Temperature Jump Boundary Conditions Research Articles

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

The lattice Boltzmann-Bhatnagar-Gross-Krook method was used to simulate Al2O3-water nanofluid to find the effects of Reynolds, Rayleigh and Hartmann numbers, slip coefficient, nanoparticle volume fraction and axial distance on forced convection heat transfer in MATLAB. The ranges of studied Reynolds number, Rayleigh number, magnetic field strength, nanoparticle volume concentration and slip coefficient include 200 ≤ Re ≤ 4000; 103 ≤ Ra ≤ 106; 0 ≤ Ha 90; 0 ≤ φ ≤ 2%; 0.005 ≤ B ≤ 0.02, respectively. The results show that increasing Reynolds number and nanoparticle volume fractions improve heat transfer in the 2D microtube under laminar, turbulent, slip and temperature jump boundary conditions. Decreasing the values of slip coefficient decreases the temperature jump and enhances the Nusselt number. A critical value for the Rayleigh number (105) and magnetic field strength (Ha 10) exists, at which the impacts of the solid volume fraction and slip coefficient effects are the most pronounced. The pressure drop shows a similar type of enhancement in magnitude, as observed in the case of the Nusselt number. However, application of nanofluids for low Reynolds numbers is more beneficial, and the effect of volume fractions are more pronounced in comparison to slip coefficient, though the effects are marginal.

New temperature jump boundary condition in high-speed rarefied gas flow simulations

The effect of the sliding friction has been important in calculating the heat flux of gas flow from the surface since there is some slip over the surface. There has not been any the temperature jump condition including the sliding friction part so far. In this paper, we will propose a new temperature jump condition that includes the sliding friction. Our new temperature jump condition will be evaluated for NACA0012 micro-airfoil in high-speed rarefied gas flow simulations using the CFD method, which solves the Navier-Stokes equations within the OpenFOAM framework with working gas as air. The airfoil case is simulated with various Knudsen numbers from 0.026 to 0.26, and the angles-of-attack (AOAs) from 0-deg to 20-deg. The surface gas temperatures predicting by our new temperature jump condition give good agreements with the DSMC data, especially the NACA0012 micro-airfoil cases with the high Knudsen numbers, Kn = 0.1, and Kn = 0.26 with AOA = 20-deg. for the lower surface.

On Temperature Jump Condition for Slip Flow in a Microchannel With Constant Wall Temperature

The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and substantial derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.

Numerical investigation of heat transfer and pressure drop in a rotating U-shaped hydrophobic microchannel with slip flow and temperature jump boundary conditions

Abstract Numerical simulations are performed to investigate the fluid flow and heat transfer in a three-dimensional rotating U-shaped microchannel with a square cross-section for Reynolds numbers of 200–1000. Water is employed as working fluid. The microchannel surface is considered to be hydrophilic (no-slip flow) and hydrophobic (slip flow). Effects of slip flow, temperature jump and rotational speed in the range of 0–300 rad/s are studied on the heat transfer, pressure drop and thermal performance coefficient. Various slip lengths ranging from zero (hydrophilic surface) to 10 μm are employed and their results are compared. It is observed that the effect of slip flow results on the leading and trailing walls is not similar due to the rotational effects. It is found that the slip flow augments the heat transfer rate in comparison with that of no-slip flow while using both slip flow and temperature jump reduces the heat transfer rate in comparison with that of slip flow. A relatively large reduction on the pressure drop and an improvement on the Nusselt number are found when the slip length increases from zero to 10 μm. The thermal performance coefficient increases about 90% for 10 μm slip length in comparison with that of no-slip condition. Moreover, for a rotating microchannel (300 rad/s), the thermal performance coefficient increases about 43% for low Reynolds numbers and about 11% for large Reynolds numbers in comparison with that of the stationary microchannel.

Near Continuum Velocity and Temperature Coupled Compressible Boundary Layer Flow over a Flat Plate

The problem of a compressible gas flows over a flat plate with the velocity-slip and temperature-jump boundary conditions are being studied. The standard single- shooting method is applied to obtain the exact solutions for velocity and temperature profiles when the momentum and energy equations are weakly coupled. A double-shooting method is applied if these two equations are closely coupled. If the temperature affects the velocity directly, more significant velocity slip happens at locations closer to the plate’s leading edge, and inflections on the velocity profiles appear, indicating flows may become unstable. As a consequence, the temperature-jump and velocity-slip boundary conditions may trigger earlier flow transitions from a laminar to a turbulent flow state.

Unsteady motion of a slightly rarefied gas caused by a plate oscillating in its normal direction

Unsteady motion of a slightly rarefied gas between two parallel plates---caused when one of the plates starts a harmonic oscillation in its normal direction---is analyzed numerically using the compressible Navier-Stokes equations and the correct temperature-jump boundary condition.

Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter δ, ratios of hotter to cooler surface temperatures T, and inner to outer radii ratio R. The results of S-model kinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T=1.1 and large radius ratios R≥0.5; however, for large temperature ratio, a pronounced disagreement is observed.

Double diffusive magnetohydrodynamic squeezing flow of nanofluid between two parallel disks with slip and temperature jump boundary conditions

In this paper, double diffusive squeezing unsteady flow of electrically conducting nanofluid between two parallel disks under slip and temperature jump condition is analyzed using the homotopy perturbation method. The obtained solutions from the analysis are used to investigate the effects of the Brownian motion parameter, thermophoresis parameter, Hartmann number, Lewis number and pressure gradient parameters, slip and temperature jump boundary conditions on the behavior of the nanofluid. Also, the results of the homotopy perturbation method are compared to the results in the literature and good agreements are established. This study is significant to the advancements of nanofluidics such as energy conservation, friction reduction and micro mixing biological samples.

Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study

A numerical simulation for mixed convective three-dimensional slip flow of water-based nanofluids with temperature jump boundary condition is presented. The flow is caused by nonlinear stretching surface. Conservation of energy equation involves the radiation heat flux term. Applied transverse magnetic effect of variable kind is also incorporated. Suitable nonlinear similarity transformations are used to reduce the governing equations into a set of self-similar equations. The subsequent equations are solved numerically by using shooting method. The solutions for the velocity and temperature distributions are computed for several values of flow pertinent parameters. Further, the numerical values for skin-friction coefficients and Nusselt number in respect of different nanoparticles are tabulated. A comparison between our numerical and already existing results has also been made. It is found that the velocity and thermal slip boundary condition showed a significant effect on momentum and thermal boundary layer thickness at the wall. The presence of nanoparticles stabilizes the thermal boundary layer growth.

The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump

The forced convection of nanofluid flow in a long microchannel is studied numerically according to the finite volume approach and by using a developed computer code. Microchannel domain is under the influence of a magnetic field with uniform strength. The hot inlet nanofluid is cooled by the heat exchange with the cold microchannel walls. Different types of nanoparticles such as Al2O3 and Ag are examined while the base fluid is considered as water. Reynolds number are chosen as Re=10 and Re=100. Slip velocity and temperature jump boundary conditions are simulated along the microchannel walls at different values of slip coefficient for different amounts of Hartmann number. The investigation of magnetic field effect on slip velocity and temperature jump of nanofluid is presented for the first time. The results are shown as streamlines and isotherms; moreover the profiles of slip velocity and temperature jump are drawn. It is observed that more slip coefficient corresponds to less Nusselt number and more slip velocity especially at larger Hartmann number. It is recommended to use Al2O3-water nanofluid instead of Ag-water to increase the heat transfer rate from the microchannel walls at low values of Re. However at larger amounts of Re, the nanofluid composed of nanoparticles with higher thermal conductivity works better.

Fluid flow and heat transfer of non-Newtonian nanofluid in a microtube considering slip velocity and temperature jump boundary conditions

Forced convection of non-Newtonian nanofluid, aqueous solution of carboxymethyl cellulose (CMC)–Aluminum oxide through a microtube is studied numerically. The length and diameter of tube are L=5 mm and D=0.2 mm, respectively which means the length is long enough compared to the diameter. The effects of different values of nanoparticles volume fraction, slip coefficient and Reynolds number are investigated on the slip velocity and temperature jump boundary conditions. Moreover the suitable validations are presented to confirm the achieved results accuracy. The results are shown as the dimensionless velocity and temperature profiles; however the profiles of local and averaged Nusselt number are also provided. It is seen that more volume fraction and slip coefficient correspond to higher Nusselt number especially at larger amounts of Re.

Heat transfer characteristics of slip flow over solid spheres

In this study, heat transfer characteristics of slip flow over an isolated impermeable solid sphere are investigated numerically. An isothermal solid sphere is considered at intermediate Reynolds numbers (0 ≤ Re ≤ 50) for Prandtl numbers in the range of 0.7–7.0. The Navier–Stokes and energy equations are solved by a control volume technique in conjunction with the velocity slip and temperature jump boundary conditions. It was found that the size of the thermal wake region according to the Knudsen number depends on the Prandtl number. At lower Prandtl numbers (0.7 ≤ Pr ≤ 2.0), the thermal wake region shrinks as the Knudsen number increases, while at higher Prandtl numbers, it grows as the Knudsen number increases. The maximum temperature jump occurs at the front stagnation point where the local Nusselt is itself maximum, owing to the maximum temperature gradient at this point. The results show that due to the opposing effects of the velocity slip and temperature jump, the average Nusselt number variation with the Knudsen number depends nonlinearly on both the Prandtl and Reynolds numbers. Furthermore, for the limiting case of Re → 0, an analytical solution for the problem is presented which has also served as a validation case.

MHD forced convection and entropy generation of CuO-water nanofluid in a microchannel considering slip velocity and temperature jump

Flow field, heat transfer and entropy generation of forced convection of CuO-water nanofluid is investigated in a parallel plate microchannel in the presence of magnetic field. Two vertical micromixers are attached on the hot walls of the microchannel. To consider the effect of the Brownian motion of the nanoparticles, the KKL model is utilized to estimate thermal conductivity of the nanofluid. The governing equations, which are accompanied with the slip velocity and temperature jump boundary conditions, are solved by the finite volume method (FVM) and SIMPLER algorithm. The study is conducted for the Reynolds numbers in the range of 10 < Re < 100, Hartmann numbers in the range of 0 < Ha < 40, Knudsen numbers ranging of 0 < Kn < 0.1 and volume fraction of nanoparticles ranging of 0 < φ < 0.04. The results show that when the Hartmann or Reynolds numbers, or the volume fraction of nanoparticles increase, the average Nusselt number and the total entropy generation rate increase. Furthermore, when Knudsen number increases, the total entropy generation rate decreases.

Conjugate heat transfer in rarefied gas in enclosed cavities

The heat transfer in buoyancy driven rarefied gas in a conjugate cavity has been investigated in this paper. The governing equations along with the slip flow and temperature jump boundary conditions are solved using finite-volume technique. The simulations are carried by varying cavity aspect ratios, conductivity ratios and cavity tilt angles. The Nusselt number values are calculated for different Knudsen, Rayleigh and Prandtl numbers. It was found that Kn number is the most influential parameter on the heat transfer; as it increases the heat transfer in the cavity decreases. The effect of all other investigated factors was found and documented; however, it is found that, in general, at high Kn Numbers their effect on the heat transfer is marginal. It is also found that cavity walls with good conducting materials will have minor effect on heat transfer while insulation material will have moderate effect on heat transfer. Two correlations for average Nusselt number are proposed: one for horizontal cavities; Nu=0.149kr0.0101Ra0.135Kn−0.393Pr0.178 and the second correlation equation introduces the effect of the cavity tilt angle along with Ra and Kn; Nu = 0.158Ra0.130, Kn−0.396, cos(θ)0.216.

Computational study of 3D rarefied gas flow in microchannel with 90 bend

The pressure driven compressible gas flow through three-dimensional microchannel with 90° bend is numerically investigated using compressible viscous Navier–Stokes equations coupled with the first-order slip and Smoluchowski temperature jump boundary conditions. The results are compared to those from equivalent straight channel geometry in terms of mass flow rate and Poiseuille number. The competition between geometry, rarefaction and compressibility effects is discussed. The effect of slip boundary condition by comparison with no-slip results is estimated. The flow structure shows that 90° bend has in general a local effect and global performances are quite similar to those of a straight channel, allowing a certain freedom in the design of microdevices. However, it is found that the inclusion of a bend in a micro-channel produces a mass flow rate enhancement. Moreover, the pressure in bend is independent on an aspect ratio and behaves somewhat similar to two-dimensional microchannels, even for the square cross section. The velocity profile near the centerline is relatively similar along the width and depth for an aspect ratio of more than four, suggesting that the bent microduct can be modeled as a two-dimensional one, although, the velocity component along the depth is never identically zero, implying that the flow is not truly two dimensional.

Ammonia Decomposition for Hydrogen Production in Catalytic Microchannels with Slip/Jump Effects

The rarefaction effects on the catalytic decomposition of NH3 in ruthenium–coated planar microchannels is numerically simulated in the Knudsen number range 0.015-0.03. A colocated finite–volume method is used to solve the governing equations. A concentration jump model derived from the kinetic theory of gases is employed to account for the concentration discontinuity at the reactive walls. A detailed surface reaction mechanism for ammonia decomposition on ruthenium along with a multi-component species diffusion model are used to study the effects of concentration jump coupled with velocity slip and temperature jump on the walls. The velocity-slip, temperature-jump and concentration-jump boundary conditions have miscellaneous effects on flow, temperature and species concentration fields. The results suggest that the velocity-slip boundary condition only slightly influences the species distribution at the edge of the Knudsen layer as well as inside the channel, while the temperature-jump boundary condition affects the heat and mass transfer characteristics the most. The concentration-jump effect, on the other hand, can counter balance the temperature-jump effects in some cases.

3D thermal conduction in a nanoscale Tri-Gate MOSFET based on single-phase-lag model

With the introduction of the new silicon on insulator (SOI)-Tri-Gate MOSFET technologies, it is very necessary to simulate the thermal performance in these nano devices. We have to notice that heat conduction given by Fourier's law ceases to be valid in nanostructures, due to the finite heat propagation speed in nanoscale regime. In this paper, we propose a thermal model given by the 3D single-phase-lag (SPL) model to predict the phonon transport in a 3D MOSFET and a Tri-Gate SOI-MOSFET. Considering the phonon-wall collisions, the SPL model is coupled with a new 3D second-order temperature-jump boundary condition. Using the finite element method we found that our proposed model is able to predict the thermal performance of a 10 nm 3D MOSFET and a 10 nm Tri-Gate SOI-MOSFET. The results reveal that the increase of the wall number leads to a decrease of the temperature field in the Tri-Gate structures. The results prove also that the channel width has an important role in the increasing of the temperature.

Investigation of Self-Heating Effects in a 10-nm SOI-MOSFET With an Insulator Region Using Electrothermal Modeling

This paper investigates the heat transfer and temperature distribution as well as electric fields in a 10-nm MOSFET and insulator region silicon-on-insulator MOSFET (IR-SOI-MOSFET). An electrothermal model based on a dual-phase-lag model coupled with a second-order temperature-jump boundary condition and drift–diffusion (D-D) model has been elaborated. The D-D model is used to take into account that the heat source by Joule effect and the width of the channel depends on the electrical fields. The finite-element method has been employed to generate the numerical results. The model has been validated on the basis of available numerical results. It is found that once the Fourier law ceases to be valid, our model is able to predict the phonon transport and electrical properties in nanostructures. In a technological viewpoint, the IR-SOI-MOSFET is more thermally efficient compared with a classical SOI-MOSFET.

A new form of the second-order temperature jump boundary condition for the low-speed nanoscale and hypersonic rarefied gas flow simulations

The accuracy of numerical simulations of rarefied gas flows, in particular the Navier-Stokes-Fourier (N–S–F) equations, depends on the employed surface boundary conditions. In the literature, the combination of the second-order slip/jump conditions has primarily been used for either the Burnett or the BGK Burnett equations for hypersonic gas flows. In this work, we suggest the second-order temperature jump condition in a new form. The second-order slip/jump conditions are implemented in the framework of OpenFOAM to employ with the N–S–F equations for low-speed nanoscale and hypersonic rarefied gas flows. We investigate both the first and second-order slip/jump boundary conditions for low speed rarefied gas flow in the pressure-driven backward facing step nanochannel as well as hypersonic gas flows over the flat plate and past a circular cylinder in cross-flow. Simulation results show that the combination of the second-order slip/jump (in new form) conditions predicts better surface properties than those of the first-order slip/jump conditions for all cases studied by comparing the Burnett and DSMC data. Especially, the N–S–F simulation results of the second-order slip/jump (in new form) conditions of the cylinder case can capture the Burnett data at Kn = 0.1, while those of the first-order conditions do not.

Effect of temperature jump on forced convective transport of nanofluids in the continuum flow and slip flow regimes

In this paper, an attempt has been made to extend the modified Buongiorno model of nanofluids originally proposed by Yang et al. (2013a, J. Heat Transf., 135, 054504) from the continuum flow regime to the slip flow regime, in consideration of the effects of both velocity slip and temperature jump near the wall. Since the use of velocity slip boundary condition has been extensively applied and well-understood in the literature, the focus of the present study is on the temperature jump boundary condition. Based on the theoretical results obtained using the Runge–Kutta–Gill method, one can conclude that the temperature jump near the wall has more significant influence on the dimensionless temperature than the dimensionless velocity and volume fraction of nanoparticles in the cross section of a channel. Moreover, the neglect of temperature jump leads to the overestimation of Nusselt number based on the bulk mean nanofluid thermal conductivity NuB, especially in the slip flow regime. Subsequently, two key parameters of nanofluids, namely Knudsen number Kn and the ratio of Brownian and thermophoretic diffusivities NBT, were discussed in order to investigate their effects on the fluid flow and heat transfer characteristics of nanofluids. The results indicated that the increase of Kn not only enhances heat transfer performance, but also reduces pressure drop, demonstrating the promising prospect of nanofluids applications in micro and nano-scales devices. Furthermore, it is found that the maximum NuB can be achieved when Kn is around 0.07 or when NBT is around 0.5, which is useful for optimizing nanoparticles for practical applications.