Effect of Thermal Non-Equilibrium on Convective Instability in a Ferromagnetic Fluid-Saturated Porous Medium

The effect of local thermal non-equilibrium (LTNE) on the onset of thermomagnetic convection in a ferromagnetic fluid-saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated. A modified Forchheimer-extended Darcy equation is employed to describe the flow in the porous medium, and a two-field model is used for temperature representing the solid and fluid phases separately. It is found that both the critical Darcy–Rayleigh number and the corresponding wave number are modified by the LTNE effects. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient Ht are presented and compared with those computed numerically. An excellent agreement is obtained between the asymptotic and the numerical results. Besides, the influence of magnetic parameters on the instability of the system is also discussed. The available results in the literature are recovered as particular cases from the present study

Pattern Formation and Stability in Magnetic Colloids

This book presents a selection of works on pattern formation and stability of magnetic colloids. Magnetic liquids can be investigated in different scenarios. Geometry (quasi 1, 2 and 3 dimensional vessels ), scales (molecules, macroscopic particles) and the type of suspension (e.g., ferromagnetic, superparamagnetic) employed in experiments completely modify the aggregation process. The observed patterns in the fluid range from surface waves to bulk chains and bundles. The approaches presented in this book use standard statistical means such as the Gibbs free energy and chemical potential. Numerical works are implemented employing methods such as Monte Carlo or Langevin dynamics simulations. Kinetic theory is used in theoretical approaches being successfully applied to algorithms such as the Lattice-Boltzmann method

Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction, in which cases heat transfer occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. We obtain a simple linear criterion that determines whether the infinite-cylinder assumption can be employed. The curvature of the cylinders enters this linear relationship through the slope and additive constant. For a given length-to-gap aspect ratio there is a critical Rayleigh number beyond which the laminar flow in the finite system is convective and so the behaviour is entirely different from the periodic case. The criterion does not depend on the Prandtl number and appears quite robust with respect to the Reynolds number. In particular, it continues to work reasonably in the turbulent regime.Comment: 25 pages, 9 figure

Heat transfer through thermomagnetic convection in magnetic fluids induced by varying magnetic fields

Magnetic fluid flow by thermomagnetic convection with and without buoyancy was studied in experiments and computational simulations. A mineral oil based ferro magnetic fluid was subjected to varying magnetic fields to induce thermomagnetic convection. As such fluids are mainly developed to increase heat transfer for cooling the fundamental effects on magnetic fluid flow was investigated using various magnetic field distributions. Computational simulations of natural and thermomagnetic convection are based on a Finite-Element technique and considered a constant magnetic field gradient, a realistic magnetic field generated by a permanent magnet and alternating magnetic fields. The magnetic field within the fluid domain was calculated by the magneto-static Maxwell equations and considered in an additional magnetic body force known as the Kelvin body force by numerical simulations. The computational model coupled the solutions of the magnetic field equations with the heat and fluid flow equations. Experiments to investigate thermomagnetic convection in the presence of terrestrial gravity used infrared thermography to record temperature fields that are validated by a corresponding numerical analysis. All configurations were chosen to investigate the response of the magnetic fluid to the applied body forces and their competition by varying the magnetic field intensity and its spatial distribution. As both body forces are temperature dependent, situations were analysed numerically and experimentally to give an indication of the degree by which heat transfer may be enhanced or reduced. Results demonstrate that the Kelvin body force can be much stronger than buoyancy and can induce convection where buoyancy is not able to. This was evident in a transition area if parts of a fluid domain are not fully magnetically saturated. Results for the transition from natural convection to thermomagnetic convection suggest that the domain of influence of the Kelvin body force is aligned with the dominance of the respective body force. To characterise the transition a body force ratio of the Kelvin body force to buoyancy was developed that identified the respective driving forces of the convection cells. The effects on heat transfer was quantified by the Nusselt number and a suitable Rayleigh number. A modified Rayleigh number was used when both body forces were active to define an effective body force by taking the relative orientation of both forces into account. Results for the alternating magnetic field presented flow fields that altered with the frequency of the applied magnetic field but with varying amplitude. This affected the heat transfer that alternated with the frequency but failed to respond instantaneously and a phase lag was observed which was characterised by three different time scales

Controlling the structure and dynamics of magnetoresponsive particle suspensions for enhanced transport phenomena

The work contained herein describes the use of various magnetic fields to control the structure and dynamics of magnetic particle suspensions, with the practical aim of enhancing momentum, heat, and mass transport. The magnetic fields are often multiaxial and can consist of up to three orthogonal components that may be either static (dc), time-dependent (ac), or some combination thereof. The magnetic particles are composed of a ferromagnetic material—such as iron, nickel, cobalt, or Permalloy—and can exist in a variety of shapes, including spheres, platelets, and rods. The shape of the particles is particularly important, as this can determine the type of behavior the suspension exhibits and can strongly affect the efficacy of various transport properties. The continuous phase can be almost any fluid so long as it possesses a viscosity that allows the particles to orient and aggregate in response to the applied field. Additionally, if the liquid is polymerizable (e.g., an epoxy system), then composite materials with particular, field-directed particle assemblies can be created. Given the many combinations of various particles, suspending fluids, and magnetic fields, a vast array of behavior is possible: the formation of anisotropic particle structures for directed heat transport for use as advanced thermal interface materials; the stimulation of emergent dynamics in platelet suspensions, which give rise to field-controllable flow lattices; and the creation of vortex fluids that possess a uniform torque density, enabling such strange behaviors as active wetting, a negative viscosity and striking biomimetic dynamics. Because the applied fields used to produce many of these phenomena are uniform and modest in strength, such adaptive fluids open up the possibility of tuning the degree of mixing or heat/mass transfer for specific operating conditions in a number of processes, ranging from the microscale to the industrial scale. Moreover, the very nature of magnetism provides for the manipulation of magnetic materials in a noncontact manner, making the application of these effects simple and robust by eliminating the need for complex, moving parts that may require maintenance and be prone to failure

Bifurcation phenomena in Taylor–Couette flow in a very short annulus with radial through-flow

In this study, the non-linear dynamics of Taylor–Couette flow in a very small-aspect-ratio wide-gap annulus in a counter-rotating regime under the influence of radial through-flow are investigated by solving its full three-dimensional Navier-Stokes equations. Depending on the intensity of the radial flow, either an axisymmetric (pure m = 0 mode) pulsating flow structure or an axisymmetric axially propagating vortex will appear subcritical, i.e. below the centrifugal instability threshold of the circular Couette flow. We show that the propagating vortices can be stably existed in two separate parameter regions, which feature different underlying dynamics. Although in one regime, the flow appears only as a limit cycle solution upon which saddle-node-invariant-circle bifurcation occurs, but in the other regime, it shows more complex dynamics with richer Hopf bifurcation sequences. That is, by presence of incommensurate frequencies, it can be appeared as 1-, 2- and 3-torus solutions, which is known as the Ruelle–Takens–Newhouse route to chaos. Therefore, the observed bifurcation scenario is the Ruelle-Takens-Newhouse route to chaos and the period doubling bifurcation, which exhibit rich and complex dynamics.Postprint (published version

Mikrokonvektīvās parādības neizotermiskās un neviendabīgās magnētisko nanodaļiņu dispersijas

Anotācija. Ferokoloīdiem – stabilām magnētisko nanodaļiņu dispersijām – piemīt vērā ņemamas magnētiskās īpašības, kuras izpaužas uz tiem iedarbojoties ar ārējo magnētisko lauku. Neizotermiskās koloidālās sistēmas savukārt izrāda ciešu saikni starp temperatūras un dispersās fāzes koncentrācijas gradientiem (Soret efekts). Tā galvenais cēlonis ir izmēru atšķirība starp binārā maisījuma komponentēm. Koncentrācijas un magnētiskā lauka gradientu mijiedarbība magnetizējamā vidē izraisa magnētiskos spēkus, kuri ietekmē siltuma un masas pārnesi. Šī teorētiskā pētījuma priekšmets ir fotoabsorbtīvo konvektīvi-difuzīvo mikrostruktūru rašanās un evolūcija ferokoloīdu slāņos ārēja magnētiskā lauka ietekmē. Tiek formulētas un risinātas dažas modeļproblēmas ar mērķi noskaidrot koncentrācijas magnētiskās konvekcijas veidošanās mehānismus koncentrācijas mikrostruktūrās, kuras tiek inducētas ar ārēja optiskā avota starojuma enerģijas absorbciju un no tās izrietošo termisko gradientu veidošanos. Ar teorētiskām metodēm tiek noteikta konvektīvās pārneses ietekme uz efektīviem transporta koeficientiem. Tiek apskatīta izstiepto fotoabsorbtīvo mikrostruktūru sekundārā hidrodinamiskā stabilitāte attiecībā pret noteicošo kontroles parametra variāciju. Skaitliskās simulācijās tika novērota izstiepto režģu destabilizācija un tai sekojoša translācijas simetrijas laušana. Savukārt, divdimensionālo tīklu stabilitātes zaudēšanai seko rotācijas simetrijas kārtas pazemināšanās. Iegūtie teorētiskie rezultāti ļauj interpretēt vai pārinterpretēt dažas fotoabsorbtīvo koncentrācijas mikrostruktūru veidošanās un evolūcijas īpatnības magnetokonvektīvas pārneses kontekstā. Koncentrācijas magnētiskās mikrokonvekcijas ietekmes analīze ļauj aprakstīt dažu iepriekš neizskaidrotu efektu mikroskopisko mehānismu. Tiek apstiprināta parazītiskās magnētiskās mikrokonvekcijas rašanās fotoabsorbtīvās mikrostruktūrās ārēja magnētiskā lauka ietekmē.Abstract. Ferrocolloids – stable dispersions of magnetic nanoparticles – possess notable magnetic properties, which become apparent in consequence of the application of the external magnetic fields and magnetic ordering of the nanoparticles. Non-isothermal colloidal systems in turn exhibit close coupling between the gradients of temperature and concentration of the dispersed phase – Soret effect - owing to the size difference between the components of the binary mixture. The interactions of the gradients of concentration and demagnetizing field in magnetizable medium contribute to the appearance of the magnetic forces affecting the regimes of heat and mass transfer. The subject of this theoretical investigation is the emergence and evolution of the photoabsorptive convective-diffusive microstructures in ferrocolloid layers under the action of the applied magnetic field. A series of model problems is formulated in order to elucidate the principal mechanisms of the formation of magnetosolutal microconvection within the concentration microstructures induced by the absorption of the incident optical intensity and the consequent appearance of the thermal gradients. The convective contributions to the effective transport coefficients are obtained by analytical and numerical methods. The secondary stability of the extended photoabsorptive microstructures is considered with respect to the variation of the control parameters. The destabilization of the extended gratings and the consequent breaking of the translational symmetry are observed in numerical simulations. In turn, the loss of stability of the bidirectional grids is followed by the reduction of the order of the rotational symmetry. The obtained theoretical results permit interpreting or reinterpreting some peculiarities of the real observations of the formation and evolution of the photoabsorptive concentration microstructures in the framework of magnetoconvective transport. The consideration of the influence of magnetosolutal microconvection in observable parameters has allowed describing the underlying microscopic mechanisms of some previously unexplained effects. In principle, the formation of the parasitic magnetic microconvection within the photoabsorptive microstructures under the action of the applied magnetic field is confirmed.Eiropas Sociālā fonda projekts «Atbalsts doktora studijām Latvijas Universitātē» Nr. 2009/0138/1DP/1.1.2.1.2./09/IPIA/VIAA/00

Linear stability of ferrofluids in a non-uniform magnetic field

The linear stability of Newtonian ferrofluids subject to non-uniform magnetic fields is consid- ered in different geometries. First, a ferrofluid column with constant magnetic susceptibility, centred on a current-carrying rigid wire and surrounded by another ferrofluid with a differ- ent susceptibility, is investigated. Ferrofluids with non-uniform susceptibilities are considered next. For a constant susceptibility the magnetic forcing is confined to the interface, but for a non-constant susceptibility the forcing is felt in the bulk of the fluid. It is postulated that a sta- tionary state of a ferrofluid with a non-uniform susceptibility in the presence of a non-uniform field, such that regions of highest susceptibility do not coincide with regions of highest field, may be unstable. An instability could be driven by the release of magnetic energy, since a minimum energy configuration may be reached when ferrofluid regions of high susceptibility and regions of high field coincide. This is explored for equilibria in a cylindrical domain, a planar domain and in a general three-dimensional domain. In a cylindrical domain, a stability condition is determined for a ferrofluid surrounding a current-carrying rigid wire, whose susceptibility varies radially. In a planar configuration, a stationary state of ferrofluid between two channel walls is found. The susceptibility and field vary normal to the wall, such that the regions of highest field and susceptibility do not coincide, and it is proven to be unstable. Methods of stabilising both systems are determined. For the cylindrical system, a constant axial field suffices, but for the planar domain it is shown that a rapidly rotating field is necessary to dampen unstable modes. Lastly, a stability condition is obtained for a general volume of ferrofluid, whose susceptibility varies slowly with position, subject to a non-uniform field.Open Acces