Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media (Ⅱ)

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.     

Heat transfer and fluid flow of benard-cell convection in rectangular container with free surface sensed by infrared thermography

The natural convection flow phenomena that occur inside an enclosed space are very interesting examples of complex fluid systems that may yield to analytical, empirical and numerical solutions, and many reports have looked into this basic problem. In the present study, heat transfer and fluid flow for natural convection in a horizontal rectangular container with a free surface are investigated using infrared thermography. The temperature field was measured and visualized at a gas-liquid (air — silicon oil) interface using infrared thermography. The heat transfer phenomena were also investigated by statistically analyzing the temperature data. The applicability of the infrared thermography to quantitative heat transfer measurement at the gas-liquid interface was evaluated. It is revealed that infrared thermography is effective not only in visualization of a gas-liquid interface but also in heat transfer measurement. A new heat transfer correlation is proposed for the gas-liquid interface of this flow system. The coefficient of heat transfer can be summarized by a specific heat transfer correlation formula regardless of several conditions, including container aspect ratio, fluid viscosity and fluid layer depth.     

RIBs in-flight production at the Laboratori Nazionali del Sud

Microscopic modeling of complex systems by cellular automata, which deal with particles at lattice sites interacting via simple local rules, involves some arbitrariness besides a drastic simplification of nature. Here we briefly report on some recent work on the influence of dynamic details on the morphological and critical properties of one of such model systems. In particular, we discuss on the similarities and differences between a kinetic nonequilibrium Ising model—which is a prototype for nonequilibrium anisotropic phase transitions—and its off–lattice counterpart, namely, an analogue in which the spatial coordinates of the particles vary continuously. We also pay attention to a related driven lattice model with nearest-neighbor exclusion.     

The influence of the wind forcing and of the changing of Coriolis parameter on the Ross Sea tidal circulation

Summary The combined effect of wind stress and the latitudinal variation of the Coriolis parameter on the tidal circulation of the Ross Sea is studied. To enhance the role of these forcing terms, the present model—based on the two-dimensional shallow-water equations—echoes that of earlier study to facilitate the comparison of the basic tidal regime. The numerical technique is described in detail along with its stability and accuracy properties. The numerical results are compared with data from direct measurements and with earlier simulations.     

Investigate the effect of anisotropic order parameter on the specific heat of anisotropic two-band superconductors

The effect of anisotropic order parameter on the specific heat of anisotropic two-band superconductors in BCS weak-coupling limit is investigated. An analytical specific heat jump and the numerical specific heat are shown by using anisotropic order parameters, and the electron–phonon interaction and non-electron–phonon interaction. The two models of anisotropic order parameters are used for numerical calculation that we find little effect on the numerical results. The specific heat jump of MgB₂, Lu₂Fe₃Si₅ and Nb₃Sn superconductors can fit well with both of them. By comparing the experimental data with overall range of temperature, the best fit is Nb₃Sn, MgB₂, and Lu₂Fe₃Si₅ superconductors.     

Tailoring the wetting response of silicon surfaces via fs laser structuring

Control over the wettability of solids and manufacturing of functional surfaces with special hydrophobic and self-cleaning properties has aroused great interest because of its significance for a vast range of applications in daily life, industry and agriculture. We report here a simple method for preparing stable superhydrophobic surfaces by irradiating silicon (Si) wafers with femtosecond (fs) laser pulses and subsequently coating them with chloroalkylsilane monolayers. It is possible, by varying the laser pulse fluence on the surface, to achieve control of the wetting properties through a systematic and reproducible variation of roughness at micro- and nano-scale which mimics both the topology of the “model” superhydrophobic surface—the natural lotus leaf—, as well as its wetting response. Water droplets can move along these irradiated superhydrophobic surfaces, under the action of small gravitational forces, and experience subsequent immobilization, induced by surface tension gradients. These results demonstrate the potential of manipulating liquid motion through selective laser patterning.     

各向异性矩形悬臂板稳态热传导解析

应用各向异性稳态热传导解析解分析了三边对流换热、另一边给定不均匀温度的各向异性矩形悬臂板温度场。讨论了各向异性角对温度场分布的影响。各向异性角的增大加剧了温度梯度。数值结果表明各向异性角为0°的悬臂板内温度梯度最小。     

Orthotropic ambipolar diffusion model for γ-manganese dioxide. The role of the reactive sub-surface

γ-manganese dioxide is considered as a continuing solid medium, when it is submitted to diffusion laws. These are derived from an appropriate adoptation of “the analytical theory of heat diffusion in the anisotropic medium”. We have taken into account the ambipolar nature of the diffusion and the internal electrical field which accompanies it. The “instantaneous or continuous point source” theory, which gives a physical interpretation to the analytical solution of the heat conduction differential equation, was applied. With this we explain how particles diffuse from the discontinuous reactive area into the γ-MnO₂ bulk.     

On the parallel shock waves in collisionless plasma with heat fluxes

A class of shock wave solutions is discussed for collisionless anisotropic plasma with heat fluxes. For the strictly parallel one-dimensional motions of a plasma the system of equations is written in divergent form and both linear and shock wave solutions are considered. Jump expressions for the parallel shocks are obtained in analytical form as functions of the shock upstream parameters.     

圆管层流脉冲流动对流换热数值分析

对等热流和等壁温边界条件下圆管内层流脉冲流动对流换热问题进行了数值模拟。在等热流边界条件下的数值计算结果与理论解吻合很好。计算结果表明:在等热流和等壁温边界下脉冲流动可引起速度、温度以及努塞尔数随时间波动,振幅越大,脉冲频率越小,波动越大。但它们的时均值均等于在相同雷诺数下稳态流动的值,脉冲流动不能强化换热。     

Analytical and numerical exploration of oscillatory convection in porous media

This study is part of the research about the influence of the thermal gradient on the composition and the stability of fluids in geological environments. This paper presents modelling results of oscillatory convection in a porous medium using the METSOR code. The model solves the heat and mass transport equations in a porous medium and takes into account the Soret effect (mass transport under thermal gradient). Oscillatory convection may occur in pure fluids and in binary mixtures (as a consequence of the Soret effect). Experimental data confirm the existence of this phenomenon in porous media. Here, the outputs of the METSOR code are verified against existing analytical solutions. A first modelling attempt of oscillatory convection in mixtures is presented (salt aquifer).     

A study of the heat transfer characteristics of a laser rod in a concentric circular tube

An analytical solution was derived from a two-dimensional heat conduction model with non-uniform boundary conditions for a side-pumped, side-cooled cylindrical laser rod. The convective heat transfer coefficient and the spatially varying fluid temperature were determined from the theoretical solutions or experimental correlations of convective heat transfer in an annular passage with prescribed heat fluxes. The first term of the analytical solution coincides with the result of the one-dimensional model. The other terms indicate that the axial temperature-rise in a laser rod has positive correlations with the axial coolant temperature-rise, the radial Biot number and the length-to-radius ratio of the laser rod. Subsequently, a conjugate numerical simulation that couples up the fluid convection and the solid conduction was performed. Compared with the analytical solution, the conjugate numerical simulation better exhibits the entrance effects of flow and heat transfer; therefore, it may provide more accurate solution in specific cases. PACS 44.10.+i; 44.90.+c     

Numerical simulation of the one-dimensional population dynamics with nonlocal competitive losses and convection

Numerical solutions of the generalized one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal competitive losses and convection are constructed. The influence function for nonlocal losses is chosen in the form of a Gaussian distribution. The effect of convection on the dynamics of the spatially inhomogeneous distribution of the population density is investigated.     

Radiative heat transfer in a planar medium with anisotropic scattering and directional boundaries

Radiation heat transfer in an absorbing, emitting and scattering medium has been the subject of many previous investigations. Most solutions are numerically complex and the existing analytical solutions are restricted in application by the simplifying assumptions involved. A plane-parallel medium is considered which scatters anisotropically. The boundaries are considered to be specular reflectors, as predicted by Fresnel's relations, while the diffusely incident radiation is refracted according to Snell's law. The emission is restricted to a medium with a uniform temperature distribution. Approximate closed-form solutions for the radiative heat flux and incident intensity are presented for dielectric layers and linear anisotropic scattering. Numerical results are also presented and show that the effects of directional boundaries, anisotropic scattering, scattering albedo and optical depth are accurately predicted by the approximate solution.     

Change of confinement scale in nuclei and the EMC effect

We study a model in which the confinement scale of quarks in a nucleus of massA changes asA ^1/3. This explains theA dependence of structure functions (emc effect) as seen in muon, electron and antineutrino deep inelastic scattering from nuclear targets. We also investigate a prediction of this model—anA dependence of theqcd scale parameter A.     

Random Sequential Adsorption on Random Trees

When gas molecules bind to a surface they may do so in such a way that the adsorption of one molecule inhibits the arrival of others. Two models which have frequently been studied are the “dimer model” and the “blocking model”, and rather complete solutions for these are known on fixed tree structures or Bethe lattices. In this paper comparisons are made between the occupation probabilities for vertices between fixed and random trees.     

水雾红外隐身的冷/热目标效应

人工水雾对抗红外成像制导导弹时,会因为蒸发对流强、辐射热流弱而使水雾形成冷目标;也可能因为辐射热流过强、散热弱而形成热目标。为详细揭示该现象,以Mie理论为基础,通过辐射传递方程和能量守恒方程的耦合计算,建立了水雾红外隐身产生冷目标或热目标效应的数学模型。应用蒙特卡洛法与本文算法作对比,验证了模型的正确性;将水雾视为吸收、发射、各向异性散射介质,考虑水雾自身辐射、多重散射和各种换热过程,比如辐射热流、两相流的热传导、热对流、紊流热扩散以及雾滴蒸发等,反映了水雾热遮蔽所产生的冷/热目标效应。     

Imaginary Part of Action, Future Functioning as?Hidden Variables

Beginning with a review the logically first stages in the project of Random Dynamics, hoping for all laws nature being emergent, we also review what can be considered a consequence of Random Dynamics, a model—by myself and Masao Ninomiya—, which in principle predicts the initial conditions in such a way as to minimize a certain functional of the history of the Universe through both past and future. This functional is indeed the imaginary part of the action, which exists (only) in our model of complex action. The main point of the present is to suggest this complex action model to be also helpfull in solving some problems for quantum mechanics. Especially as our model almost makes it possible in principle to calculate the full history of the universe, it even makes it in principle calculable, which one among several measurement results in a quantum experiment will actually be realized!     

Mathematical simulation of conjugate turbulent natural convection in an enclosure with local heat source

A numerical analysis of turbulent regimes of the natural convection in a closed rectangular region with heat-conducting walls of finite thickness was carried out in the presence of a locally concentrated heat source under the conditions of the radiative-convective heat exchange with the ambient medium on one of the external boundaries. The mathematical model was constructed on the basis of the Reynolds equations in dimensionless variables stream function — vorticity vector — temperature. Special attention was paid to the investigation of the influence of the Grashof number er 10⁸≤Gr<10¹⁰, of the unsteadiness factor 0< τ <1000, and the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 6.8·10⁻⁵ on both the local and integral characteristics of the problem.     

Unsteady conjugate thermogravitational convection in a cylindrical region with local energy source

The mathematical modelling of unsteady regimes of natural convection in a closed cylindrical region with a heat-conducting shell of finite thickness was carried out in the presence of a local heat source under the conditions of convective heat exchange with the ambient medium. The mathematical model was constructed in dimensionless variables “stream function — vorticity vector — temperature” in the cylindrical coordinate system. The influence of the Rayleigh number, 10⁴ ≤ Ra ≤ 10⁶, of the unsteadiness factor 0 < τ < 300, of the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 4.3·10⁻², and the energy source sizes on both local characteristics (streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) was analysed in detail. Thermohydrodynamic peculiarities due to the geometry of the object of research were established.