Numerical study of surface tension driven convection in thermal magnetic fluids

Microgravity conditions pose unique challenges for fluid handling and heat transfer applications. By controlling (curtailing or augmenting) the buoyant and thermocapillary convection, the latter being the dominant convective flow in a microgravity environment, significant advantages can be achieved in space based processing. The control of this surface tension gradient driven flow is sought using a magnetic field, and the effects of these are studied computationally. A two-fluid layer system, with the lower fluid being a non-conducting ferrofluid, is considered under the influence of a horizontal temperature gradient. To capture the deformable interface, a numerical method to solve the Navier???Stokes equations, heat equations, and Maxwell???s equations was developed using a hybrid level set/ volume-of-fluid technique. The convective velocities and heat fluxes were studied under various regimes of the thermal Marangoni number Ma, the external field represented by the magnetic Bond number Bom, and various gravity levels, Fr. Regimes where the convection were either curtailed or augmented were identified. It was found that the surface force due to the step change in the magnetic permeability at the interface could be suitably utilized to control the instability at the interface.published or submitted for publicationis peer reviewe

On buoyant convection in binary solidification

We consider the problem of nonlinear steady buoyant convection in horizontal mushy layers during the solidification of binary alloys. We investigate both cases of zero vertical volume flux and constant pressure, referred to as impermeable and permeable conditions, respectively, at the upper mush???liquid interface. We analyze the effects of several parameters of the problem on the stationary modes of convection in the form of either hexagonal cells or non-hexagonal cells, such as rolls, rectangles and squares. [More ...]published or submitted for publicationis not peer reviewe

On Mathematical Modeling, Nonlinear Properties and Stability of Secondary Flow in a Dendrite Layer

This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, which is found to be caused by the temperature variations of the secondary flow, is detected to be the same as that for the stable and preferred horizontal flow pattern within the dendrite layer

Spatial Instability of Electrically Driven Jets with Finite Conductivity and Under Constant or Variable Applied Field

We investigate the problem of spatial instability of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton’s method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One of these modes is enhanced by the strength Ω of the applied field, while the other mode decays with increasing Ω. The growth rates of both modes increase mostly with decreasing the axial wavelength of the disturbances. For the case of variable applied field, we found the growth rates of the spatial instability modes to be higher than the corresponding ones for constant applied field, provided Ω is not too small

On three-dimensional rotating viscoelastic jets in the Giesekus model

We investigate three-dimensional nonlinear rotating viscoelastic curved jets in the presence of gravity force. Applying the Giesekus model for the viscoelastic stress parts of the jet flow system and using perturbation methods with a consistent scaling, a relatively simple system of equations with realistic three-dimensional centerlines is developed. We determine numerically the relevant solution quantities of the model in terms of the radius, speed, tensile force, stretching rate, strain rate and the jet centerline versus arc length and for different parameter values associated with gravity, viscosity, rotation, surface tension and viscoelasticity. Considering the jet flow system in full 3-dimensions and in the presence of gravity can be significant, impacting the jet speed, strain rate, tensile force, stretching rate and the centerline curvature are notably increased in magnitude and the jet radius size is reduced and this becomes more dominant with larger values of the arc length, gravity, rotation and viscoelasticity. In particular, for a typical value of the gravity and for an order one value of the arc length, we found that gravity makes jet speed higher by at least a factor of 2 and makes jet radius lower by a factor of 0.6 or smaller as we compare to the corresponding values when gravity is not considered

Effect of Hydraulic Resistivity on a Weakly Nonlinear Thermal Flow in a Porous Layer

Heat and mass transfer through porous media has been a topic of research interest because of its importance in various applications. The flow system in porous media is modelled by a set of partial differential equations. The momentum equation which is derived from Darcy’s law contains a resistivity parameter. We investigate the effect of hydraulic resistivity on a weakly nonlinear thermal flow in a horizontal porous layer. The present study is a realistic study of nonlinear convection flow with variable resistivity whose rate of variation is arbitrary in general. This is a first step for considering more general problems in applications that involve variable resistivity that may include both variations in permeability and viscosity of the porous layer. Such problems are important for understanding properties of underground flow, migration of moisture in fibrous insulations, underground disposal of nuclear waste, welding process, petrochemical generation, drug delivery in vascular tumor, etc. Using weakly non-linear procedure, the linear and first-order systems are derived. The critical Rayleigh number and the critical wave number are obtained from the linear system using the normal mode approach for the two-dimensional case. The linear and first-order systems are solved numerically using the fourth-order Runge-Kutta and shooting methods. Numerical results for the temperature are presented in tabular and graphical forms for different resistivities. Through this study, it is observed that a stabilizing effect on the dependent variables occurs in the case of a positive vertical rate of change in resistivity, whereas a destabilizing effect is noticed in the case of a negative vertical rate of change in resistivity. The results obtained indicate that the convective flow due to the buoyancy force is more effective for weaker resistivity

Mathematical Modeling of Peristaltic Flow of Chyme in Small Intestine

Mathematical models based on axisymmetric Newtonian incompressible fluid flow are studied for the peristaltic flow of chyme in the small intestines, which is an axisymmetric cylindrical tube. The flow is modeled more realistically modeled by assuming that the peristaltic rush wave is a non-periodic mode composed of two sinusoidal waves of different wavelengths, which propagate at the same speed along the outer boundary of the tube. Both cases of flow in a tube and in an annulus that are modeled and investigated in the present paper correspond respectively to the cases of flow of chyme in the small intestine in the absence and presence of a cylindrical endoscope. For the realistic values of the parameters for these two flow cases, we determine the expressions for the leading order pressure drop, the pressure, the axial velocity, and the frictional forces at the boundaries, and evaluated the roles played by these quantities in the investigated flow systems. The presence of the two-wave peristaltic mode was found to facilitate lower positive (adverse) pressure gradient and less magnitude of the forces by the boundaries on the flow of chyme

Modeling and computation for unsteady blood flow and solute concentration in a constricted porous artery

We investigated a physical system for unsteady blood flow and solute transport in a section of a constricted porous artery. The aim of this study was to determine effects of hematocrit, stenosis, pulse oscillation, diffusion, convection and chemical reaction on the solute transport. The significance of this study was uncovering combined roles played by stenosis height, hematocrit, pulse oscillation period, reactive rate, blood speed, blood pressure force and radial and axial extent of the porous artery on the solute transported by the blood flow in the described porous artery. We used both analytical and computational methods to determine blood flow quantities and solute transport for different parametric values of the described physical system. We found that solute transport increases with increasing stenosis height, blood pulsation period, convection and blood pressure force. However, transportation of solute reduces with increasing hematocrit, chemical reactive rate and radial or axial distance

Spatial Instability of Electrically Driven Jets with Finite Conductivity and Under Constant or Variable Applied Field

We investigate the problem of spatial instability of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton’s method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One of these modes is enhanced by the strength Ω of the applied field, while the other mode decays with increasing Ω. The growth rates of both modes increase mostly with decreasing the axial wavelength of the disturbances. For the case of variable applied field, we found the growth rates of the spatial instability modes to be higher than the corresponding ones for constant applied field, provided Ω is not too small

Analysis of Rotating Flow Around a Growing Protein Crystal

We consider the problem of steady flow around a growing protein crystal in a medium of its solution in a normal gravity environment. The whole flow system is assumed to be rotating with a constant angular velocity about a vertical axis which is anti-parallel to the gravity vector. Convective flow takes place due to the solute depletion around the growing crystal which leads to a buoyancy driven flow. Such convective flow can produce inhomogeneous solute concentration, which subsequently generate non-uniformities in the crystal’s structure finalizing lower quality protein crystal. Using scaling analysis within a diffusion boundary layer around the crystal, we estimate the magnitude of the convective flow velocity and other dependent variables of the flow system for cases of weak, moderate and strong rotation and either strong or weak buoyancy. We find, in particular, that for moderate rate of rotation, convective flow is weakened significantly as the rotation rate increases. This result may be of interest for production of high quality protein crystal since the effect of the convective flow around the growing protein crystal is found to be weakened significantly by the rotational constraint