Generalized Hybrid Nanofluid Model with the Application of Fully Developed Mixed Convection Flow in a Vertical Microchannel *

The fully developed mixed convection hybrid nanofluid flow in a vertical microchannel is examined in detail. The simplified hybrid model that omits the nonlinear terms due to the interaction of different nanoparticle volumetric fractions is derived and compared with the existing one. The generalized model describing hybrid nanofluid suspended with multiple kinds of solid particles is suggested. The argument that the corresponding nanofluid solutions obtained by the homogenous model can be recovered from the results of the regular problems through simple arithmetic operations is checked. Solutions in similarity form for this flow problem are formulated by means of a set of similarity variables. The effects of various parameters on important physical quantities are analyzed and discussed.     

Experimental quantification of natural convective heat transfer within annulus space filled with a H2O-Cu nanofluid saturated porous medium. Application to electronics cooling

This experimental study deals with cooling electronics contained in a hemispherical cavity whose cupola is maintained isothermal, being its base inclined at an angle varying from 0° (horizontal disc with the cupola oriented upwards) to 135°. The active component is a dome centered on this base. The space between the differentially heated elements of the assembly is filled with a porous medium of high porosity saturated by a water–copper nanofluid whose volume fraction varies between 0% (pure water) and 7%. The Rayleigh number based on the radius of the cupola reaches high values up to 7.29 × 10¹⁰ given the important surface heat flux generated by the device during operation. The ratio between the thermal conductivity of the solid matrix and that of the base fluid ranges between 0 (interstitial volume without porous medium) and 41.4 corresponding to the intended applications. This experimental study done with an industrial prototype at scale 1 quantifies the natural convective heat transfer via the Nusselt number determined for many configurations obtained by varying the solid-fluid thermal conductivity ratio, the inclination angle, the Rayleigh number, and the volume fraction. The study clearly shows that the cooling performance of the Cu-H₂O nanofluid degrades with its age and the number of times it has been used. Analysis of the results reproducibility also proves the irreversibility of the performance. The measured values were compared with those obtained in a recent numerical study based on the volume control method. The observed deviations taking into account the experimental uncertainty margins validate the mathematical model implemented in the numerical approach.     

Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media

A model for double-diffusive convection in a heterogeneous porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source using the Brinkman model. In particular, we analyse the effect of slip boundary conditions on the stability of the model. Because of the many applications in micro-electro-mechanical systems (MEMS) and other microfluidic devices, a study of this problem is necessary. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.     

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.     

分离结晶过程中熔体热毛细对流的转变

为了了解微重力条件下新型分离结晶生长过程中熔体热毛细对流的基本特征,利用有限差分法进行了数值模拟,熔体深径比A取1和2,自由界面无因次宽度B分别取0.05、0.075和0.1.当熔体上表面为自由表面时,得到了分离结晶Bridgman生长过程中熔体热毛细对流的流函数和温度分布.计算结果表明:当Ma数较小时,在上下两个自由表面的表面张力的驱动下,熔体内部产生了两个流动方向相反的流胞,流动为稳态流动,随着Ma数的增加,上下自由表面速度增大,温度分布的非线性增加;当Ma数超过某一临界值后,流动将转化为非稳态流动;与熔体上表面为固壁时相比,A=1时的临界Ma数减小,而A=2时的临界Ma数增大;流动失稳的物理机制是流速的变化和阻力的变化之间存在滞后.     

槽式太阳能集热器内耦合换热特性研究

对槽式太阳能集热器内的耦合换热过程建立了统一求解模型,推导了无量纲控制方程,并进行了耦合求解.结果表明:随Ra增加,管内自然对流形成的涡逐渐向右侧管壁方向移动,等温线中心向下偏移;环形空间内自然对流形成的涡向顶部移动,等温线向下偏转;随管径比增加,管内的混合对流换热系数增加,管外环形空间的换热系数减小.内管内外表面的温度梯度及局部换热系数均随着角度的增加而增加.在θ=π/4和θ=π/2的截面内,环形空间中间区域内温度沿半径方向不降反升,出现偏转;而在θ=3π/4和θ=π的截面内,圆管内部中间区域内的温度沿着径向不升反降,也出现偏转.     

Reduced basis method for multi-parameter-dependent steady Navier–Stokes equations: Applications to natural convection in a cavity

This work focuses on the approximation of parametric steady Navier–Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute an output, and give sharp error bounds. The computations are split into an offline part, where the values of the parameters are not yet identified, but only given within a range of interest, and an online part, where the problem is solved for an instance of the parameters. The offline part is expensive and is used to build a reduced basis and prepare all the ingredients – mainly matrix–vector and scalar products, but also eigenvalue computations – necessary for the online part, which is fast.     

振动颗粒物质中倍周期运动对尺寸分离的影响

实验研究了竖直振动颗粒床中,倍周期运动对尺寸分离的影响.实验中,当振动加速度足够大时,系统中出现稳定的对称对流,进一步增大振动加速度到某个临界值时,还会出现倍周期运动.观察表明,背景颗粒的对流运动对分离过程起主导作用,对流速度决定着分离过程的快慢,而在2倍周期和4倍周期分岔之后,分离时间有所减慢.对引起对流运动的起因进行了分析,以此为基础分析了倍周期运动产生影响的物理机理,并对分离时间进行了定量计算,结果与实验值符合很好. 关键词： 颗粒物质 “巴西果”效应 倍周期分岔 对流     

溶解与热对流对固体颗粒运动影响的直接数值模拟

对牛顿流体内溶解与热对流对单颗粒在垂直管道中的沉降运动进行了直接数值模拟.流体运动由守恒方程计算,密度和黏性的变化考虑流场温度变化的影响,通过积分黏性应力和压力获得颗粒的受力跟踪颗粒运动,溶解引起的相变及其形状的变化由溶解潜热、溶解质量与分散相边界处的温度梯度的关系建立的方程决定.通过颗粒和流体间相互的作用力和力矩及边界条件的施加实现相间耦合.分别模拟了颗粒在等温流体、热流体、冷流体及颗粒溶解四种情况下的沉降过程.结果表明,在一定雷诺数内,热对流产生的颗粒尾迹处涡的脱落以及溶解引起的颗粒表面形态的变化引起了颗粒的横向摆动,并使颗粒沉降速度发生了变化. 关键词： 溶解 热对流 颗粒两相流 直接数值模拟