Showing papers in "Applied Mathematics and Mechanics-english Edition in 2012"
TL;DR: In this article, the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface were studied and the convergence of the series solutions was examined.
Abstract: This article studies the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.
260 citations
TL;DR: In this article, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM), which reduces the traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations to nonlinear ordinary differential equations to model the problem.
Abstract: In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.
221 citations
TL;DR: In this paper, the boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed, where the stretching velocity is assumed to vary as a power function of the distance from the origin.
Abstract: The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles ϕ, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type.
86 citations
TL;DR: In this article, the scaling group of transformations were used to obtain exact solutions for the translation symmetry and scaling symmetry for laminar fluid flow in the presence of thermal stratification.
Abstract: The problem of laminar fluid flow, which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy, is investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations, namely, the scaling group of transformations. An exact solution is obtained for the translation symmetrys, and the numerical solutions are obtained for the scaling symmetry. This solution depends on the Lewis number, the Brownian motion parameter, the thermal stratification parameter, and the thermophoretic parameter. The conclusion is drawn that the flow field, the temperature, and the nanoparticle volume fraction profiles are significantly influenced by these parameters. Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids. Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids, leading to an increase in the efficiency of direct absorption solar collectors.
70 citations
TL;DR: In this paper, the combined effects of viscous dissipation and Newtonian heating on boundary layer flow over a moving flat plate are investigated for two types of water-based Newtonian nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu) and titania (TiO2).
Abstract: The combined effects of viscous dissipation and Newtonian heating on boundary layer flow over a moving flat plate are investigated for two types of water-based Newtonian nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu) and titania (TiO2). The governing partial differential equations are transformed into ordinary differential equations through a similarity transformation and are solved numerically by a Runge-Kutta-Fehlberg method with a shooting technique. The conclusions are that the heat transfer rate at the moving plate surface increases with the increases in the nanoparticle volume fraction and the Newtonian heating, while it decreases with the increase in the Brinkmann number. Moreover, the heat transfer rate at the moving plate surface with Cu-water as the working nanofluid is higher than that with TiO2-water.
61 citations
TL;DR: In this paper, the partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill-based shooting method.
Abstract: The magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill-based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.
54 citations
TL;DR: In this paper, the authors studied the two-temperature generalized thermoelasticity theory (2TT) for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity.
Abstract: The thermoelastic interaction for the three-phase-lag (TPL) heat equation in an isotropic infinite elastic body with a spherical cavity is studied by two-temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of TPL is a hyperbolic partial differential equation with a fourth-order derivative with respect to time. The medium is assumed to be initially quiescent. By the Laplace transformation, the fundamental equations are expressed in the form of a vector-matrix differential equation, which is solved by a state-space approach. The general solution obtained is applied to a specific problem, when the boundary of the cavity is subjected to the thermal loading (the thermal shock and the ramp-type heating) and the mechanical loading. The inversion of the Laplace transform is carried out by the Fourier series expansion techniques. The numerical values of the physical quantity are computed for the copper like material. Significant dissimilarities between two models (the two-temperature Green-Naghdi theory with energy dissipation (2TGN-III) and two-temperature TPL model (2T3phase)) are shown graphically. The effects of two-temperature and ramping parameters are also studied.
53 citations
TL;DR: In this paper, the magnetohydrodynamic (MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated, and the governing partial differential equations are converted into the ordinary differential equations by suitable transformations.
Abstract: The magnetohydrodynamic (MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equations are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method (HAM). The expressions for square residual errors are defined, and the optimal values of convergence-control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nusselt number are tabulated to analyze the effects of dimensionless parameters.
46 citations
TL;DR: In this paper, a mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths, and the model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus.
Abstract: Fluid mechanical peristaltic transport through esophagus is studied in the paper. A mathematical model has been developed to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube lengths. The Ostwald-de Waele power law of a viscous fluid is considered here to depict the non-Newtonian behaviour of the fluid. The model is formulated and analyzed specifically to explore some important information concerning the movement of food bolus through esophagus. The analysis is carried out by using the lubrication theory. The study is particularly suitable for the cases where the Reynolds number is small. The esophagus is treated as a circular tube through which the transport of food bolus takes place by periodic contraction of the esophageal wall. Variation of different variables concerned with the transport phenomena such as pressure, flow velocities, particle trajectory, and reflux is investigated for a single wave as well as a train of periodic peristaltic waves. The locally variable pressure is seen to be highly sensitive to the flow index “n”. The study clearly shows that continuous fluid transport for Newtonian/rheological fluids by wave train propagation is more effective than widely spaced single wave propagation in the case of peristaltic movement of food bolus in the esophagus.
40 citations
TL;DR: In this article, the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks was analyzed.
Abstract: A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.
40 citations
TL;DR: In this article, the magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface is investigated.
Abstract: This paper investigates the magnetohydrodynamic (MHD) boundary layer flow of an incompressible upper-convected Maxwell (UCM) fluid over a porous stretching surface. Similarity transformations are used to reduce the governing partial differential equations into a kind of nonlinear ordinary differential equations. The nonlinear problem is solved by using the successive Taylor series linearization method (STSLM). The computations for velocity components are carried out for the emerging parameters. The numerical values of the skin friction coefficient are presented and analyzed for various parameters of interest in the problem.
TL;DR: In this article, the second-order piston theory is used to analyze a double-wedge airfoil with free-play and cubic nonlinearities in supersonic flows.
Abstract: The nonlinear aeroelastic response of a two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flows is investigated. The second-order piston theory is used to analyze a double-wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon are detected by the averaging method and the multi-variable Floquet theory. The analytical results are further verified by numerical simulations. Finally, the influence of the freeplay parameters on the aeroelastic response is analyzed in detail.
TL;DR: In this article, the theoretical, experimental, and numerical aspects of the VCLVIT-induced surface deformation on the wetting and spreading, the deflection of the microcantilever, and the elasto-capillarity and electroelasto capillarity are discussed.
Abstract: Young’s equation is a fundamental equation in capillarity and wetting, which reflects the balance of the horizontal components of the three interfacial tensions with the contact angle (CA). However, it does not consider the vertical component of the liquid-vapor interfacial tension (VCLVIT). It is now well understood that the VCLVIT causes the elastic deformation of the solid substrate, which plays a significant role in the fabrication of the microfluidic devices because of the wide use of the soft materials. In this paper, the theoretical, experimental, and numerical aspects of the problem are reviewed. The effects of the VCLVIT-induced surface deformation on the wetting and spreading, the deflection of the microcantilever, and the elasto-capillarity and electroelasto-capillarity are discussed. Besides a brief review on the historical development and the recent advances, some suggestions on the future research are also provided.
TL;DR: In this paper, the effects of slip and heat transfer on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid were studied under the long wavelength approximation by using a regular perturbation method.
Abstract: In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.
TL;DR: In this paper, the effects of various physical parameters on the flow and mass transfer characteristics of an electrically conducting upper convected Maxwell (UCM) fluid at a porous surface are studied in the presence of a chemically reactive species.
Abstract: The magnetohydrodynamic (MHD) flow and mass transfer of an electrically conducting upper convected Maxwell (UCM) fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the Keller-box method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.
TL;DR: In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied, where the effects of input nonlinearities are taken into account.
Abstract: Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.
TL;DR: In this paper, the authors investigated the effects of frictional heating (viscous dissipation) and internal heat generation or absorption on the hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.
Abstract: This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature (VWT) and variable heat flux (VHF). The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction parameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.
TL;DR: In this paper, the authors examined the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets.
Abstract: The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.
TL;DR: In this article, the propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids, and the effects of variations in nonwet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.
Abstract: The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.
TL;DR: Takahashi et al. as discussed by the authors analytically investigated the unsteady peristaltic transport of the Maxwell fluid in a finite tube, where the walls of the tube are subjected to the contraction waves that do not cross the stationary boundaries.
Abstract: This paper analytically investigates the unsteady peristaltic transport of the Maxwell fluid in a finite tube The walls of the tube are subjected to the contraction waves that do not cross the stationary boundaries The analysis is carried out by a long wavelength approximation in the non-dimensional form The expressions for the axial and radial velocities are derived The pressures across the wavelength and the tubelength are also estimated The reflux phenomenon is discussed, which culminates into the determination of the reflux limit Mathematical formulations are physically interpreted for the flow of masticated food materials such as bread and white eggs in the oesophagus It is revealed that the Maxwell fluids are favorable to flow in the oesophagus as compared with the Newtonian fluids This endorses the experimental finding of Takahashi et al (Takahashi, T, Ogoshi, H, Miyamoto, K, and Yao, M L Viscoelastic properties of commercial plain yoghurts and trial foods for swallowing disorders Rheology, 27, 169–172 (1999)) It is further revealed that the relaxation time does not affect the shear stress and the reflux limit It is found that the pressure peaks are identical in the integral case while different in the non-integral case
TL;DR: In this article, an effective singly active control is proposed and used to synchronize a fractional order Duffing system, and the numerical results demonstrate the effectiveness of the proposed methods.
Abstract: With the increasingly deep studies in physics and technology, the dynamics of fractional order nonlinear systems and the synchronization of fractional order chaotic systems have become the focus in scientific research In this paper, the dynamic behavior including the chaotic properties of fractional order Duffing systems is extensively investigated With the stability criterion of linear fractional systems, the synchronization of a fractional non-autonomous system is obtained Specifically, an effective singly active control is proposed and used to synchronize a fractional order Duffing system The numerical results demonstrate the effectiveness of the proposed methods
TL;DR: In this article, a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates is presented.
Abstract: This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.
TL;DR: In this paper, the dispersion equation of a torsional surface wave in an inhomogeneous crustal layer over a homogeneous half space was derived for three types of inhomogeneity: exponential, quadratic, and hyperbolic.
Abstract: The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types, namely, exponential, quadratic, and hyperbolic discussed separately. The dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equation of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.
TL;DR: It is determined that the RAS leads to decrease in the renal mass flow, which may cause the activation of the renin-angiotension system and results in severe hypertension.
Abstract: The effects of the renal artery stenosis (RAS) on the blood flow and vessel walls are investigated. The pulsatile blood flow through an anatomically realistic model of the abdominal aorta and renal arteries reconstructed from CT-scan images is simulated, which incorporates the fluid-structure interaction (FSI). In addition to the investigation of the RAS effects on the wall shear stress and the displacement of the vessel wall, it is determined that the RAS leads to decrease in the renal mass flow. This may cause the activation of the renin-angiotension system and results in severe hypertension.
TL;DR: In this article, a numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation, where the surface of the cone is subjected to a variable surface heat flux.
Abstract: A numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation. The surface of the cone is subjected to a variable surface heat flux. The fluid considered is a gray, absorbing-emitting radiation but a non-scattering medium. With approximate transformations, the boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime. The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, accurate, and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, and local and average Nusselt number in air and water. The present results are compared with the previous published work and are found to be in excellent agreement.
TL;DR: In this paper, a problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic (MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure.
Abstract: A problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic (MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure. The time-dependent permeability and the oscillatory suction velocity are considered. The computational results are presented graphically for the velocity, the temperature, and the concentration fields for various values of skin friction coefficients, Nusselt numbers, and Sherwood numbers. The study reveals that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof number.
TL;DR: In this paper, the effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated.
Abstract: The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt numbers at the plates are discussed numerically and presented through graphs.
TL;DR: In this article, an unsteady magnetohydrodynamic boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically.
Abstract: An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.
TL;DR: In this paper, a generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, which is improved for those systems whose exact homocalic generating solutions cannot be explicitly derived.
Abstract: A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic, and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method.
TL;DR: In this article, the combined effects of thermal and mass convection of viscous incompressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed.
Abstract: The combined effects of thermal and mass convection of viscous incompressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part (the zeroth-order) and a perturbed part (the first-order). The first-order quantities are obtained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graphically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.