A fuel droplet vaporization model in a hot air stream

The gasification behavior of a fuel droplet has been studied. The convective heat transfer is focused on in most literature on droplet evaporation. In this paper, a mathematic model of droplet evaporation is improved. Considering the presence of simultaneous mass and heat transfer at the interface between phases, a proper heat transfer equation for droplet evaporation model is established. Based on the model, a computer simulation program was developed, and the predictions of the model are compared with the experimental data. Sample calculations show the capabilities of the model for droplet evaporation.     

Drag on a sphere oscillating in an elastico-viscous fluid

Résumé On montre que la force agissant sur une sphère qui vibre autour d'une position moyenne dans une étendue infinie de liquide élastique et visqueux se compose de deux parties. L'une est en phase avec l'accélération et se produit parce que si la sphère se déplace le liquide se déplace nécessairement lui-même. L'autre s'oppose toujours au mouvement de la sphère et agit ainsi comme une force amortissante ne se trouvant pas en phase avec l'accélération. On trouve que pour toutes les valeurs de la fréquence, la résistance totae sur la sphère est beaucoup plus faible dans ce liquide que dans le liquide Newtonien correspondant.     

Drag on a circular cylinder oscillating in an elastico-viscous fluid

Résumé On calcule la force agissant sur un cylindre soumis à de petites oscillations latérales dans une masse infinie de fluide élastique et visqueux. On trouve que l'élasticité dans le liquide a pour effet de réduire à la fois la masse virtuelle du cylindre et la grandeur de la force d'amortissement agissant sur le cylindre.     

Drag on an elliptic cylinder in a fluid particle suspension

An elliptic cylinder is performing oscillations parallel to either of the principal axes of the cross-sectional ellipse in a fluid particle suspension. The stream function governing the flow and the velocity components are determined in terms of Mathieu functions. The drag on the cylinder is evaluated and expressed in terms of two parametersK andK. The effects of the variation of the frequency parameter, eccentricity parameter and relaxation time parameter on the drag parametersK, K is studied numerically.     

蠕动流中圆球阻力系数的入口效应

本文研究了圆球在半无穷长圆管入口处的蠕动流。得到了速度分布,压力分布和流函数的无穷级数形式的分析解.采用配置法将无穷级数截断并确定出级数中各项系数.求出了均匀入口流绕静止圆球以及圆球以瞬时速度在管内静止流体中运动这两种情形下圆球的阻力系数以及圆球表面上的应力分布.结果表明,当圆球在入口处运动时会遭受到较无穷圆管内为大的阻力.本文还对配置法的收敛性进行了数值实验.试验证明,该法具有好的收敛性.     

Measurement of velocity and concentration in a stream of a helium‐air mixture by hot‐wire/film anemometry

A method for simultaneous measurement of instantaneous velocity and concentration values in a stream of the air/helium mixture was suggested. The method applies the hot‐element anemometry principles using dual sensor.     

Drag in couple stress fluids

Summary A general expression is derived for the drag experienced by an axially symmetric body in the slow steady flow of Stokes' couple stress fluids. The result is compared with that obtained for micropolar fluids and then applied to the particular case of flow past a sphere.

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Résumé On a dérivé une relation générale pour la traînée subie par un corps de symétrie axiale dans un courant continu de fluide de Stokes à contraintes couplée. Cette expression est comparée à celle obtenue pour des fluides micropolaires, puis elle est appliquée au cas particulier du flux subi par une sphère.

     

Towards the Minimum Drag on a Body of Given Volume in Slow Viscous Flow

By merging a natural variational principle with a minimizingprocedure it is possible to obtain an upper bound on the minimumpossible drag on a body of given volume moving through a fluidat zero Reynolds number, and constant speed. A discussion isalso given of the possibility of finding a lower bound to thisquantity.     

纤维丛的全测地子流形

本文证明了底空间Ｍ是纤维丛Ｐ的全测地子流形；并且在ｄｉｍＰ－ｄｉｍＭ＝２时证明了若Ｐ是平坦的，则Ｐ的每一纤维也是全测地子流形．     

On noise modeling in a nerve fibre

We present a novel mathematical approach to model noise in dynamical systems. We do so by considering the dynamics of a chain of diffusively coupled Nagumo cells affected by noise. We show that the noise in a variable representing the transmembrane current can be effectively modeled as fluctuations in the model parameters corresponding to electric resistance and capacitance of the membrane. These fluctuations may account for the interactions between the membrane and the surrounding (physiological) solution as well as for the thermal effects. The proposed approach to model noise in a nerve fibre is an alternative to the standard technique based on the consideration of additive stochastic current perturbation (the Langevin type equations) and differs from it in important mathematical aspects, particularly, it points out to the non-Markov dynamics of transmembrane potential. Our scheme relates to a time scale which is shorter than the relaxation times of involved physiological processes.     

A stream cipher based on a spatiotemporal chaotic system

A stream cipher based on a spatiotemporal chaotic system is proposed. A one-way coupled map lattice consisting of logistic maps is served as the spatiotemporal chaotic system. Multiple keystreams are generated from the coupled map lattice by using simple algebraic computations, and then are used to encrypt plaintext via bitwise XOR. These make the cipher rather simple and efficient. Numerical investigation shows that the cryptographic properties of the generated keystream are satisfactory. The cipher seems to have higher security, higher efficiency and lower computation expense than the stream cipher based on a spatiotemporal chaotic system proposed recently.     

The nonsimilar laminar wall jet along a moving wall,in a free stream and in a free stream/moving wall

The flow of a laminar wall jet along either a moving plate, or in a free stream, or in combined moving plate and free stream is considered. The plate is isothermal and its temperature is different from that of the ambient fluid. The governing boundary-layer equations are converted into non-dimensional form and are solved numerically. Velocity and temperature profiles as well as the variation of wall shear stress and wall heat transfer are presented for all cases considered. For the case of a moving plate new results have been found although this problem has been investigated in the past. For the case of the free stream and the combined moving plate/free stream all the results are new and are presented for the first time in the literature. The three cases have been tackled with a unified way.     

Mass transfer from a vertical flat plate due to natural convection with a constant counterflow

This paper first examines the mass transfer from a vertical flat surface of a soluble material due to natural convection. A perturbation term is then introduced into the stream function to model the introduction of a constant counterflow. The effect this counterflow has on both the overall mass transfer and the overall velocity profile is studied in detail.     

Output stream of a binding neuron

For a binding neuron with threshold 2 stimulated by a Poisson stream, we determine the intensity of the output stream and the probability density for the lengths of the output interpulse intervals. For threshold 3, we determine the intensity of the output stream. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1619–1638, December, 2007.     

Optimal shape design in a fibre orientation model

We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example is shown. This research was supported by the Charles University Grant Agency under Contract 6/2005/R, MSM 0021620839 (MŠMT ČR), and the Academy of Finland, Grant #204741.