Modeling and parameter identification of a maltodextrin DE 12 drying process in a convection oven

The drying kinetics of maltodextrin DE 12 in a convection oven are modeled using Fick's second law of diffusion and following the William, Landel and Ferry (WLF) equation for the moisture and temperature dependence of the effective diffusivity. An experimental design with a temperature range from 70°C to 140°C and sample amount varying from 4 to 12 ml is used. The resulting diffusion equation describing the dynamics of moisture content is highly nonlinear and possesses Dirichlet and Neumann boundary conditions. Ordinary differential equations are added to take the time-dependent variation of temperature into account. The method of lines is applied to discretize the partial differential equation w.r.t. the space variable leading to a highly stiff and numerically unstable system of ordinary differential equations. The data fitting problem is formulated to estimate some unknown model parameters simultaneously for 18 data sets under consideration.     

Thermomagnetic convection in magnetic fluids influenced by a time-modulated magnetic field

Material– and flow properties of magnetic fluids can be influenced by applying an external magnetic field. In this work we will particularly consider the onset of convection in magnetic fluids which is influenced by a magnetic force. In a horizontal magnetic fluid layer the force arises if a temperature gradient and an external magnetic field is applied. The behaviour of the onset of convection is investigated for a static and a time–modulated magnetic field. For the case of a static magnetic field the onset of convection depends on the strength of the field and for a time–modulated magnetic field an additional dependence on the frequency of magnetic field variation is found. The experimental results presented here confirm in principle the theoretical predictions about the influence of static and time–modulated magnetic forces on the onset of convection. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Onset of Rayleigh-Bénard Convection in a Fluid Layer of Slowly Increasing Depth

A two-scaling approach is used to investigate the onset of convection in a fluid layer whose depth is a slowly increasing function of horizontal distance. It is shown that whatever the value of the imposed temperature difference between the boundaries (provided, of course, that the lower one is hotter) there are regions which are stable and regions which are unstable to small perturbations. As the depth increases the amplitude of steady solutions increases from exponentially small values to take on the familiar square-root behavior of weakly nonlinear solutions. The solution in this narrow transition region is described in terms of the second Painlevé transcendent. In the exceptional case when the perturbation takes the form of longitudinal rolls, this equation needs some modification in that the second derivative is replaced by the fourth. The flow in a horizontal layer when the temperature difference between the boundaries increases slowly may be treated in exactly the same way. The necessary modifications to theory and results are given in an Appendix.     

Concave solutions of a general self-similar boundary layer problem for power-law fluids

In this paper, we give a rigorous mathematical analysis for a third order nonlinear boundary value problem. The boundary value problem can be applied to steady free convection around a vertical impermeable flat plate in a fluid-saturated porous medium, or steady flow of a power-law fluid induced by impermeable stretching walls in the frame of boundary layer approximation. We establish the uniqueness, existence and nonexistence of (normal) concave solutions or generalized concave solutions to the problem, and obtain some results about boundedness and asymptotic behavior of the (normal) concave solution or the generalized concave solution.     

Thermomagnetic convection induced by a time-modulated driving force in magnetic fluids

It is well-known that the flow properties of magnetic fluids – so called ferrofluids – can be modified by applying an external magnetic field. Under certain conditions, the magnetic force induced by this external field causes a convective flow. What has yet to be investigated is what happens when this driving force is modulated in time. For this purpose, a horizontal ferrofluid layer has been exposed to an intermittent magnetic field, which causes a time-modulated force. This force depends on the strength of the external magnetic field and the fluid temperature, and therefore the flow phenomenon generated is called thermomagnetic convection. In addition, if the fluid layer is heated from below, the classical thermal convection contributes to the flow system. In our studies, both effects – thermomagnetic and thermal – contribute together to the convection. The experimental results presented here confirm previous theoretical investigations about the influence of the frequency of the driving force on the strength of the convective flow, which reach minimum values at certain frequencies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Averaging a transport equation with small diffusion and oscillating velocity

A complete asymptotic expansion is constructed for the transport equation with diffusion term small with respect to the convection. Error estimates are obtained by using matched asymptotic expansion technique and building all the boundary layer terms in time and in space, necessary for obtaining an accurate error estimate. Copyright © 2003 John Wiley & Sons, Ltd.     

On the stability of mixed convective motions in a vertical layer with wave-like boundaries

The stability of the stationary and oscillatory convective motions which develop in a vertical layer with periodically curved boundaries is studied for the case of longitudinal fluid injection. The amplitude of the boundary undulations and the flow of fluid along the layer are both assumed to be small, and methods of perturbation theory are used. The characteristic properties of the incremental spectrum of the spatially periodic motions are studied and the most dangerous types of perturbations as well as the forms of the stability regions are determined.

Theoretical investigations of the effect of spatial inhomogeneity of the boundary conditions on the stability of convection were sparse, and they deal mainly with horizontal layers of fluid /1–3/. Stationary, spatially periodic motions in a vertical layer with curved boundaries were investigated in /4/ for the case of free convection (when the flow was closed), and their stability was investigated in /5/. It was established that the presence of a small but finite flow of fluid along the layer leads to an increase in the number of different modes of flow, and to the appearance of non-stationary convective motions in the region near the threshold.     

The heat transfer problem in the wall region of a turbulent boundary layer

The problem of heat transfer in the wall region of a turbulent boundary layer has been investigated. The resonant triad in the theory of hydrodynamic stability was used to obtain the velocity field induced by the coherent structures in the wall region of the turbulent boundary layer, while the small scale turbulence was represented by a simple model. By such a new approach of modeling, the 3-D temperature field is calculated, the mean temperature profile in the wall region and the Nusselt number characterizing the heat flux, which was found to be in good agreement with the experimental observations are obtained. The instantaneous temperature field had streaky structures, thus offering a mechanism for their generation found in numerical simulations. Project supported by the National Natural Science Foundation of China (Grant No. 19132011).     

Mathematical modeling of solidification process near the inner core boundary of the Earth

Radially symmetric analytic solutions of the heat and mass transfer equations governing convection in the Earth’s fluid core are found in terms of deviations from the adiabatic reference state. We demonstrate that an increase of the convective velocity leads to a decrease of the light constituent mass fraction and specific entropy. Where fluid is rising/descending, convective motions decrease/increase the mass fraction and entropy at the inner core boundary (ICB). The influence of convective motions on the thermal fluxes at the core mantle boundary is studied. On the basis of exact solutions we demonstrate that the liquid is supercooled near the ICB. An important point is that an increase in the convective velocity directed to the ICB increases the constitutional supercooling. We show that the anelastic model (AM) can be used only at small supercoolings near the ICB. The most probable solidification scenario “constitutional supercooling and morphological instability” should be described by a mushy layer theory near the ICB and by the AM in the rest region of the fluid outer core. On the basis of dendritic theory and selection mechanisms of crystal growth the dendrite tip radius and interdendritic spacing in the mushy layer at the ICB are determined in the presence of convection.     

Robust heteroclinic cycles

Summary One phenomenon in the dynamics of differential equations which does not typically occur in systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust for symmetry-preserving perturbations and stable. Cycles have been observed in a number of simulations and experiments, for example in rotating convection between two plates and for turbulent flows in a boundary layer. Theoretically the existence of robust cycles has been proved in the unfoldings of some low codimension bifurcations and in the context of forced symmetry breaking from a larger to a smaller symmetry group. In this article we review the theoretical and the applied research on robust cycles.     

Analytic solution of natural convection flow of a non‐newtonian fluid between two vertical flat plates by using decomposition method

An analysis has been performed to study the natural convection of a non‐Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non‐Newtonian nature of fluid on the heat transfer are studied. The governing boundary layer and temperature equations for this problem are reduced to an ordinary form and are solved by Adomian decomposition method (ADM) and numerical method. Velocity and temperature profiles are shown graphically. The obtained results are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and non‐linear equations and so can be found widely applicable in engineering and science. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1384–1395, 2010     

Preparation and structural stability investigation of CoN/CN soft X-ray multilayers

The structural stability of heat-treated CoN/CN soft X-ray multilayers fabricated by dual-facing-target sputtering has been investigated by using complementary measurement techniques. The high temperature annealing results imply that the destructive threshold of the Co/C multilayers is improved by 100–200 degrees centigrade through doping with N. The low-angle X-ray diffraction of CoN/CN soft X-ray multilayers indicates that the period expansion of the multilayers is only 4 % at 400°C, and the interface pattern still exists even if they were annealed at 700°C. The Raman spectra analyses give the evidence that the formation of the sp³ bonding in the CN sublayers can be suppressed effectively by doping N with atoms, and thus the period expansion resulting from the changes in the density of CN layers can be decreased considerably. The X-ray photoelectron spectra analyses present the information of the existence of the strong covalent bonding betweenC andN atoms, and the ionic bonding between Co and N atoms, which can slow down the tendency of the structural relaxation. The interstitial N atoms decrease the mobility of Co atoms, and thus the fcc-Co and hcp-Co coexist even though the annealing temperature is much higher than the phase transformation temperature of 420°C, leading to the suppression of the grain growth.     

含开边界二维Stokes问题的Galerkin边界元解法

本文推导了含有开边界的二维有限域上Stokes问题的边界积分方程, 得出基于单层位势的第一类间接边界积分方程.对与之等价的边界变分方程用Galerkin边界元求解以得出单层位势的向量密度. 对于含有开边界端点的边界单元,采用特别的插值函数, 以模拟其固有的奇异性.论文用若干数值算例模拟了含有开边界的有限区域上不可压缩粘性流体的绕流.       

Ein neues Isotopentrennverfahren

Summary An isotope process is described which employs the principle of thermal diffusion employed byClusius and which creates the required circulatory flow not by means of convection but by a forced controllable boundary layer flow. Experimental results are given and compared to results from other processes.      

A comparative analysis of moisture transport models as applied to an epoxy binder

The results of experimental and theoretical investigations into the kinetics of moisture sorption by a neat epoxy resin obtained from RAE Industries (Reapox 520, D523) are reported. The sorption process was realized in atmospheres with a constant relative humidity of 33, 53, 75, 84, and 97% and a temperature of 50°C. The results obtained showed that the diffusion behavior of epoxy resin did not obey Fick’s law under the experimental conditions considered. Consequently, the application of a non-Fickian diffusion model was necessary. For this purpose, two-phase moisture sorption models, a model with a time-dependent diffusivity, a two-phase material model, as well as relaxation and convection models of anomalous diffusion, were considered. The model parameters were obtained from the approximation of experimental sorption data. A comparative analysis of the sorption models was performed, and the specific features of their applications were estimated. The two-phase material model and the model with varying diffusivity were found to be the most suitable ones due to a good agreement between calculation results and experimental data and the rather small (three or four) number of parameters, which make them more flexible and physically more justified than the classical Fick’s model with its two parameters. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 555–570, July–August, 2007.     

平行球面间轴对称层流边界层方程的新解法

本文给出了与Mangler变换类似的变换,它将平行球面间进口段内层流轴对称边界层流动转换成二维平面层流边界层流动,使问题得到简化.简化后的方程可以用已有的平面层流边界层理论和数值方法来求解,从而为求解平行球面间扩散层流进口段问题提供了一条新的途径.     

Transient conduction in a plate with counteracting convection and thermal radiation at the boundaries

During the flash dehydroxylation of powdered kaolinite it is desirable that a rapidly propagating thermal wave penetrates the cold powder particles in a way that raises the particle interior to the reaction temperature of 600°C without the particle exterior being heated beyond 1000°C. In a production unit this is achieved by performing the heat treatment in a device where particles are heated by convection from hot gas and are subject to heat loss by thermal radiation to cool walls. This paper concerns the fundamental heat transfer problem of the process, decoupled from the thermal effects of the dehydroxylation reaction. Using a plate as the approximation for the particle shape a semi-analytical solution for the plate temperature distribution is obtained as a function of the five dimensionless process parameters: Biot number, radiation number, wall/gas and particle/gas temperature ratios and mode of convection. Accuracy is demonstrated by comparison with an existing numerical solution for the limiting case of pure radiative heating of a plate initially at absolute zero.     

Influence of parametric modulation on the onset of thermomagnetic convection

Magnetic fluids – so called ferrofluids – are suspensions of nano-scaled particles in an appropriate carrier liquid. The flow properties of these fluids can be influenced by applying an external magnetic field. It is possible to introduce a magnetic force in a horizontal ferrofluid layer which is able to drive a convective flow. The magnetic force arises in the presence of an external magnetic field if a temperature gradient exists in the fluid gap. The behaviour of the onset of convection depends on the strength of the external magnetic field and on the temperature gradient. In this paper the onset of convection under the influence of time-modulated magnetic field has been investigated. The experimental results presented here show a shift in the onset of convection depending on the frequency of the external magnetic field. This behaviour confirms in principle the theoretical predictions which are also presented here. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear stability of boundary layers for the Boltzmann equation with cutoff soft potentials

The study on the boundary layer is important in both mathematics and physics. This paper considers the nonlinear stability of boundary layer solutions for the Boltzmann equation with cutoff soft potentials when the Mach number of the far field is less than −1. Unlike the collision frequency is strictly positive in the hard potential or hard sphere model, the collision frequency has no positive lower bound for the cutoff soft potentials, so the decay in time cannot be expected. Instead, the present paper proves that the solution will always be in a small region around the boundary layer by noticing the decay property of collision operator in velocity.     

Modelling of thin polymer films

If we bond substrates like metal sheets by a thin polymer film we know about the existence of a boundary layer between the polymer and the substrate. The properties of this boundary layer differ from the bulk properties and influence the overall behavior of the bond. Here we present a mechanical theory based on a scalar-valued order parameter that allows us to describe these effects. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)