Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ( $\eta =2A/\lambda _{a}$ ); the product of the fluid relaxation time times the angular frequency known as the Deborah number ( $De=\lambda _{1}\omega$ ); the aspect ratio between the microchannel height and the wavelength ( $\epsilon =2 H_{0}/\lambda _{a}$ ); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ( $\alpha =H_{0}/\delta _{\nu }$ ). In the limit when $\eta \ll 1$ , we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$ , and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$ . Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.

Numerical Examination on Impact of Hall Current on Peristaltic Flow of Eyring-Powell Fluid under Ohmic-Thermal Effect with Slip conditions

Aims:: This article is intended to investigate and determine combined impact of Slip and Hall current on Peristaltic transmission of Magneto-hydrodynamic (MHD) Eyring-Powell fluid. Background: The hall term arises taking strong force-field under consideration. Velocity, thermal and concentration slip conditions are applied. Energy equation is modeled by considering Joule-thermal effect. To observe non-Newtonian behavior of fluid the constitutive equations of Eyring-Powell fluid is encountered. Objective: Flow is studied in a wave frame of reference travelling with velocity of wave. The mathematical modeling is done by utilizing adequate assumptions of long wavelength and low Reynolds number. Method: The closed form solution for momentum, temperature and concentration distribution is computed analytically by using regular perturbation technique for small fluid parameter(A). Results: Graphical results are presented and discussed in detail to analyze behavior of sundry parameters on flow quantities (i.e. velocity, temperature and concentration profile). It is noticed that Powell-Eyring fluid parameters (A,B) have a significant role on the outcomes. Conclusion: The fluid parameter A magnifies the velocity profile whereas, the other fluid parameter B shows the opposite behavior.

Thermo-diffusion impacts on the flow of an elastico-viscous fluid over an inclined heated plane with magnetized wall

The focus is in this article is to scrutinize the simultaneous significances of magnetic diffusion, thermo-diffusion and angular location on the hydromagnetic flow of an elastico-viscous fluid over an inclined heated plane with magnetized wall. The flow medium is considered to be uniformly permeable (Darcy-Brinkman porous medium) and the flow of the fluid is considerably affected due to the appearance of a strong magnetic field in the direction normal to the flow surface. The significances of Hall current, induced magnetic field and Coriolis force on flow nature is also included in the study. The leading non-dimensionalized equations are explored by regular perturbation analysis. Ultimately, the expressions for velocity field, induced magnetic field, temperature and concentration are obtained. We further derived the surface skin friction, surface current density, heat and mass fluxes. The computation of results is performed with the aid of Mathematica software and results are presented in graphical and tabular forms for distinct flow impacting parameters. Numerical simulation explores that mass diffusion factor brings growth in the fluid velocity, temperature and normal induced magnetic field while it reduces the main induced magnetic field. Magnetic diffusion develops the primary flow and primary induced magnetic field and lessens the normal flow and normal induced magnetic field. Inclination angle of the heated plane upgrades primary induced magnetic field while downgrading normal induced magnetic field.

MHD Free Convection from a Semi-infinite Vertical Porous Plate with Diffusion-Thermo Effect

An analytical solution for two-dimensional unsteady MHD free convective mass transfer flows of viscous incompressible optically thin fluid past a semi-infinite vertical porous plate in the presence of thermal radiation and chemical reaction is presented in this paper. A uniform magnetic field is applied normally to the plate with a first-order chemical reaction. The non-dimensional governing equations are solved analytically by using the regular perturbation technique. The effects of various physical parameters like radiation parameter Q, Dufour effect Du, chemical reaction parameter K, thermal Grashof number Gr, Hartmann number M, porosity parameter k, etc., are studied and demonstrated graphically. One of the significant findings of this analysis includes that an intensification of the chemical reaction effect causes a downfall in the fluid concentration. In contrast, another important outcome of the present study is that the rate of heat transfer and shear stress at the wall increases under the diffusion thermo effect or Dufour effect. Still, it tends to fall for high radiation. Further, the rate of mass transfer rises under the chemical reaction effect.

ANALYSIS OF HEAT AND MASS TRANSFER ON THE PERISTALTIC MOVEMENT OF CARREAU NANOFLUIDS

In this investigation, we have analyzed the peristaltic movement of MHD Carreau nanofluids in a curved channel by taking the thermophoresis and Brownian motion effects into account. The governing equations of the fluid flow like the equations of continuity, momentum, temperature and concentration are modulated and abridged by using the theory of lubrication approximations. A regular perturbation is used to solve the simplified coupled nonlinear differential equations. The changes of various fluid parameters on axial velocity, temperature and concentrations are carefully calculated, and the graphical results are analyzed. According to the result of this study, it is determined that the resulting velocity of nanofluid decreases significantly when the applied radial magnetic field is strengthened. In addition, the curvature parameter has a significant impact on the concentration function, and when the curvature of the channel is increased, the absolute value of the nanoparticle concentration distribution diminishes.

Numerical and Analytical Studies of Soret-Driven Convection Flow Inside an Annular Horizontal Porous Cavity

This paper studies the species separation of a binary fluid in a porous cavity between two horizontal concentric cylinders, submitted to a temperature gradient. The thickness of the cavity is e=Ro−Ri, where Ri and Ro are the internal and external radius, respectively. The numerous previous experiments performed in thermogravitational vertical columns (TGCs) showed that in order to obtain a significant separation, the thickness of the cell must be very small, compared with its height. Therefore, in our configuration, we considered e≪Ri. The solution is assumed to be axisymmetric. Under the assumptions of parallel flow and forgotten effect, an analytical solution is obtained using Maple software, and the results are compared with those found numerically using Comsol Multiphysics. In natural convection, our results are in very good agreement with those evaluated with a regular perturbation method in powers of the dimensionless gap width ε=eRi of order 15, and with the Galerkin method. The species separation calculated for our configuration is very close to the one obtained in a TGC column of height: H=πRi. One of the main interests of the analytical solution presented here is that it can be used as a basic solution for a stability study analysis.

Pricing timer options: second-order multiscale stochastic volatility asymptotics

We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated. doi:10.1017/S1446181121000249

The Constructive Solution of the Fractal Composite Reservoir with Stress-Sensitivity Formation

The concentric two-zone composite reservoir model is a boundary value problems (BVPs) of modified Bessel equations. In this paper, we propose a constructive method to solve the BVPs for the system of modified Bessel equations with Robin mixed outer boundary condition and apply it to solve a two-zone fractal composite reservoir seepage model with stress-sensitivity formation. By using Pedrosa variable substitution, regular perturbation technique, Laplace transform, and Stehfest numerical inversion technique, the unified expression for the solutions of the reservoir model with three outer boundary (infinite, impermeable, and constant pressure) conditions is constructed. Type curves of bottom-hole pressure and pressure derivative are drawn, and sensitivity analysis of reservoir parameters are carried out. In comparison with the traditional approach, the solutions of this model are simple and regular, with continued fraction form, the constructive method is efficient and easy to operate. The application of this method avoids the complicated and trivial derivative operation and the use of Cramer’s rule to solve the system of linear equations. It can help to better understand the relationship between the solutions of the reservoir model and the inner and outer boundary conditions. The constructive method can be applied not only to solve the fractal composite reservoir model but also to solve more general reservoir model, BVPs of fluid diffusion, heat conduction, and so on.