Computational treatment of free convection effect on flow of elastico-viscous fluid past an accelerated plate with constant heat flux

Effect of free convection on the visco-elastic fluid (Walter - B’ type) flow past an infinite vertical plate accelerating in its own plane with constant heat flux is examined analytically. It is found that for given values of Grashof number, Prandtl number and Newtonian parameter; flow velocity at any point increases with the increase in time and non-Newtonian parameter, however, it decreases with both, the heating and cooling of the plate.     

Three‐dimensional solidification with two possible crystallization states: Existence of solutions with flow in the melt

In this paper we discuss the existence of solutions of a system of nonlinear and singular partial differential equations constituting a phase field model with convection for non‐isothermal solidification/melting of certain metallic alloys in the case where two different kinds of crystallization are possible. Each one of these crystallization states is described by its own phase field, while the liquid phase is described by another one. The model also allows the occurrence of fluid flow in non‐solid regions, which are a priori unknown, and then we have a free‐boundary value problem. Thus, the model relates the evolutions of these three phase fields, the temperature of the solidification/melting process and the fluid flow in non‐solid regions. Copyright © 2009 John Wiley & Sons, Ltd.     

A Spectral method determination of the first critical Rayleigh number in a cylindrical container

The onset of laminar axisymmetric Rayleigh–Bénard convection is investigated analytically for fluid in a cylindrical container. All surfaces are considered to be solid and no-slip for the flow, whereas for the thermal boundary conditions both a perfectly conducting and an insulated side wall are considered. The governing Boussinesq equations are perturbed and an approximate solenoidal flow field and a temperature field are determined, using the assumption of separation of variables. Subsequently, a Chebysev–Galerkin spectral method is employed to reduce the equations to a system of first-order nonlinear ordinary differential equations. The approximate representation of the flow and temperature fields make it possible to perform the calculations analytically. The first critical Rayleigh number (Ra_cr) is then calculated using local stability analysis. The resulting value of Ra_cr compares favorably with previous numerical and experimental studies. The analytical solution presented here allows for deeper insights into the physics of this extensively studied problem to be identified.     

Dissipative Structure in the Course of Drying Suspensions and Solutions

Summary: Convectional, sedimentation and drying dissipative patterns during the course of dryness of suspensions and solutions are reviewed. The whole processes of convection were analyzed in the seven steps: irregular circulation accompanied with the upward heat transportation, global convectional flow from the central area toward outside edge at the surface layers of liquid, cooperative formation of distorted Benard cells, reversal of global flow of convection, growing of the spoke lines from the outside edge toward central area at the liquid surface layers, cluster and further bundle formation of the spoke lines, and the convectional flow by the pinning effect. The sedimentary colloidal particles were suspended above the substrate by the electric double layers and moved by the balancing of the external force fields including convectional flow and sedimentation. Principal macroscopic drying patterns are broad rings and spoke lines. Microscopic patterns such as star, needle, street road, string and cross-like are formed. The stratified structures form from micro to macro scales. Information on the size, shape, conformation and/or flexibility of particles or polymers is transferred cooperatively, and further accompanied with the amplification and selection processes during the course of dryness.     

Impacts of Forced Convection Generated via High Precision Stirring on Scanning Electrochemical Microscopy Experiments in Feedback Mode

In this study, the effects of forced convection on scanning electrochemical microscopy (SECM) experiments in feedback mode using ferrocenemethanol as redox mediator are presented. Forced convection, which enhances the mass transfer inside the system, was generated via an electrical high precision stirrer integrated into the SECM setup. A thin‐film interdigitated array electrode serving as model substrate was investigated with probe scan curves in z‐direction and SECM imaging in constant height mode utilizing ultramicroelectrodes (UME) with diameters (d_probe) of 25 μm and 12.5 μm. It was found that forced convection increased the overall current during SECM imaging without distorting distinctive features of the imaged structure when working with a 25 μm UME at substrate‐to‐tip distances of 14 μm and 11 μm. Furthermore, the electrochemical contrast was improved under hydrodynamic conditions for a substrate‐to‐tip distance of 11 μm and scan rates of 5 μm s^?1, 10 μm s^?1, 20 μm s^?1 and 40 μm s^?1. When further decreasing the gap between the UME and the substrate to 9 μm almost no effects of the forced convection were observed. Consequently, for a 25 μm UME, forced convection led to higher currents and improved performance during SECM experiments in feedback mode at substrate‐to‐tip distances of 14 μm and 11 μm, whereas no effects were observed for a 12.5 μm UME at a distance of 8 μm.     

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.