formation region. This distinctive change affects the correlation of the overall Nusselt number with Reynolds number, i.e., the exponent of the Reynolds number has a lower value for 200 < Re < 2000 than that for 70 < Re < 200 and Re > 2000.     

Analytical solution of gaseous slip flow in long microchannels

In this paper we provide solution of the Navier–Stokes equations for gaseous slip flow in long microchannels with a second-order accurate slip boundary condition at the walls. The obtained solution is general enough to allow evaluation of various slip models proposed in the literature. We compare our solution against the first-order accurate slip boundary condition and show that the solution has a weak dependence on Reynolds number, which was neglected in the earlier theory. It is emphasized that first-order slip models do not predict the “Knudsen paradox” (appearance of a minima in normalized volume flux at Knudsen number approximately unity), or a change in curvature of centerline pressure at Knudsen numbers of 0.16. A comparison with Boltzmann’s solution suggests that the derived solution agrees reasonably well up to Knudsen number approximately 5, which shows that the validity of Navier–Stokes to rarefied gases can possibly be increased by using a high order slip boundary condition and proper choice of the slip coefficients. This result is significant from the perspective of numerical simulations of rarefied gases.     

An experimental study of convective heat transfer in silicon microchannels with different surface conditions

An experimental investigation has been performed on the laminar convective heat transfer and pressure drop of water in 13 different trapezoidal silicon microchannels. It is found that the values of Nusselt number and apparent friction constant depend greatly on different geometric parameters. The laminar Nusselt number and apparent friction constant increase with the increase of surface roughness and surface hydrophilic property. These increases become more obvious at larger Reynolds numbers. The experimental results also show that the Nusselt number increases almost linearly with the Reynolds number at low Reynolds numbers (Re<100), but increases slowly at a Reynolds number greater than 100. Based on 168 experimental data points, dimensionless correlations for the Nusselt number and the apparent friction constant are obtained for the flow of water in trapezoidal microchannels having different geometric parameters, surface roughnesses and surface hydrophilic properties. Finally, an evaluation of heat flux per pumping power and per temperature difference is given for the microchannels used in this experiment.     

Heat transfer in rectangular microchannels during volumetric heating of the substrate

Convective heat transfer in microchannels with rectangular and square cross sections are analyzed for volumetric heat generation in the substrate due to an imposed magnetic field. Gadolinium was used as the substrate material and water as the working fluid. Gadolinium is a magnetic material that exhibits high temperature rise during adiabatic magnetization around its transition temperature of 295 K. A thorough investigation for velocity and temperature distributions was performed by varying channel aspect ratio, Reynolds number, and heat generation rate in the substrate. With the increase in Reynolds number, the outlet temperature decreased and the average Nusselt number increased.     

A numerical study of laminar convective heat transfer in microchannel with non-circular cross-section

Three-dimensional numerical simulations of the laminar flow and heat transfer of water in silicon microchannels with non-circular cross-sections (trapezoidal and triangular) were performed. The finite volume method was used to discretize the governing equations. Numerical results were compared with experimental data available in the literature, and good agreements were achieved. The effects of the geometric parameters of the microchannels were investigated, and the variations of Nusselt number with Reynolds number were discussed from the field synergy principle. The simulation results indicate that when the Reynolds numbers are less than 100, the synergy between velocity and temperature gradient is much better than the case with Reynolds number larger than 100. There is an abrupt change in the intersection angle between velocity and temperature gradient around Re=100. In the low Reynolds number region the Nusselt number is almost proportional to the Reynolds number, while in the high Reynolds number region, the increasing trend of Nusselt number with Reynolds number is much more mildly, which showed the applicability of the field synergy principle. In addition, for the cases studied the fully developed Nusselt number for the microchannels simulated increases with the increasing Reynolds number, rather than a constant.     

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.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Local heat transfer characteristics of array impinging jets from elongated orifices

The aim of this research is to enhance the heat transfer on an impinged surface under an impinging jet array by minimizing a cross-flow effect. Conventional round orifices (aspect ratio, AR = 1) are substituted by the elongated orifices with aspect ratio AR = 4 and 8 with the same jet exit area. Two types of orifice arrangements; in-line and staggered arrays are compared. The experimental investigation was carried out at constant distance from orifice plate to impinged surface H = 2D_E (D_E is equivalent diameter of orifice). The heat transfer characteristic was visualized using thermochromic liquid crystal sheet (TLCs) and the Nusselt number distribution was evaluated by an image processing technique. The flow characteristic on the impinged surface was also visualized by oil film technique. The results show that the cross-flow in a case of the jets issued from the orifices with AR = 4 is considerably less significant than that in cases of the ones delivered from the orifices with AR = 1 and 8. At Reynolds number of 13,400, the Nusselt numbers for the jet arrays issued from the elongated orifices with AR = 4 with in-line and staggered arrangements are respectively 6.04% and 12.52% higher than those for the case of AR = 1.