This paper presents the fluid flow in nanochannels with permeable walls using the molecular dynamics (MD) simulations. A three-dimensional Couette flow has been carried out to investigate the effect of the permeable surface on the fluid density distributions and the slip velocity. The ordering layer of molecules is constructed near the smooth surface but it was destroyed by the permeable ones resulting in the density drop in porous wall. The fluid density in porous wall is large under strong fluid-structure interaction (FSI) and it is decreased under weak FSI. The negative slip is observed for fluid flow past solid walls under strong FSI, no-slip under medium FSI and positive slip under weak FSI whatever it is smooth or porous. Moreover, the largest slip velocity and slip length occur on the smooth surface of solid wall. As predicted by Maxwell theory, the molecule is bounced back when it impinges on the smooth surface. The molecules, however, can reside in porous wall by replacing the molecules that are trapped in the pores. Moreover, the molecule can escape from the pore and enter the channel becoming a free molecule. After travelling for a period time in the channel, the molecule can enter the pore again. During the molecular movement, the momentum exchange has been implemented not only between fluid molecules and wall but also between the fluid molecules themselves in the pore, and the multi-collision between fluid molecules takes place. The reduced slip velocity at the porous wall results in the larger friction coefficient compared to the smooth surface wall. The molecular boundary condition predicted by Maxwell theory on the smooth surface is no longer valid for flow past the permeable surface, and a novel boundary condition should be introduced.

The Present investigation has been carried out to study the performance of nano enhanced phase change material (NEPCM) based heat sink for thermal management of electronic components. Enthalpy based finite volume method is used for the analysis of phase change process in NEPCM. To enhance the thermal conductivity of phase change material (PCM), copper oxide nano particles of volume fractions 1%, 2.5% and 5% are added to PCM. A heat flux of 2500 W/m 2 is taken as input to the heat sink. The thermal performance of the heat sink with PCM is compared with NEPCM for each volume fraction of nano particle for both finned and unfinned configurations. It is observed that the nano particle volume concentration plays a major role in removing the heat from the chip in case of unfinned heat sink configuration. However, for finned heat sink configuration, the volume concentration effect is not appreciable. In addition, the performance of NEPCM based finned heat sink is studied under cyclic loading in both natural and forced convection boundary conditions. It is observed that under forced convection the solidification time is reduced.

This article presents a theoretical and numerical study on the heat conduction of gas confined in a nanoscale cube. An effective thermal conductivity model of confined gas using a modified mean free path is proposed for the heat conduction in transition regime inside a closure. Excellent agreement of the present model with the results from our simulations by the method of direct simulation Monte Carlo (DSMC) has been achieved for different boundary conditions of side walls. The temperature jumps and the reduction of local heat flux near the side walls are observed from the DSMC results.

To compare and understand the laminar thermal-hydraulic performance of plate-fin channel with rectangle plain fin by using variable thermophysical properties of the most commonly used nanofluids (Al 2 O 3 -water), a three-dimensional numerical study is investigated by using the single-phase approach at a constant wall temperature boundary condition. Different models published in literatures are considered for the thermal conductivity and viscosity. On this basis, a parametric analysis is conducted to evaluate the effects of various pertinent parameters including nanoparticle volume fraction (0%–4%), Brownian motion of nanoparticle and Reynolds number (800–1500) on the heat transfer and flow characteristics of plain fin channel in detail. All the numerical results demonstrate that the addition of Al 2 O 3 nanoparticle can enhance the heat transfer and flow pressure loss of base fluid because of the higher thermal conductivity and viscosity for nanofluids. And these enhancements are more obvious by increasing the volume fraction of nanoparticle, increasing Reynolds number, and considering the effects of nanoparticle Brownian motion. In addition, there are significantly differences in the thermal and flow fields for different nanofluids models at a fixed Reynolds number, which means that the effective theoretical formulas and empiric corrections for the nanofluids thrmophysical properties need to be studied extensively in the future.

In this study, we simulate the flow and heat transfer during hot-wire anemometry and investigate its thermal behavior and physics using the Computational Fluid Dynamics (CFD) tool. In this regard, we use the finite-volume method and solve the compressible Navier-Stokes equations numerically in slightly non-continuum flow fields. We do not use any slip flow model to include the transitional flow physics in our simulations. Using the CFD method, we simulate the flow over hot–wire and evaluate the uncertainty of CFD in thermal simulation of hot-wire in low transitional flow regimes. The domain sizes and the mesh distributions are carefully chosen to avoid boundary condition error appearances. Following the past researches, we do not take into account the conduction heat transfer passing through hot-wire mounting arms in our simulations. Imposing a fixed temperature condition at the face of hot-wire, we simulate the flow over and the heat transfer from hot-wire and calculate the convection heat transfer coefficient and the local Nusselt number values. To be sure of the accuracy of our CFD code, we simulate a number of similar test cases and compare our numerical solutions with the available numerical solutions and/or experimental data.

In the industrial fabrication processes of density-graded closed-cell metallic foams, it is of great importance to control the solidification immediately after foams are formed so as to obtain the final products with well distributed density-graded pores and less defects. This paper presented an analytical work aiming to predict the solidification front of density-graded metallic foam under constant temperature boundary condition. Numerical simulations based on ideal density-graded circular pores demonstrated good agreement with the analytical solutions. The 2D porous morphology of a real density-graded aluminum foam was further reconstructed with microCT, on the basis of which the propagation of solidification front inside this real density-graded foam was numerically investigated. An equivalent shape factor for this real foam was calculated to provide an insight for the influence of different pore shapes on solidification. Compared with other pores, the solidification speed of elliptical pores (a common pore shape in real foams) is moderate, i.e., slower than circular pores but quicker than triangular pores for same porosity.

The recently confirmed violation of the no-slip boundary condition in the flow of small-molecule liquids through microchannels and nanochannels has technological implications such as friction reduction. However, for significant friction reduction at low cost, the microchannel wall needs to be chemically inhomogeneous. The direct fluid dynamic consequence of this requirement is a spatial variation in the local degree of liquid slippage. In this work, the pressure-driven flow in a channel with periodically patterned slippage on the channel walls is studied using a spectrally accurate semi-analytical approach based on Fourier decomposition. The method puts no restrictions on the pitch (or wavelength) and amplitude of the pattern. The predicted effective slip length in the limits of small pattern amplitude and thick channels is found to be consistent with previously published results. The effective degree of slippage decreases with the patterning amplitude. Finer microchannels and longer pattern wavelengths promote slippage.

Head-on collisions of binary micro-droplets are of great interest in both academic research and engineering applications. Numerical simulation of this problem is challenging due to complex interfacial changes and large density ratio between different fluids. In this work, the recently proposed lattice Boltzmann flux solver (LBFS) is applied to study this problem. The LBFS is a finite volume method for the direct update of macroscopic flow variables at cell centers. The fluxes of the LBFS are reconstructed at each cell interface through lattice moments of density distribution functions (DDFs). As compared with conventional multiphase lattice Boltzmann method, the LBFS can be easily applied to study complex multiphase flows with large density ratio. In addition, external forces can be implemented more conveniently and the tie-up between the time step and mesh spacing is also removed. Moreover, it can deal with complex boundary conditions directly as those do in the conventional Navier-Stokes solvers. At first, the reliability of the LBFS is validated by simulating a micro-droplet impacting on a dry surface at density ratio 832 (air to water). The obtained result agrees well with experimental measurement. After that, numerical simulations of head-on collisions of two micro droplets are carried out to examine different collisional behaviors in a wide range of Reynolds numbers and Weber numbers of 100 ≤ Re ≤ 2000 and 10 ≤ We ≤ 500. A phase diagram parameterized by these two control parameters is obtained to classify the outcomes of these collisions. It is shown that, at low Reynolds number ( Re =100), two droplets will be coalescent into a bigger one for all considered Weber numbers. With the increase of the Reynolds number, separation of the collision into multiple droplets appears and the critical Weber number for separation is decreased. When the Reynolds number is sufficiently high, the critical Weber number for separation is between 20 and 25.

In the past decades, the Lattice Boltzmann method has gained much success in variety fields especially in multiphase flow, porous media flow, and other complex flow, and become a promising method for computational fluid dynamic (CFD). The outlet boundary condition (OBC) and its numerical scheme are critical issues in CFD, which may influence the accuracy and stability of the calculation. The common OBCs i.e. Neumann boundary condition (NBC), extrapolation boundary condition (EBC), and convection boundary condition (CBC), which have been widely investigated in single-phase LB model, have rarely been investigated in multiphase LB model. The previous research on the OBCs for two-phase LB model only aims at small density ratio. While in most industrial applications, the density ratio often ranges from a hundred to a thousand, and a large density ratio would bring some problems such as parasitic current and bad stability in LB method. Lee and Fischer have proposed an improved LB model which is suitable for large density ratio two-phase flow. In order to assess the OBCs for large density ratio LB model, the OBCs are investigated. And it is found that the existing OBC numerical scheme cannot be directly applied to the large density ratio LB model. In present study, a novel numerical scheme for the OBCs is proposed assuming that the outlet velocity is gained by the outlet boundary condition instead of the momentum equation which is an improvement of previous scheme, and it can be used in large density ratio LB model. The performance of the proposed OBC scheme is examined for different density ratios. The results show that the proposed OBC scheme could converge in a stable manner. Comparing with the reference flow condition, the CBC scheme shows a better performance than the NBC scheme and the EBC scheme. The NBC scheme would lead a large droplet deformation, large velocity peaks at the outlet, and large errors for both small and large density ratio. And the EBC scheme keeps a good droplet shape, but it would lead large velocity peaks at the outlet and large error when large density ratio is considered. The CBC scheme always shows superior performance including a good droplet shape, smooth outlet velocity profile, and small errors no matter whether the density ratio is small or large. Hence the CBC scheme could be applied in large density ratio LB model for the outlet boundary condition, which has a good accuracy and stability in the calculation.

MD is commonly used in computational physics to determine the atomic response of nanostructures. MD stands for molecular dynamics. With theoretical basis in statistical mechanics, MD relates the thermal energy of the atom to its momentum by the equipartition theorem. Momenta of atoms in an ensemble are determined by solving Newton’s equations with inter-atomic forces derived from Lennard-Jones potentials. MD therefore assumes the atom always has heat capacity as otherwise the momenta of the atoms cannot be related to their temperature. In bulk materials, the continuum is simulated in MD by imposing PBC on an ensemble of atoms, the atoms always having heat capacity. PBC stands for periodic boundary conditions. MD simulations of the bulk are valid because atoms in the bulk do indeed have heat capacity. Nanostructures differ from the bulk. Unlike the continuum, the atom confined in discrete submicron geometries is precluded by QM from having the heat capacity necessary to conserve absorbed EM energy by an increase in temperature. QM stands for quantum mechanics and EM for electromagnetic. Quantum corrections of MD solutions that would show the heat capacity of nanostructures vanishes are not performed. What this means is the MD simulations of discrete nanostructures in the literature not only have no physical meaning, but are knowingly invalid by QM. In the alternative, conservation of absorbed EM energy is proposed to proceed by the creation of QED induced non-thermal EM radiation at the TIR frequency of the nanostructure. QED stands for quantum electrodynamics and TIR for total internal reflection. The QED radiation creates excitons (holon and electron pairs) that upon recombination produce EM radiation that charges the nanostructure or is emitted to the surroundings — a consequence only possible by QM as charge is not created in statistical mechanics. Invalid discrete MD simulations are illustrated with nanofluids, nanocars, linear motors, and sputtering. Finally, a valid MD simulation by QM is presented for the stiffening of NWs in tensile tests. NW stands for nanowire.

Experimental investigations are conducted to determine the two-phase frictional pressure drop of refrigerant R134a and the thermal entrance length for flow in a helically coiled mini-tube of 2mm inner diameter. The objective of this work is to study the effect of the tube curvature on the frictional pressure drop in two-phase flow as well as the thermal entrance length in laminar single phase flow. The two-phase frictional pressure drop is investigated through flow boiling of the refrigerant under uniform wall temperature boundary conditions. A generalized correlation is proposed to predict the single phase and two-phase frictional pressure drop through the coiled tube. A large set of experimental data is collected to evaluate the prediction performance of the proposed two-phase correlation. The results of the prediction are fairly good when compared with the measured pressure drop from experiments. A Computational Fluid Dynamics (CFD) analysis is also performed to compare with the thermal entrance length study from experiments. The results from the experimental analyses and CFD are seen to be in good agreement. It is found that the thermal entrance length for the coiled tube is 27–103.3% larger than a straight tube of equal length and cross-section.

Microfluidics and its applications to Lab-on-a-Chip have attracted a lot of attention. Because of the small length scale, the flow is characterized by a low Re number. The governing equations become linear. Boundary element method (BEM) is a very good option for simulating the fluid flow with high accuracy. In this paper, we present a 2D numerical modeling of the electrothermal flow using BEM. In electrothermal flow the volumetric force is caused by electric field and temperature gradient. The physics is mathematically modeled by (i) Laplace equation for the electrical potential, (ii) Poisson equation for the heat conduction caused by Joule heating, (iii) continuity and Stokes equation for the low Reynolds number flow. We begin by solving the electrical potential and electric field. The heat conduction is caused by the Joule heating as the heat generation term. Superposition principle is used to solve for the temperature field. The Coulomb and dielectric forces are generated by the electrical field and temperature gradient of the system. We analyze the Stokes flow problem by superposition of fundamental solution for free-space velocity caused by body force and BEM for the corresponding homogeneous Stokes equation. It is well known that a singularity integral arises when the source point approaches the field point. To overcome this problem, we solve the free-space velocity analytically. For the BEM part, we also calculate all the integral terms analytically. With this effort, our solution is more accurate. In addition, we improve the robustness of the matrix system by combining the velocity integral equation with the traction integral equation. Our purpose is to design a pump for the microfluidics system. Since the system is a long channel, the flow is fully developed in the area far away from the electrodes. With this assumption, the velocity profile is parabolic at the inlet and outlet of the channel. So we can get appropriate boundary conditions for the BEM part of Stokes equation. Consequently, we can simulate the electrothermal flow in an open channel. In this paper, we will present the formulation and implementation of BEM to model electrothermal flow. Results of electrical potential, temperature field, Joule heating, electrothermal force, and velocity field will be presented.

A carbon nanotube (CNT) aerogel is a low-density network of small diameter single-walled CNTs held together by van del Waals forces. Due to the excellent mechanical, thermal, and electrical properties of individual CNTs and the potential to fuse the junctions in the aerogel, CNT aerogels are candidates for ultralight structural media, radiation detectors, thermal insulators, and electrical conductors. Using molecular dynamics (MD) simulation, we predict the thermal conductance of the junction formed between two CNTs. To access the range of conditions present in the aerogel, we test the effects of different boundary conditions, the CNT lengths, and the rotational angle of the CNTs. A 3-D network model of the aerogel is built that will be used with the MD predictions to estimate the aerogel thermal conductivity.

Prescribed pressure is the most common flow boundary condition used in microchannel flow simulations. In the Direct Simulation Monte Carlo (DSMC) method, boundary pressure is controlled by the number flux of the simulating molecules which enter the domain through the boundary. This number flux, in the conventional DSMC algorithm, is calculated iteratively using sampled values of velocity and number density and an expression derived from the Maxwell distribution function. This procedure does not work well for low speed flows where the role of the molecules entering from the flow boundaries becomes important. The statistical scatter of the DSMC results is generally known to be the main reason; however, the Maxwell distribution used in the pressure boundary treatment is valid just for equilibrium conditions. Accordingly, current implementations of the DSMC pressure boundary treatment are limited to boundaries with sufficiently small variations of flow variables. This is not, however, the case for many practical cases in which high gradients of the flow variables close to the boundaries lead to considerable non-equilibrium effects. In this study, therefore, an expression for the inward number flux of species is derived using the Chapman-Enskog velocity distribution to improve the pressure boundary condition in dealing with gradients of the flow properties close to the boundary. The resulting algorithm is then used for modeling a micro-channel binary gas mixture flow with prescribed pressure boundary conditions. The results are compared to those obtained from the conventional DSMC simulations using the Maxwell distribution.

Heat conduction between two parallel solid walls separated by liquid argon is investigated using three-dimensional molecular dynamics (MD) simulations. Liquid argon molecules confined in silver and graphite nano-channels are examined separately. Heat flux and temperature distribution within the nano-channels are calculated by maintaining a fixed temperature difference between the two solid surfaces. Temperature profiles are linear sufficiently away from the walls, and heat transfer in liquid argon obeys the Fourier law. Temperature jump due to the interface thermal resistance (i.e., Kapitza length) is characterized as a function of the wall temperature. MD results enabled development of a phenomenological model for the Kapitza length, which is utilized as the coefficient of a Navier-type temperature jump boundary condition using continuum heat conduction equation. Analytical solution of this model results in successful predictions of temperature distribution in liquid-argon confined in silver and graphite nano-channels as thin as 7 nm and 3.57 nm, respectively.

In this study we introduce our numerical and experimental works for the thermal conductivity reduction by using a porous material. Recently thermal conductivity reduction has been one of the key technologies to enhance the figure of merit (ZT) of a thermoelectric material. We carry out numerical calculations of heat conduction in porous materials, such as, phonon Boltzmann transport (BTE), molecular dynamics simulations (MD), in order to investigate the mechanism of the thermal conductivity reduction of a porous material. In the BTE, we applied the periodic boundary conditions with constant heat flux to calculate the effective thermal conductivity of porous materials. In the MD simulation, we calculated phonon properties of Si by using the Stillinger-Weber potential at constant temperature with periodic boundary conditions in the x , y and z directions. Phonon dispersion curves of single crystal of Si calculated from MD results by time-space 2D FFT are agreed well with reference data. Moreover, the effects of nano-porous structures on both the phonon group velocity and the phonon density of states (DOS) are discussed. At last, we made a porous p-type Bi 2 Te 3 by nano-particles prepared by a beads milling method. The thermal conductivity is one-fifth of that of a bulk material as well as keeping the same Seebeck coefficient as the bulk value. However electrical conductivity was much reduced, and the ZT was only 0.048.

Heat transfer between nanostructured surfaces separated by a thin gas film is studied in the free-molecular flow and in the transition regime. Besides topographic features the surfaces are characterized by regions with different boundary conditions displaying either diffuse or specular reflection of the molecules. The thermal conductivity of the materials on both sides of the gas film is assumed to be very high such that isothermal conditions may be applied at both surfaces. We analyze the problem using a combination of analytical techniques in the free-molecular flow regime and Monte-Carlo simulations. Under certain conditions, when the surfaces are held at different temperatures heat transfer is accompanied by a transfer of momentum such that a force is created parallel to the surfaces. This force can be significant and vanishes in the classical regime when the continuum transport equations can be applied. It is only observed if the reflection symmetry in a direction parallel to the surfaces is broken. We derive an analytical expression for the thermally-induced force as a function of the geometric parameters characterizing the surface topography and compare the results to Monte-Carlo simulations. The latter provide numerical solutions of the Boltzmann equation both in the free-molecular flow and in the transition regime. The scenario studied points to a novel method for conversion of thermal into kinetic energy and may find applications in small-scale energy converters.

Although the thermal conductivity of nanoporous materials has been investigated in the past, previous models have overestimated the small pore limit. Various authors had proposed a cylindrical boundary geometry to mimic the pore’s environment. This permits to solve the phonon Boltzmann equation analytically [1] or numerically [2], but for fixed porosity it leads to a saturation of the thermal conductivity at small pore diameters. We show that such saturation is a spurious effect of the cylindrical boundary approximation. By implementing a Monte Carlo calculation with correct boundary conditions, we obtain considerably different thermal conductivities than predicted by the cylindrical boundary geometry. The approach is illustrated in the case of Si and SiGe nanoporous materials.

The multiphysiochemical transport in electroosmosis of dilute electrolyte solutions (<1mM) through microporous media with granular random structures has been modeled in this work by our numerical framework consisting of three steps. First, the three-dimensional microstructures of porous media are reproduced by a random generation-growth method. Then the effects of chemical adsorption and electrical dissociation at the solid-liquid interfaces are considered to determine the electrical boundary conditions, which vary with the ionic concentration, the pH, and the temperature. Finally the nonlinear governing equations for the electrokinetic transport are solved by a highly efficient lattice Poisson-Boltzmann algorithm. The simulation results indicate that the electroosmotic permeability through the granular microporous media increases monotonically with the porosity, the ionic concentration, the pH and the environmental temperature. When the surface electric potential is higher than 50 mV, the permeability increases with the electric potential exponentially. The electroosmotic permeability increases with the pH exponentially, but with the temperature linearly. The present modeling results may improve our understanding of hydrodynamic and electrokinetic transport in geophysical systems, and help guide the design of porous electrodes in micro energy systems.

In this paper, we assume that a nanofluid is a mixture consisting of a continuous base fluid component and a discontinuous nanoparticle component. Then, based on the analysis of Buongiorno in 2006 for critical slip mechanisms in nanofluids, we consider the effects of Brownian diffusion and thermophoresis of nanoparticles on heat and mass flux in nanofluid. With the coupled conservation equations, we analyze the heat conduction properties of general nanofluids under three conditions: 1) stationary fluid with uniform temperature, 2) stationary fluid under constant temperature boundary, and 3) stationary fluid under constant heat flux boundary. The results show that nanofluid effective thermal conductivity depends on the thermal conductivity of nanoparticle and basic fluid, particle concentration, particle size, particle distribution, Brownian and thermal diffusion, boundary condition and time. It indicates that the nanofluid effective thermal conductivity can be well predicted for stationary fluid with uniform temperature from classical effective medium theory such as Maxwell’s approach. However, the measurements applying steady or unsteady heat conduction methods for pure materials fail to predict correctively the effective thermal conductivity of nanofluid and are influenced by boundary conditions. Preliminary conclusions include approximate correlations of effective thermal conductivity of dilute nanofluids using steady state and quasi-steady state measuring methods.