Melting Heat in Radiative Flow of Carbon Nanotubes with Homogeneous-Heterogeneous Reactions

The present article provides mathematical modeling for melting heat and thermal radiation in stagnationpoint flow of carbon nanotubes towards a nonlinear stretchable surface of variable thickness. The process of homogeneousheterogeneous reactions is considered. Diffusion coefficients are considered equal for both reactant and autocatalyst.Water and gasoline oil are taken as base fluids. The conversion of partial differential system to ordinary differential system is done by suitable transformations. Optimal homotopy technique is employed for the solutions development of velocity, temperature, concentration, skin friction and local Nusselt number. Graphical results for various values of pertinent parameters are displayed and discussed. Our results indicate that the skin friction coefficient and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.     

单壁碳纳米管声子谱及比热计算

利用卷曲法计算了有限长单壁碳纳米管的声子色散关系．讨论了单壁碳纳米管的比热随管径、温度的变化趋势．结果表明碳管的比热随温度、管径的增大而增大,并逐渐趋于一恒定数值．根据色散关系的计算结果,给出了有限长（5,5）型单壁碳纳米管的振动模式以及部分振动模式的频率随长度的变化关系． 关键词： 碳纳米管 声子 比热     

Nonlinear transport and heat dissipation in metallic carbon nanotubes

We show that the local temperature dependence of thermalized electron and phonon populations along metallic carbon nanotubes is the main reason behind the nonlinear transport characteristics in the high bias regime. Our model is based on the solution of the Boltzmann transport equation considering both optical and zone boundary phonon emission as well as absorption by charge carriers. It also assumes a local temperature along the nanotube, determined self-consistently with the heat transport equation. By using realistic transport parameters, our results not only reproduce experimental data for electronic transport but also provide a coherent interpretation of thermal breakdown under electric stress. In particular, electron and phonon thermalization prohibits ballistic transport in short nanotubes.     

Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet

An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow to a melting stretching/shrinking sheet. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, before being solved numerically using the Runge-Kutta-Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, stretching/shrinking parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique.     

围绕变壁温水平圆柱热源接触熔化的理论分析

研究围绕变壁温热源的接触熔化,建立表面温度随角度变化的水平圆柱热源接触熔化模型.对紧密接触熔化区的液体传热与运动状态进行分析,运用Nusselt液膜理论建立熔化控制方程,并采用理论求解,得到稳定熔化时的熔化速度解析解,所得结果包含了文献关于定壁温热源熔化的分析结果.通过分析不同温度分布下发生接触熔化的熔化速度、液膜厚度和压力分布情况,得到温度分布对熔化影响的规律.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

架空管道停输介质温度分布的影响因素分析

考虑环境温度、对流换热系数、初始温度和析蜡潜热等因素的影响,研究热油管道停输过程中介质的径向温度场分布及变化规律,对确定安全停输时间具有重要的指导作用。本文建立了架空热油管道停输径向传热物理模型及数学模型,利用FLUENT软件模拟了架空管道停输温降过程特定半径处温度变化过程。该方法能够确定不同半径处原油凝固时刻,为管道维修争取更多的时间。     

On the stability of the flow and heat transfer over a moving thin needle with prescribed surface heat flux

The steady flow and heat transfer over a moving thin needle with prescribed surface heat flux is studied. The similarity equations are obtained by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and their behaviors are discussed for different values of the needle size and the velocity ratio parameter. Results show that the decreasing of the needle size enhance the skin friction coefficient and the local Nusselt number on the needle surface. It is found that dual solutions exist (upper and lower branches) for a certain range of the velocity ratio parameter. A stability analysis of the solutions are performed and it shows that the upper branch solution is stable, while the lower branch solution is unstable.     

Different methods to calculate heat transfer coefficient in a double-tube heat exchanger: A comparative study

An experimental study performed to compare the results of different methods used in the literature for the calculation of heat transfer coefficient in double-tube heat exchangers. Then, a new fundamental approach was proposed which used the temperature profile and the local heat transfer coefficients. In this method, the heat transfer coefficient has been calculated for the total length of the heat exchanger including developing and fully developed regions. Numerous experimentations have been conducted in a double-tube heat exchanger. A significant difference observed between the results obtained from the suggested approach and those of the previous methods.     

径向热管传热的数值计算及结果分析

采用计算流体力学软件首先对无吸液芯径向热管管壁的温度进行数值计算,其次模拟无吸液芯径向热管中蒸汽的层流对流换热的情况,得出其温度场分布和速度场分布,并对结果进行分析。     

斜抽运无机液体激光器的流场热分布

激光二极管斜抽运的多增益段串接的液体激光器能够明显地提高激光光束质量、获得较高的输出功率.针对斜抽运子增益段工作时所涉及的流动、传热和壁面耦合,建立了计算子增益段流场热分布的流-热-固耦合模型,应用有限单元法完成了其瞬态流场热分布的数值模拟.该方法排除了不精确的换热系数对计算结果的影响,使得换热系数不再是计算的先决条件,而只是计算结果之一,并且为评价流道形状、流速、吸收系数等因素对流场热的影响,以及进一步改进和控制液体激光介质的流场热分布,提供了可靠的分析方法.数值模拟研究表明:换热系数是空间位置的函数,     

Size and temperature dependence of the specific heat capacity of carbon nanotubes

The specific heat capacity (C_v) of carbon nanotubes for different temperatures and radii is calculated and presented. These calculations are based upon the continuum model of Zhang et al. The change in dimensionality behaviour (from quasi-1D to quasi-2D) as a function of temperature for tubes of different radii is investigated. It is found that for a range of radii the changeover occurs between 180 K and 400 K. Thicker nanotubes have intrinsically stronger quasi-2D behaviour beyond this temperature range than thinner nanotubes. The present numerical results confirm a qualitative discussion of this behaviour presented earlier by Benedict et al. For a given temperature, the variation of C_v as a function of radius is also discussed. An expression has been obtained to show the linear variation of C_v in the appropriate low temperature region.     

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid

We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method(OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fourier's law of heat conduction.     

Variable viscosity effects on the flow of MHD hybrid nanofluid containing dust particles over a needle with Hall current—a Xue model exploration

This study scrutinizes the flow of engine oil-based suspended carbon nanotubes magneto-hydrodynamics (MHD) hybrid nanofluid with dust particles over a thin moving needle following the Xue model. The analysis also incorporates the effects of variable viscosity with Hall current. For heat transfer analysis, the effects of the Cattaneo-Christov theory and heat generation/absorption with thermal slip are integrated into the temperature equation. The Tiwari-Das nanofluid model is used to develop the envisioned mathematical model. Using similarity transformation, the governing equations for the flow are translated into ordinary differential equations. The bvp4c method based on Runge-Kutta is used, along with a shooting approach. Graphs are used to examine and depict the consequences of significant parameters on involved profiles. The results revealed that the temperature of the fluid and boundary layer thickness is diminished as the solid volume fraction is raised. Also, with an enhancement in the variable viscosity parameter, the velocity distribution becomes more pronounced. The results are substantiated by assessing them with an available study.     

Local and nonlocal parallel heat transport in general magnetic fields

A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.     

基于显热回收的分离式热管传热特性的实验研究

针对新风空调机组,采用倾角为15°的分离式热管用于显热回收.研究充液率,迎面风速及空气进口温度对显热效率的影响,分析了其影响规律.研究表明,采用热管空调机组设计风速范围内,充液率介于66％～75％时,其换热效率最高.迎面风速较低时,空气进口温度介于34℃～36℃,其显热效率较高.因此,采用分离式热管机组适合用于高热地区...     

Precursor state of skyrmions in MnSi: a heat capacity study

The magnetic phase diagram of MnSi based on the detailed magneto‐heat capacity study is presented. It shows the A‐phase, a precursor to the formation of stable skyrmion lattice, along with the intermediate, helical, conical, ferromagnetic and paramagnetic phases. The field isotherms of specific heat in and around the transition temperature reveal the different magnetic modulations. The local minima represent the relatively low entropy state due to the formation of A‐phase as a precursor to the stable skyrmion lattice. The field‐induced second‐order phase transition is observed by melting the intermediate phase. The region of existence of first‐order phase transition is found to be, effectively, from helical to the intermediate phase. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A molecular dynamics simulation on the convective heat transfer in nanochannels

The understanding of the flow and heat transfer processes for fluid through micro- and nanochannels becomes imperative due to its wide application in micro- and nano-fluidic devices. In this paper, the method to simulate the convective heat transfer process in molecular dynamics is improved based on a previous study. With this method, we simulate a warm dense fluid flowing through a cold parallel-plate nanochannel with constant wall temperature. The characteristics of the velocity and temperature fields are analysed. The temperature difference between the bulk average temperature of fluid and the wall temperature decreases in an exponential form along the flow direction. The Nusselt number for the laminar flow in parallel-plate nanochannel is smaller than its corresponding value at macroscale. It could be attributed to the temperature jump at the fluid–wall interface, which decreases the temperature gradient near the wall. The results also reveal that the heat transfer coefficient is related to the surface wettabilities, which differs from that in the macroscopic condition.     

Soret and Dufour effects on MHD non-Darcian mixed convection heat and mass transfer over a stretching sheet with non-uniform heat source/sink

An analysis has been carried out to study the effects of thermal-diffusion and diffusion-thermo on non-Darcian mixed convection heat and mass transfer of an incompressible, electrically conducting fluid over a stretching sheet embedded in a porous medium in the presence of an external magnetic field and non-uniform heat source/sink. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Similarity equations are then solved numerically using shooting algorithm with Runge-Kutta-Fehlberg scheme over the entire range of physical parameters. The effects of various physical parameters on the dimensionless velocity, temperature and concentration profiles are depicted graphically. Present results are compared with previously published work on various special cases of the problem and the results are found to be in very good agreement. Numerical results for local skin-friction, local Nusselt number and local Sherwood number are tabulated for different physical parameters.