Temperature Jump Boundary Conditions Research Articles

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and Al2O3, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions are derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Second-Order Slip Effects on Heat Transfer of Nanofluid with Reynolds Model of Viscosity in a Coaxial Cylinder

Abstract The present work makes an analysis on the effects of second-order velocity slip and temperature jump boundary conditions for third-grade nanofluid over a coaxial cylinder. In the modeling of blood-based nanofluids containing metal or metal oxide nanoparticles, the viscosity is approximated to second-order Maclaurin’s series for the first time and the effective density is handled to a combination of temperature and nanoparticles volume fraction. The governing equations are transformed into a dimensionless system of nonlinear differential equations and solved by homotopy analysis method (HAM). The accuracy and efficiency of the HAM solutions are verified by ℏ $$\hbar $$ -curves and residual error curves using package BVPh2.0. The physical interpretations are illustrated by graphs and tables. The results revealed that the Nusselt number increases with an increase of nanoparticle volume fraction. The second-order velocity slip has a significant weakened effect on the skin friction. In addition, the Brownian motion and thermophoresis movement are collaborating to increase the temperature profile.

Near Continuum Flows Over a Rotating Disk

We analyze the near continuum flow created by a rotating disk facing a stagnant gas. The flow-field properties change from the traditional continuum solutions, due to the introductions of new velocity-slip and temperature-jump boundary conditions. To compute the velocity profiles, a self-similar transformation simplifies the Navier-Stokes equations into a system of ordinary differential equations. The introduction of new boundary conditions generates new parameters which can be adjusted at different degrees of rarefaction. Shooting methods are adopted to solve the differential equations with the new boundary conditions. Based on the solved velocity profiles, exact solutions for the temperature distribution are obtained. The gas temperature at the disk surface shifts towards the free stream temperature, while the heat flux between the gas and surface is reduced. Stream function solutions for the flow at the disk surface are presented to demonstrate the effects of the slip boundary conditions. The torque generated by the disk is obtained with different disk rotating speed, and the gas at the disk surface has different slip velocities.

Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels

A fully conjugate heat transfer analysis of gaseous flow in short microchannels is presented. Navier–Stokes equations, coupled with Maxwell and Smoluchowski slip and temperature jump boundary conditions, are used for numerical analysis. Results are presented in terms of Nusselt number, heat sink thermal resistance, and resulting wall temperature as well as Mach number profiles for different flow conditions. The comparative importance of wall conduction, rarefaction, and compressibility are discussed. It was found that compressibility plays a major role. Although a significant penalization in the Nusselt number, due to conjugate heat transfer effect, is observed even for a small value of solid conductivity, the performances in terms of heat sink efficiency are essentially a function only of the Mach number.

A high order accurate numerical method for solving two‐dimensional dual‐phase‐lagging equation with temperature jump boundary condition in nanoheat conduction

Dual‐phase‐lagging (DPL) equation with temperature jump boundary condition (Robin's boundary condition) shows promising for analyzing nanoheat conduction. For solving it, development of higher‐order accurate and unconditionally stable (no restriction on the mesh ratio) numerical schemes is important. Because the grid size may be very small at nanoscale, using a higher‐order accurate scheme will allow us to choose a relative coarse grid and obtain a reasonable solution. For this purpose, recently we have presented a higher‐order accurate and unconditionally stable compact finite difference scheme for solving one‐dimensional DPL equation with temperature jump boundary condition. In this article, we extend our study to a two‐dimensional case and develop a fourth‐order accurate compact finite difference method in space coupled with the Crank–Nicolson method in time, where the Robin's boundary condition is approximated using a third‐order accurate compact method. The overall scheme is proved to be unconditionally stable and convergent with the convergence rate of fourth‐order in space and second‐order in time. Numerical errors and convergence rates of the solution are tested by two examples. Numerical results coincide with the theoretical analysis. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1742–1768, 2015

Rarefied gas flow simulations of NACA 0012 airfoil and sharp 25–55-deg biconic subject to high order nonequilibrium boundary conditions in CFD

The NACA 0012 airfoil and the sharp 25–55-deg biconic cases are usually considered in evaluating the accuracy of new forms of velocity slip and temperature jump wall boundary conditions in the Navier–Stokes–Fourier equations. These cases have been investigated by many researchers in previous works with the first order Maxwell slip and Smoluchowski jump boundary conditions. Recently, we proposed a new form of the second order temperature jump for simulating rarefied gas flows and obtained accurate results for low-speed microflows. The current work is an extension of our previous CFD work where we applied both the second order velocity slip condition and the second order temperature jump boundary condition in new forms to simulate rarefied external gas flows for these cases. The second order boundary conditions are implemented into the rhoCentralFoam solver in the OpenFOAM software. The NACA 0012 airfoil case is investigated with angles-of-attack of 0 and 10 degrees and Mach numbers of 0.8 and 2. The sharp 25–55-deg biconic case is simulated at Mach of 15.6. The simulation results obtained for the NACA 0012 airfoil show that the combination of the second order slip/jump boundary conditions gives suitable agreements with DSMC for surface gas temperature and drag coefficients in comparison with those of the first order conditions. However, the results of the biconic case figure out that the second order conditions are not superior to the first order conditions.

A new coupling method for slip-flow and conjugate heat transfer in a parallel plate micro heat sink

The present study investigates the effect of temperature jump boundary condition on conjugate heat transfer in parallel plate micro channel heat sink. A new method for coupling equations between fluid and solid domains with temperature jump boundary condition is proposed and implemented in the open-source computational fluid dynamics package, OpenFOAM. The method and the code have been hydro-dynamically and thermally validated with data from previous studies. Both constant wall temperature and constant heat flux boundary conditions are considered. Impacts of effective parameters including Knudsen number and conductivity ratio on overall heat transfer characteristics of the heat sink have been discussed in detail. Results show that temperature jump has a significant effect on temperature field and heat transfer in heat sink.

Effect of second-order temperature jump in Metal-Oxide-Semiconductor Field Effect Transistor with Dual-Phase-Lag model

The present numerical investigation is concerned with the role of second-order temperature jump in a horizontal planar micro-channel heat transfer. We solve numerically Dual-Phase-Lag model in a two dimensional configuration coupled with a new jump boundary condition. The nanodevice of model consists of Metal-Oxide-Semiconductor Field Effect Transistor with either uniform or non-uniform heat generation. A new temperature jump boundary condition of first and second order is used especially in the oxide–semiconductor interface. The finite element method is used to bring forth the results for a 10nm channel length of the transistor. Thermal properties of transistor device have been investigated for different orders of the temperature jump boundary condition. It has already been deduced that the increasing orders of temperature jump boundary condition lead to an increase of phonon-wall collisions. This new condition can lead to a significant increase in the heat flux and the calculated lattice temperature.

Heat and mass transfer inside micro-tubes with uniform injection

This work deals with a numerical study of the transport phenomena along a micro-tube subjected to an injection at the wall. The governing equations expressing the conservation of mass, momentum and energy with first-order slip velocity and temperature jump boundary conditions were solved numerically. The numerical model based on the Finite Volume Method was validated using the available data. The study reveals significant impact of slip velocity and temperature jump conditions on the hydrodynamic and thermal flows. For very small injection rates, all profiles and quantities remain unchanged compared to the impermeable wall case.

Gaseous Slip Flow Mixed Convection in Vertical Microducts of Constant but Arbitrary Geometry

Consideration is given to the buoyancy effects on fully developed gaseous slip flow in vertical microducts of constant but arbitrary geometry. The thermal boundary condition is assumed to be the constant wall heat flux of the first kind, H1. The rarefaction effects are treated using the first-order slip velocity and temperature jump boundary conditions. The method of solution being considered, in which the governing equations in cylindrical coordinates and three of the boundary conditions are exactly satisfied, is mainly analytical. The remaining slip boundary conditions on the duct wall are applied to the solution through the least-squares matching method. As an application of the method, the hydrodynamic and thermal features are obtained for five duct geometries including a trapezoid, double trapezoid, isosceles triangle, rhombus, and ellipse. A complete parametric study indicates that both Poiseuille and Nusselt numbers are decreasing functions of Knudsen number and increasing functions of the mixed convection parameter. It is also observed that the functionality of these parameters on the duct aspect ratio is generally nonmonotonic and dependent upon the Knudsen number.

A novel SPH method for the solution of Dual-Phase-Lag model with temperature-jump boundary condition in nanoscale

This paper proposes a newly developed smoothed-particle hydrodynamics (SPH) method for the solution of one-dimensional heat conduction problem within a nanoscale thin slab for Knudsen numbers of 0.1 and 1 under the effect of Dual-Phase-Lag (DPL) model. A novel temperature-jump boundary condition is applied to the Lagrangian particle-based mesh-free SPH method in order to take into account the boundary phonon scattering phenomenon in the micro- and nano-scales. The formulation and discretization of the non-Fourier DPL heat conduction equation containing a third-order combined spatial-time derivative together with a temperature-jump boundary condition are presented and then a proper nanoscale time-stepping of the SPH method has been introduced. The dimensionless temperature and heat flux distributions have shown a good agreement with the existing numerical and analytical data for different dimensionless times, temperature to heat flux phase-lag ratios, and the Knudsen numbers. It is found that the developed SPH method have accurately simulated the complex behavior of the DPL model with relatively low computational cost.

Heat transfer characteristics of plug flows with temperature-jump boundary conditions in parallel-plate channels and concentric annuli

In this study, heat transfer characteristics of plug flows in micro/nano scale were investigated by taking rarefaction effects into account. For this, thermal analysis of plug flows in parallel-plates and concentric annuli was performed for the constant heat flux condition at the walls, which were asymmetrically heated. First-order temperature-jump boundary condition was implemented at the wall assuming a gaseous plug flow, whereas its absence would correspond to either liquid plugs or plug flows at macro scale. Closed form expressions were analytically derived for obtaining temperature distributions and Nusselt numbers as a function of key parameters such as Knudsen number, Prandtl number, wall heat flux ratio, and annulus aspect ratio. The results show that Nusselt number may increase or decrease depending on the major parameters such as rarefaction, wall heat flux ratio and annulus aspect ratio.

Numerical Analysis of Flow and Heat Transfer Characteristics on Micro Couette Flow

In this paper, Couette flow is mainly discussed by studying the general flow behaviour mechanism and importing the velocity slip and temperature jump boundary condition. By analyzing velocity, temperature and pressure profiles at different Knudsen numbers, we concluded that Couette flow is driven by shear stress. The shear stress lies in stream direction. Viscous heat causes the increasing of the fluid’s temperature. With the increasing of Knudsen numbers, the increasing speed increases. It’s in the beginning of transition region that the heat flux has the maximum.

Investigation of highly non-linear dual-phase-lag model in nanoscale solid argon with temperature-dependent properties

The one-dimensional non-linear non-Fourier heat conduction within a thin film of solid argon is numerically investigated under the framework of the Dual-Phase-Lagging (DPL) model including the boundary phonon scattering. The thermal properties of the solid argon including the thermal conductivity and sound group velocity are considered to be temperature-dependent, and the results are compared with those obtained from the Molecular-Dynamics simulation for the following cases: (I) constant applied temperature and (II) constant applied heat flux at the left boundary. In addition, each case is studied under two conditions of constant and temperature-dependent volumetric heat capacity. It is concluded that the combination of the DPL model with the mixed-type temperature boundary condition is able to accurately predict the heat flux and temperature distribution obtained from the molecular dynamics simulation. It is also found that using the temperature jump boundary condition along with the DPL model is essential to precisely capture the nanoscale heat transport. The results of our simulation showed that the Knudsen number increases up to 3.86 near right boundary for the temperature dependent volumetric heat capacity.

Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions

In this paper, second order velocity slip and temperature jump boundary conditions are used to solve the momentum and energy equations along with isoflux thermal boundary condition at the surface of the micropipe. The flow is assumed to be hydrodynamically and thermally fully developed inside the micropipe and viscous dissipa- tion is included in the analysis. The solution yields closed form expressions for the temperature field and Nusselt number (Nu) as a function of various modeling parameters, namely, Knudsen number and Brinkman number (Br). For the given values of Br, the maximum difference of Nu between continuum flow with first order slip model and continuum and, second order slip model is found to be 35.67 and 34.62 %, respectively. Present solution exhibits good agreement with the other theoretical models.

Effects of High-Order Slip/Jump, Thermal Creep, and Variable Thermophysical Properties on Natural Convection in Microchannels With Constant Wall Heat Fluxes

Natural convection gaseous slip flows in open-ended vertical parallel-plate microchannels with symmetric wall heat fluxes are numerically investigated. A second-order model, including thermal creep effects, is considered for velocity slip and temperature jump boundary conditions with variable thermophysical properties. Simulations are performed for wide range of Rayleigh numbers from 5 × 10− 6 to 5 × 10− 3 in the continuum to slip flow regime. The developing and fully developed solutions are examined by solving the Navier–Stokes and energy equations using a control volume technique. It is found that the second-order effects reduce the temperature jump and the slip velocity, whereas thermal creep strongly increases the slip velocity in both developing and fully developed regions. Moreover, the rarefaction effects increase the flow and heat transfer rates considerably, while decreasing the maximum gas temperature and friction coefficient as compared to the continuum limit. It was also shown that the axial temperature variations of the gas layer adjacent to the wall in the modeling of the thermal creep are of paramount importance and neglecting these variations, which is common in literature, leads to unphysical velocity and temperature distributions.

Challenges in the Design and Fabrication of a Lab-on-a-Chip Photoacoustic Gas Sensor

The favorable downscaling behavior of photoacoustic spectroscopy has provoked in recent years a growing interest in the miniaturization of photoacoustic sensors. The individual components of the sensor, namely widely tunable quantum cascade lasers, low loss mid infrared (mid-IR) waveguides, and efficient microelectromechanical systems (MEMS) microphones are becoming available in complementary metal–oxide–semiconductor (CMOS) compatible technologies. This paves the way for the joint processes of miniaturization and full integration. Recently, a prototype microsensor has been designed by the means of a specifically designed coupled optical-acoustic model. This paper discusses the new, or more intense, challenges faced if downscaling is continued. The first limitation in miniaturization is physical: the light source modulation, which matches the increasing cell acoustic resonance frequency, must be kept much slower than the collisional relaxation process. Secondly, from the acoustic modeling point of view, one faces the limit of validity of the continuum hypothesis. Namely, at some point, velocity slip and temperature jump boundary conditions must be used, instead of the continuous boundary conditions, which are valid at the macro-scale. Finally, on the technological side, solutions exist to realize a complete lab-on-a-chip, even if it remains a demanding integration problem.

Gaseous Slip-Flow Mixed Convection Through Ordered Microcylinders

The fully developed longitudinal slip-flow mixed convection between a periodic bunch of vertical microcylinders arranged in regular arrays is investigated in the present work. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The rarefaction effects are taken into consideration using first-order slip velocity and temperature jump boundary conditions. The method considered is mainly analytical, in that the governing equations and three of the boundary conditions are exactly satisfied. The remaining symmetry condition on the right-hand boundary of the typical element is applied to the solution through the point-matching technique. The results indicate that both the pressure drop and Nusselt number are not dependent on the type of the boundary conditions at small and moderate blockage ratios. At higher blockage ratios, the pressure drop is higher for the H2 case, whereas the opposite true for the Nusselt number. Furthermore, the pressure drop is an increasing function of the blockage ratio and a decreasing function of the Knudsen number. The same trend is observed for the Nusselt number, except at higher blockage ratios at which the functionality of this parameter on the blockage ratio may change.

H2 Forced Convection for Slip Flow in an Equilateral Triangular Duct

The slip flow and temperature jump boundary conditions are derived for H2 constant flux forced convection in ducts. An exact solution is found for the fully developed equilateral triangular duct. Closed-form formulas for the temperature distribution and the Nusselt number are presented. The exact H2 Nusselt number for the no-slip case is 308/163.

Analysis of Gaseous Flow Between Parallel Plates by Second‐ Order Velocity Slip and Temperature Jump Boundary Conditions

AbstractIn this study the momentum and energy equations are solved to analyze the flow between two parallel plates by employing second‐order velocity slip and temperature jump conditions. The flow is considered to be laminar, incompressible, hydrodynamically/thermally fully developed, and steady state. In addition to the isoflux condition, viscous dissipation is included in the analysis. Closed form expressions for the temperature field and Nusselt number are obtained as a function of the Knudsen number and Brinkman number. The Nusselt number obtained by employing the second‐order model is found to be lower compared to the continuum value and agrees well with the other theoretical models. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21116