Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

There is a growing interest for applications of heat and mass transfer in microchannels. Consequently, several numerical and experimental studies related to transport phenomena in microchannels have been carried-out. The flow problem in microchannels is different from the macro-scale problems due to rarefaction effects, surface roughness, viscous dissipation heating as well as other effects. As a result, a number of studies have been proposed for investigating the micro-flow problem and how each of these phenomena affect heat and mass transfer characteristics. Naturally, there is particular focus on how the observed micro-scale phenomena differ from the traditionally known macro-scale effects. In the realm of simulation studies for heat transfer in micro-sized channels, this paper proposes a comparison between hybrid solution strategies for solving steady heat transfer problems within microchannels. The Generalized Integral Transform Technique (GITT) is employed as the main solution methodology; however, different solution approaches are investigated in order to determine advantages and drawbacks of each alternative. The presented results can serve as guidance for choosing an optimum solution methodology for thermally developing heat transfer in microchannels using GITT implementations.

The present paper is devoted to experimental investigations of the flow and the associated heat transfer in two-dimensional microchannels. Scaling laws pertaining to the hydrodynamics and heat transfer in microchannels are not yet clearly established. The published results are affected by a significant scatter, owing to the various conditions used in the experiments, and, most likely, owing to the difficulty of measurements at micronic scales. The present facility was designed to modify easily the channel height e. It was then possible to investigate hydrodynamics and heat transfer in channels of height ranging from 1 mm, which corresponds to conventional size, up to 0.1 mm, where size effects are expected. Size effects were therefore tested in the same set-up and with the same channel walls for all the experiments, which were carried out with demineralized water. Measurements of the overall friction coefficient and of local Nusselt numbers show that the classical laws of hydrodynamics and heat transfer are verified for e>0.4 mm. For lower values of e, a significant decrease of the Nusselt number is observed whereas the Poiseuille number keeps the conventional value of laminar developed flow. The transition to turbulence is not affected by the channel size.

In order to study the fundamental physical mechanisms of fluid flow and heat transfer in microchannels, many effects should be taken into account. The effect of axial heat conduction on heat transfer in microchannels is one of the hottest topics. Experimental investigation was carried out to analyze heat transfer characteristics of methanol flowing through microchannel heat sink, which consists of 10 parallel triangular microchannels. Experimental results show that the temperature distribution on the heated wall do not change linearly along the channel, which mainly caused by the axial heat conduction in the wall. The ratio of the power due to the axial heat flux to the Joule heating in the heater, and the axial heat conduction number were used to evaluate the heat conduction effect in the wall. Many factors play important roles in the axial heat conduction, including geometric configuration, material of the wall, and Reynolds number. The experimental study reveals that the axial heat conduction effect is gradually strengthened as the Reynolds number decreases.

The paper presents both three and two-dimensional numerical analysis of convective heat transfer in microchannels. The three-dimensional geometry of the microchannel heat sink followed the details of the experimental facility used during a previous research step. The heat sink consisted of a very high aspect ratio rectangular microchannel. Two channel heights, namely 1mm and 0.3mm (0.1mm), were used for 3D (2D) numerical model respectively. Water was employed as the cooling liquid. The Reynolds number ranged from 200 to 3000. In the paper, the thermal entrance effect is analyzed in terms of heat transfer efficiency. Finally, the comparison between measured and computed heat flux and temperature fields is presented. Contrary to the experimental work, the numerical analysis did not reveal any significant scale effect in heat transfer in microchannel heat sink up to the smallest size considered (0.1 mm).

The paper presents both three and two-dimensional numerical analysis of convective heat transfer in microchannels. The three-dimensional geometry of the microchannel heat sink followed the details of the experimental facility used during a previous research step. The heat sink consisted of a very high aspect ratio rectangular microchannel. Two channel spacings, namely 1 mm and 0.3 mm (0.1 mm), were used for three-dimensional (two-dimensional) numerical model, respectively. Water was employed as the cooling liquid. The Reynolds number ranged from 200 to 3000. In the paper, thermal entrance effects and conduction/convection coupling effects are considered both for the test case of uniform channel inlet conditions and the complete geometry of the experiment. Finally, the comparison between measured and computed heat flux and temperature fields is presented. Contrary to the experimental work, the numerical analysis did not reveal any significant scale effect on heat transfer in microchannel heat sink down to the smallest size considered (0.1 mm).

Numerical simulation of laminar heat transfer in microchannels with rough surfaces characterized by fractal Cantor structures

The Boltzmann equation is the governing equation for rarefied gas dynamics, which is relevant to the aerodynamic design of rarefied hypersonic vehicles. Direct solution of the Boltzmann equation for realistic gas flows using either analytic or computational techniques is almost impossible. However, the Direct Simulation Monte Carlo (DSMC) method has been developed to provide realistic solutions for rarefied gas flows. Bird formally introduced this method hi 1969, and ever since several arguments have developed as to whether the DSMC method provides solutions of the Boltzmann equation. This paper demonstrates that the Boltzmann equation and the DSMC method have a common origin which rests on the fundamental tenets of kinetic theory. These fundamental tenets are mathematically condensed into the Boltzmann equation. On the other hand, the DSMC method is a numerical implementation of these same fundamental tenets. Thus, the Boltzmann equation and the DSMC method express the same idea but use a different language. The Boltzmann equation uses the language of mathematics whereas the DSMC method uses the language of physics. It is explained how both approaches are related and it is concluded that the DSMC method does indeed provide solutions of the Boltzmann equation. It is also shown that both approaches can be easily extended to a wider range of problems than the literature has recognised (such as to high-density gases and liquids). One important issue is how to set the range of the molecular potential used in deflection angle formulae. It is shown that, contrary to traditional expectations, within a macroscopic volume the range of the potential is always finite. Finally, the thorny issue of molecular chaos is examined and it is concluded that it is not as limiting as commonly feared.

Simulation and experimental investigation of pressure loss and heat transfer in microchannel networks containing bends and T-junctions

The flow characteristics and heat transfer in micro couette flow were studied numerically using three methods: Burnett equations, direct simulation Monte Carlo (DSMC) method and information preservation (IP) method. The results of these three methods are compared to each other. Convergent solutions to the conventional Burnett equations with second order velocity-slip and temperature-jump boundary conditions were obtained on arbitrary fine numerical grids for all Knudsen numbers (Kn) up to the limit of the equations' validity. The non-dimensional wall shear stress and heat flux shows good agreement with DSMC results and are better than first order slip boundary condition. The velocity slip and temperature jump calculated from Burnett equations fit DSMC results well when Kn < 0.3 but departure at higher Kn number. The IP method shows an identical velocity distribution with DSMC at low speed, but costs much less time. Perfect agreement was achieved in the density, velocity, temperature and pressure distributions between the results of Burnett equations and IP method at Kn = 0.02 and 0.1. Burnett equations and IP method are better than Navier-Stokes equation and DSMC method, respectively, in the flow and heat transfer in MEMS or NEMS systems

Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions

An experimental investigation of saturated flow boiling heat transfer and pressure drop in square microchannels

Heat transfer in rough microchannels under rarefied flow conditions

Microchannels are of current interest for use in heat exchangers where very high heat transfer performance is desired. Microchannels provide very high heat transfer coefficients because of their small hydraulic diameters. In this study, an investigation of fluid flow and heat transfer in microchannels is conducted. A review of the literature published regarding fluid flow and heat transfer in microchannels is provided in this study. A thorough background on the theory of internal convective heat transfer is provided as well. A critical analysis of some of the published heat transfer experiments on microchannels is also given. It was found that some of the experimental methods published recently employ experimental and data reduction techniques which may result in errors for reported Nusselt numbers. A brief computational fluid dynamics (CFD) investigation into the heat transfer and fluid flow performance of some channels with designed bumps is also presented. It was found that designed channels offer enhanced Nusselt numbers in the turbulent regime at the cost of a higher friction factor when compared to a plain channel. Fluid flow and heat transfer experiments were conducted on a copper microchannel heat exchanger (MHE). An experimental method of imposing a constant surface temperature to the MHE was used. A description of the experimental apparatus and procedure is provided. The friction factor results from the experiments agree fairly well with theoretical correlations. The experimental Nusselt number results agree with theory very well in the transition/turbulent regime, but the results show a higher Nusselt number in the laminar regime than predicted by theoretical correlations. A full description of the data reduction and analysis of the experimental data is given. A CFD model was created to simulate the fluid in the inlet plenum and the microchannels. The results from these simulations are presented, and they show good agreement with the experimental data in the transition/turbulent regime as well as with theoretical correlations for laminar and turbulent flow.

Results of numerical simulations of high-altitude aerothermodynamics of the EXPERT reentry capsule along its descent trajectory are presented. Aerodynamic characteristics for different angles of attack and rolling of the capsule at altitude of 150 down to 20 km are studied. An engineering local bridging method is used in computations. The uncertainty of the engineering method in the transitional regime is determined by comparisons with results obtained by DSMC simulations. I. Introduction During disorbiting, the spacecraft experiences the influence of the atmosphere with significantly varying parameters. To estimate the aerodynamic loads and to predict the landing area, one should know, already at the stage of design, the coefficients of aerodynamic forces and moments of the spacecraft for varying temperature, density, flight velocity, and angles of attack and sideslip for numerous possible descent trajectories. Thousands of various variants have to be computed. At the beginning of descent, at high altitudes where the gas is strongly rarefied, numerical simulations do not involve many difficulties, because theoretical approaches have been developed for simple shapes and the Test Particle Monte Carlo method can be readily used for more complicated shapes. On the other hand, various engineering approaches have been developed for calculating aerodynamic characteristics of various bodies at the final segment of the descent trajectory, in the continuum regime, which are fairly effective. The main problem is the analysis of spacecraft aerodynamics in the transitional regimes between the free-molecular and continuum regimes. The Navier-Stokes equations yield, strictly speaking, incorrect results in the transitional regime and require special modifications for taking into account flow slipping. The Direct Simulation Monte Carlo (DSMC) method provides rather accurate values of aerodynamic characteristics with allowance for physical and chemical processes but requires large amounts of computer memory and performance. Application of the software based on the DSMC method is unreasonably expensive at the initial stage of spacecraft design and trajectory analysis. A possible solution of this problem is the approximate engineering methods. These methods allow calculating aerodynamic characteristics of bodies of arbitrary geometry for multiple variants of free-stream parameters within a reasonable time and then to refine the results at the most important segments of the flight trajectory by the DSMC method. The use of fast approximate engineering methods is the most acceptable approach to solving problems of spacecraft aerodynamics at the stage of conceptual design. The present paper describes the computations of aerodynamics of the EXPERT capsule by an engineering local bridging method at altitudes of 150 down to 20 km with flow parameters corresponding to the expected descent trajectory. The results in the transitional regime are refined by the DSMC method. The errors of the engineering method are studied in detail, and the contribution of various elements of the EXPERT capsule to aerodynamic characteristics is analyzed. II. EXPERT geometry The KHEOPS configuration (Fig. 1) is a blunted pyramidal shape featuring four flaps. The computational model was constructed by the RuSat software system. The total number of panels is approximately 36 thousand. The nose is made in the form of an ellipse with a misalignment of 0.9165. The local radius of the nose part is 0.6 m. The ellipse-cone junction is described by a clothoid. The conical body has a cone angle of 12.5°. The cone is truncated by planes at an angle of 8.35° to the axis of symmetry. Four control flaps are deflected by 20 °.

Reduced mass flow rates of a rarefied Couette and Poiseuille flow in a long rectangular channel are calculated in the whole range of the gas rarefaction and a wide range of the width to height ratio. Furthermore, walls may be made of different materials so that different tangential momentum accommodation coefficients (TMACs) may be applied. Analytical solutions are given for the slip regime, where all four surrounding walls may have a different TMAC. Due to a simplified modeling assumption, these solutions can be used to correct the well-known flow rates of a fully diffuse channel for different TMACs in the whole range of the gas rarefaction. If the slip solution and the diffuse solution are known, the procedure can principally be adapted for any channel shape. The results of the analytical model expressions are validated with simulation data of the plane Couette and Poiseuille flow and the Poiseuille flow through a pipe, which are found in the literature. In addition, the analytical solution is compared to results of the Direct Simulation Monte Carlo (DSMC) method of a Couette and a Poiseuille flow in a rectangular channel, which are provided as tabulated data for a variation of the gas rarefaction parameter at different aspect ratios and different combinations of TMACs. The procedure to calculate the mass flow rate of the certain flow as well as the application limits are discussed.