Regular Perturbation Technique Research Articles

The Onset of Buoyancy and Surface Tension Driven Convection in a Ferrofluid Layer by Influence of General Boundary Conditions

This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions. The lower surface is rigid with insulating to temperature perturbations, while the upper surface is stress-free and subjected to general thermal boundary condition. The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue. It is analyzed that increasing Biot number, decreases the magnetic and Marangoni number is to postponement the onset. Additionally, magnetization nonlinearity parameter has no effect on FTC in the non-existence of Biot number. The results under the limiting cases are found to be in good agreement with those available in the literature.

Onset of surface driven convection in selfrewetting fluid layer overlying a porous medium

The onset of thermocapillary convective motion in a self-rewetting fluid layer overlying a porous medium with thermally dependent surface tension is studied analytically. Surface tension is assumed to be a quadratic function of temperature. The top surface of a fluid layer is deformably free and the bottom is rigid. We considered boundaries to be insulating to temperature perturbations. The governing equation that satisfies the composite system is analyzed by the normal mode approach and solved by the regular perturbation technique for linear stability. A mathematical expression is derived for the critical Marangoni number by solving coupled equations. The influence of crispation number, thermal diffusivity ratio, and other physical parameters involved therein are analyzed for the convective stability of the bilayer system. It has been found that the start of convection is delayed when the crispation number goes down and the thermal diffusivity ratio goes up. Also, the impact of the ratio of the thickness of the fluid to the thickness of the porous matrix and the other physical parameters on controlling the convective motion of the configuration is examined in detail.

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.

Hyundai Motor invests in Pajarito Powder

In the present work, we study with the aid of regular perturbation techniques under what physical conditions, the thermal and electrical simultaneous interactions that occur between a gel and a stratum corneum of the skin, can operate in direct contact to avoid possible damage to the human skin. This doubly conjugate asymptotic analysis was formulated in terms of a pair of dimensionless conservation equations for the energy and electrical charge in each medium and it was solved by using asymptotic perturbation techniques, identifying a dimensionless parameter, denoted as β, that measures the competition of electrical conductivities in the two medium affected by the electrical pulse. Because the electrical conductivity of the stratum corneum is very small, this parameter assumes usually very large values compared with unity and the theoretical predictions show the relevance that this parameter has on the increment of the temperature in both media. Therefore, we consider that this parameter can guide a positive performance of this class of medical treatments based on electric signals because delimits, under transient conditions, up to where the simultaneous presence of thermal and electrical effects control the reversible skin electroporation. The asymptotic analysis was validated with experimental data of other authors and a numerical solution of the full governing equations.

Clariant and Air Liquide present MegaZonE: novel catalyst layering technology for enhanced methanol synthesis performance

In the present work, we study with the aid of regular perturbation techniques under what physical conditions, the thermal and electrical simultaneous interactions that occur between a gel and a stratum corneum of the skin, can operate in direct contact to avoid possible damage to the human skin. This doubly conjugate asymptotic analysis was formulated in terms of a pair of dimensionless conservation equations for the energy and electrical charge in each medium and it was solved by using asymptotic perturbation techniques, identifying a dimensionless parameter, denoted as β, that measures the competition of electrical conductivities in the two medium affected by the electrical pulse. Because the electrical conductivity of the stratum corneum is very small, this parameter assumes usually very large values compared with unity and the theoretical predictions show the relevance that this parameter has on the increment of the temperature in both media. Therefore, we consider that this parameter can guide a positive performance of this class of medical treatments based on electric signals because delimits, under transient conditions, up to where the simultaneous presence of thermal and electrical effects control the reversible skin electroporation. The asymptotic analysis was validated with experimental data of other authors and a numerical solution of the full governing equations.

Analytical calculation and finite element evaluation of electromagnetic leakage field distribution in surface-mounted permanent magnet synchronous motors taking the rotor eccentricity effect into account

PurposeThe purpose of this paper is to present an analytical calculation for estimating the leakages field distribution in surface-mounted permanent magnet synchronous motors (SMPMSMs) according to a sub-domain field model for eccentricity fault detection.Design/methodology/approachThe magnetic field domain is classified into four sub-domains of PMs, air gap, stator core and outer region. In the proposed method, the governing equations taking the rotor eccentricity effect into account per region and the interface boundary conditions between sub-domains are formulated using the regular perturbation technique, Taylor series and Fourier series expansion. Maxwell's equations are solved in different regions in the polar coordinate system regarding the boundary conditions.FindingsThe radial and tangential components of electromagnetic field distribution in all sub-domains of one SMPMSM are obtained using the proposed method analytically. Finite element analysis is used to validate the results of the proposed method; the results indicated that the analytical model matches the finite-element prediction up to 30% eccentricity, except for some peak values that depend on the harmonic order value. The results of this paper demonstrated that in the event of eccentricity, an asymmetric magnetic field is generated in the outer region of the machine. Although its amplitude is small, it can be an indicator for detecting eccentricity faults from the outside environment of the machine.Originality/valueThe formulas presented in this paper can be applied as a new technique for detecting eccentricity faults in these motors from the outside environment.

Doubly conjugate asymptotic analysis for the temperature and electric fields in a combined gel and stratum corneum system

In the present work, we study with the aid of regular perturbation techniques under what physical conditions, the thermal and electrical simultaneous interactions that occur between a gel and a stratum corneum of the skin, can operate in direct contact to avoid possible damage to the human skin. This doubly conjugate asymptotic analysis was formulated in terms of a pair of dimensionless conservation equations for the energy and electrical charge in each medium and it was solved by using asymptotic perturbation techniques, identifying a dimensionless parameter, denoted as β, that measures the competition of electrical conductivities in the two medium affected by the electrical pulse. Because the electrical conductivity of the stratum corneum is very small, this parameter assumes usually very large values compared with unity and the theoretical predictions show the relevance that this parameter has on the increment of the temperature in both media. Therefore, we consider that this parameter can guide a positive performance of this class of medical treatments based on electric signals because delimits, under transient conditions, up to where the simultaneous presence of thermal and electrical effects control the reversible skin electroporation. The asymptotic analysis was validated with experimental data of other authors and a numerical solution of the full governing equations.

Double-diffusive penetrative convection in a fluid overlying a porous layer

In the present study, the commencement of double-diffusive convection with an internal heat source is studied using a linear instability analysis. The system consists of a fluid layer on top of a porous layer saturated with the same fluid. The boundaries are insulating to temperature perturbations, and the regular perturbation technique is applied to obtain the Rayleigh number. The results of detailed stability characteristics are presented for crucial physical factors, such as thermal Rayleigh number, the inverse Lewis number, depth ratio, the solute Rayleigh number, and heat source strength.

Soret radiation and chemical reaction effect on MHD Jeffrey fluid flow past an inclined vertical plate embedded in porous medium

In this manuscript a study of the unsteady magneto-hydrodynamic mixed convection Jeffrey fluid flow over an inclined permeable moving plate in presence of thermal radiation, heat generation, radiation, aligned magnetic field, thermophoresis effect and homogenous chemical reaction, subjected to variable suction has been undertaken. The governing equations are solved by using a regular perturbation technique. The expressions for the distributions of velocity, temperature and species concentration are obtained. With the aid of these, the expressions for skin friction, Nusselt number and Sherwood number also have been derived. The influences of various physical Parameters involved in the problem on the above mentioned quantities are discussed with the help of graphs and tables. From the significant findings, it has been found that the velocity increases with an increase in Jeffrey fluid in the presence of permeability. It shows reverse effects in the case of magnetic parameter, radiation parameter and chemical reaction parameter. Comparisons with previously published work performed and the results are found to be in the excellent agreement.

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.

A numerical technique and effect of magnetic field dependent (MFD) viscosity on thermal instability in a ferrofluid pores with Coriolis force for Darcy model

PurposeThe effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.Design/methodology/approachThe thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained.FindingsThe conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number Ta is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number Ta leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.Originality/valueThis research paper is new and original.

A Mathematical Model of Blood Flow in Merging Veins under a Magnetic Resonance Imaging Influence

Venous blood flow through the superior and inferior vena cavae and via a merger to the right atrium of the heart is investigated. Based on the Newtonian assumption for blood, the model is developed using Boussinesq’s approximation for the continuity, momentum, energy, and mass diffusion equations, which are non-linear partial differential equations. The governing equations are non-dimensionalized and solved by the regular perturbation technique. Expressions for the concentration, temperature, and velocity are obtained, analyzed, and presented graphically and quantitatively, and discussed. The results show that an increase in the magnetic field strength and conflux angle produce fluctuations in the flow velocity.

Effect of Hall Currents on Unsteady Magnetohydrodynamic Two-Ionized Fluid Flow and Heat Transfer in a Channel

An unsteady magnetohydrodynamic (MHD) heat transfer two-fluid flow of ionized gases through a horizontal channel between parallel non-conducting plates, by taking Hall currents into account is studied. The governing partial differential equations that describe the flow and heat transfer under the adopted conditions are solved for the velocity and temperature distributions by a regular perturbation technique. Profiles for the velocity and temperature distributions as well the rates of heat transfer coefficient are presented graphically, and a parametric study is performed. The results reveal that the combined effects of the Hartmann number, Hall parameter, and the ratios of viscosities, heights, electrical and thermal conductivities have a significant impact on an unsteady MHD heat transfer two-ionized fluid flow characteristics.

Periodic permeable free convective 3-dimensional flow of a second grade fluid with slip effect

This study addresses the development of a mathematical model and theoretical analysis of a free convective three-directional flow of an incompressible second-grade fluid through a highly porous medium bounded by a vertical infinite plate in slip flow regime subjected to a constant suction. The free stream velocity is rumored to be constant while permeability of the medium is presumed to be periodic. It is well known that the assumption of either time dependent or constant permeability of a porous medium leads to two-dimensional flows, of course, the flow comes to be three-dimensional due to variation in permeability of the porous medium. Approximate solutions of velocity and temperature fields, heat flux and skin friction are established by applying the regular perturbation technique. Results are discussed and visualized graphically in the light of physical parameters emerging in the mathematical model of the physical phenomenon with carefully selected and viable data. The significance of current study reveals that presence of slip parameter reduces the thickness of boundary layer causing the enhancement in the main flow velocity component. With increasing permeability parameter fluid velocity is decelerated whereas it is accelerated with increasing Grashof number. With increasing non-Newtonian parameter, a similar response is noted as for the permeability parameter. It is also noted that permeability parameter, Prandtl number, Grashof number and elastic parameter provide mechanism to control the skin friction. In addition, Reynolds number also plays a vital role to control the skin friction. Furthermore, Reynolds number significantly boosts the coefficient of heat transfer, and Prandtl number causes to reduce the thermal boundary layer thickness.

PRICING TIMER OPTIONS: SECOND-ORDER MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS

AbstractWe 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.

Electroosmosis augmented MHD peristaltic transport of SWCNTs suspension in aqueous media

This article analyzes the flow of single-walled carbon nanotubes (SWCNTs) suspended water-based ionic solution driven by combined effects of electroosmosis and peristalsis mechanisms. The analysis is performed in the presence of the transverse magnetic field, thermal radiation, mixed convection, and the slip boundary condition imposed on the channel walls. Poisson–Boltzmann ionic distribution is linearized by employing the Debye–Huckel approximation. The scaling analysis of the problem is rendered subject to the lubrication approach. The resulting nonlinear system of equations is executed to obtain approximate solutions using regular perturbation techniques and the graphical results are computed for various flow properties. Pumping and trapping phenomena are also discussed under the effects of pertinent parameters. Computed results show that a reduction in EDL thickness intensifies the fluid velocity as well as temperature. Improvement in thermal conductivity of base fluid is noticed with increasing SWCNTs volume fraction. It is further examined that axial velocity magnifies with Helmholtz–Smoluchowski velocity.

Peristaltic motion of Maxwell fluid subject to convective heat and mass conditions

This article concentrates on peristalsis of Maxwell fluid in a symmetric channel with heat and mass convective conditions. Analysis is given in presence of viscous dissipation. The relevant problems statements are constructed and solved for the series solutions of stream function, temperature and concentration. Regular perturbation technique is adopted for small wave number. Heat transfer coefficient is also derived. Results of temperature, concentration and heat transfer coefficient are graphically analyzed. Trapping phenomenon is studied. It is observed that heat and mass transfer Biot numbers have opposite effects on fluid temperature and concentration. Concentration distribution decays with the increase in Schmidt number and Soret number. Heat transfer coefficient has oscillatory behavior and magnitude of heat transfer coefficient increases when heat transfer Biot number enhances. In addition, similar trapping pattern is observed for relaxation parameter and wave number.

Effects of variable heat source on convective motion in an anisotropic porous layer

The onset of convective motion in a fluid saturated anisotropic porous medium layer is examined analytically in the occurrence of the qualitative effect of the source of variable internal heat. Three different kinds of heat source functions: (i) N (z) = z (linear) (ii)N(z) = z2 (parabolic) and (iii) N (z) = z 3 (cubic) are considered. The resulting eigenvalue problem was analytically solved using regular perturbation technique. A parametric study is carried out by varying the following parameters: the heat source parameter (X), thermal anisotropy parameter(n), and mechanical anisotropy parameter(ξ). Results indicates that the effects of the increasing values of λ and ξ will enhance the convection of a anisotropic porous layer system while the increasing of n will help to stabilize the system. It is also noted that for case (iii) the system is more stable, while for case (i) the system is more unstable

An Analytical Approach to Study the Blood Flow over a Nonlinear Tapering Stenosed Artery in Flow of Carreau Fluid Model

The current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. The flow governing equations are derived under the consideration of mild stenosis. Mathematical analysis has been carried out by considering the blood as non‐Newtonian nature. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the second‐order in dimensionless Weissenberg number (We). The performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number (We). The obtained results demonstrate that for shear‐thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in We. Hence, the presented numerical analysis reveals many aspects of the flow by considering the blood as a non‐Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio‐mathematical studies.