Stability Analysis on Compressible Walters B′ Viscoelastic Fluid

The thermosolutal convection in a couple-stress fluid in a porous medium in the presence of uniform rotation and uniform vertical magnetic field (separately) is studied. Using linearized stability theory and normal mode analysis, the dispersion relation is obtained in each case. In the case of magneto thermosolutal convection, the stable solute gradient, magnetic field and couple-stress are found to have stabilizing effects, whereas medium permeability has a destabilizing effect on the system for stationary convection. For rotatory thermosolutal convection, the stable solute gradient and rotation are found to have stabilizing effects, whereas medium permeability and couple-stress have both stabilizing and destabilizing effects for stationary convection. Further, the solute gradient, magnetic field, and rotation are found to introduce oscillatory modes, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

The thermosolutal instability of couple-stress fluid in the presence of uniform vertical rotation is considered. Following the linearized stability theory and normal mode analysis, the dispersion is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system, whereas the couple-stress has both stabilizing and destabilizing effects. The dispersion relation is also analyzed numerically. The stable solute gradient and the rotation introduce oscillatory modes in the system, which did not occur in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Thermosolutal instability of an electrically conducting fluid in porous medium in presence of a uniform rotation and a uniform magnetic field, simultaneously, has been considered. The stable solute gradient and rotation postpone the onset of instability. For a non-rotating system, the medium permeability and magnetic field have destabilizing and stabilizing effects, respectively. However, in the presence of rotation, when the magnetic field has a stabilizing/destabilizing effect, the medium permeability has a destabilizing/stabilizing effect under certain condition. The rotation, magnetic field and stable solute gradient introduce oscillatory modes in the system which were non-existent in their absence.

The thermosolutal instability of a Rivlin-Ericksen fluid in a porous medium is considered in the presence of uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the stable solute gradient and the magnetic field have stabilizing effects on the system, whereas the Hall currents have a destabilizing effect on the system. The medium permeability has both stabilizing and destabilizing effects on the system depending on the Hall parameter M. The kinematic viscoelasticity has no effect for stationary convection. Also, the dispersion relation is analysed numerically. The stable solute gradient and the magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system, which were nonexistent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

In the present paper, the effect of Hall currents, compressibility and suspended particles on thermosolutal convection of Rivlin-Ericksen fluid in porous medium is studied. Using linearization theory and normal mode analysis, a dispersion relation is derived. For the case of stationary convection, Rivlin Ericksen fluid behaves like a Newtonian fluid. By analyzing the dispersion relation, it is found that compressibility, suspended particles, Hall currents and permeability destabilizes the convection. The solute gradient and magnetic field stabilizes the same. Oscillatory modes are introduced due to the presence of solute gradient and Hall currents.

Stability of thermosolutal convection in a micropolar fluid saturated with a porous layer with Soret-Dufour effect is investigated. Normal Mode Technique is used to discuss the sufficient conditions of stability and instability. The effect of Lewis number, Dufour number, Soret number, stable solute gradient, coupling parameter and micropolar heat conduction parameter on thermal Rayleigh number is examined. Critical thermal Rayleigh number and critical wave numbers are obtained for stationary convection and presented graphically for various values of different parameters. Dufour number and Soret number are stabilizing the system in the presence of micropolar fluid. Permeability, micropolar heat conduction parameter and solutal Rayleigh number destabilizes the system.

The aim of the present research was to study the effect of magnetic field on the layer of electrically conducting couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that the couple-stress parameter and magnetic field have stabilizing effect on the system whereas the medium permeability has a destabilizing effect on the system. The magnetic field introduces oscillatory modes in the system which was non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.

The thermosolutal instability of a partially-ionized plasma in porous medium is considered in the presence of a uniform vertical magnetic field to include the effects of collisions and Hall currents. For the case of stationary convection, Hall currents and medium permeability have destabilizing effects whereas the stable solute gradient has stabilizing effect on the system. The collisional effects disappear for stationary convection. The sufficient conditions for the existence of overstability are obtained.

Electro-elastic instability in electroosmotic flows of viscoelastic fluids through a model porous system

Radial and tangential velocity distributions are measured for laminar flow of two Newtonian and one viscoelastic fluids in the disk and cylinder system. Velocities are determined from time lapse photographs of small particles suspended in the fluid which is illuminated in thin sections by a collimated beam of light. Measurements are made at Reynolds numbers of 0.0616, 24.4, and 97.6 for the Newtonian fluids and at 0.0371 for the viscoelastic fluid. The distributions are compared with the analyses of Kramer and Johnson in Part I. A toroidal secondary flow is observed which circulates in opposite directions for Newtonian and viscoelastic fluids, and a study of the dependence of the secondary flow direction on fluid properties and disk speed is reported. Complex flow patterns which appear in the region in which the direction of secondary flow changes are described. For Newtonian fluids tangential velocity computations agree to ±5% with the experimental measurements up to a Reynolds number of 24.4, and predicted radial velocities agree with experimental data within 20% at the Reynolds number of 24.4. At a Reynolds number of 97.6 predicted tangential velocities differ from experimental measurements by as much as ±50% while radial velocities differ from experimental values by a factor of two to three. The second order fluid predicts tangential velocities which are twice as large as experimental values and radial velocities which are in error by as much as a factor of six. The WJFLMB model predicts tangential and radial velocities which agree with experiment to within ±20% and ±40%, respectively. A Weissenberg Rheogoniometer is used to measure non-Newtonian viscosity, complex viscosity, and primary normal stress differences of the viscoelastic fluids, and to measure viscosities of the Newtonian fluids.

Targeted drug delivery is one of the most promising aspects of cancer diagnosis and treatment. Gold nanoparticles are widely used for drug delivery and in the treatment of tumors, but due to the low absorption of infrared light, tumor cells get destroyed. However, iron‐oxide‐coated gold nanoparticles could be used for drug delivery to a targeted spot with the help of an external magnetic field. The present article aims to investigate the thermal instability of the blood flow transporting gold and iron‐oxide nanoparticles through the artery. The Casson fluid model is used to characterize the blood flow, and Maxwell equations, together with Navier–Stokes equations, are used to describe the flow behavior. Further, the linear stability theory and normal mode analysis are used to obtain the secular equation of the thermal Rayleigh number. The influence of pertinent flow governing parameters such as heat source parameter, Chandrashekhar number, the diameter of nanoparticles, and volume fraction of nanoparticles are discussed graphically on the convective instability of the system. The addition of gold nanoparticles makes the system unstable due to their large size and heat generation within the system. On the other hand, the magnetic field stabilizes the system by controlling the trajectory of the nanoparticles injected into the blood vessels.

The stability of a horizontal layer of an electrically conducting, viscoelastic fluid (Oldroyd fluid) heated from below in the presence of a magnetic field is considered, on the assumption that both bounding surfaces are free. Linear stability theory is used to derive an eigenvalue system of sixth order, and an exact eigenvalue equation for a neutral instability is obtained. Critical Rayleigh numbers, wave numbers, and frequencies for the onset of instability are presented graphically as functions of the Chandrasekhar number for various values of the Prandtl number and the elastic parameters. It is shown that the effects which arise in consequence of the coupling between the magnetic field and the viscoelastic behaviour of a fluid are exceedingly complicated.

With the increasing level of microelectronic techniques, such as MEMS, the effective heat transfer become crucial to their performance. Genernally, the flow in microscale behaves laminar because of the extremely low Reynolds number (Re), which results in very low heat transfer effeciceny. So far, an increasingly efforts have been paid to develop techiniques to improve the heat transfer therein. As is well known in the conventional scale, flow instabilities and turbulence could significantly promote the mixing and heat transfer. Therefore, a great deal of efforts have been paid to to perturb the low Reynolds number flows in order to increase the contact interfaces between fluids with different temperature in microchannel. For example, some efforts are paid to design and utilize specially designed microchannel to excite the unstable flow motion. Another alternative way is to adopt different kinds of working fluid such as nano-fluid, non-Newtonian fluid and so forth. The viscoelastic fluid, a kind of Non-Newtonian fluid, shows nontrivial flow phenomena such as die swell effect (Barus effect), rod climbing effect (Weissenberg effect), Kaye effect, tubeless siphon effect, etc. Moreover, it has been proven that purely elastic flow instabilities or elastic turbulence is possible to be induced under inertialess or creeping flow conditions. This provides another efficient way to realize heat transfer enhancement, which is also the focus of present paper. In this paper, we carried out experimental and numerical investigations on the heat transfer characteristics of viscoelastic fluid and Newtonian fluid in three dimensional (3D) curvilinear microchannel. For the experiments, microelectronics manufacturing technology was taken to fabricate microchips. Platinum films were embedded in a Polydimethyl-siloxane (PDMS) microchannel in order to measure micro heater and channel wall temperature. The polymer solutions (PAAM) were the chosen viscoelastic fluid and sucrose solutions (Newtonian fluid) were used for comparison. For the numerical simulation, the log-conformation algorithm were implemented into the open source software OpenFOAM in order to simulate the viscoelastic flow at high Weissenberg number. Before simulating the viscoelastic fluid flow passing through the target channel, the numerical solver was firstly validated by two benchmark problems i.e., flow around a cylinder and passing a cross-slot by comparing the obtained dimensionless drag coefficient and flow patterns with those in the existing literatures. Combing the experimental and numerical results, the present identified the heat transfer enhancement by the occurrence of elastic instability and turbulence in a curved microchannel.

This study experimentally investigates the entry of hydrophobic/hydrophilic spheres into Newtonian and Boger fluids. By considering solution of 82% glycerin and 18% water and solution of 80% glycerin, 20% water and 100 ppm polyacrylamide, Newtonian and Boger fluids are made, respectively. It has been tried that liquids' surface tension, density, and viscosity are almost the same. Thus, all dimensionless numbers are approximately the same at a similar impact velocity except for the elasticity number. A PcoDimaxS highspeed camera captures the spheres' trajectory from the impact to the end of the path. Regarding the range of released height (0.5–100 cm), the impact velocities are approximately in the range of 0.31–4.43 ms−1. The role of fluid elasticity in combination with the sphere surface wettability on the air cavity formation/evolution/collapse is mainly studied. Also, the kinetics of the sphere motion (velocity, acceleration, and hydrodynamic force coefficient) is studied. The results show that air drawn due to the sphere's impact with the Newtonian liquid is more, and the pinch-off takes place later. Also, shedding bubbles are cusped-shaped in the Boger fluid, while in the Newtonian fluid, they are elliptical. In addition, the most significant impact of surface wettability is observed in the Newtonian fluid. Finally, the results reveal that the sphere in the Newtonian fluid can move faster and travel a longer distance in a specific time interval. The differences observed are closely related to the viscoelastic fluid's elasticity property and extensional viscosity.