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Nonlocal analysis of Rayleigh-type wave propagating in a gradient layered structure
The present article aims to study the propagation behavior of Rayleigh-type waves using the nonlocal theory of elasticity in a layered structure constituted of a gradient transversely isotropic stratum perfectly bonded with a gradient monoclinic substrate. At first a constitutive relation is established for the assumed layered structure. Thereafter in view of suitable boundary conditions dispersion relation for the propagation of Rayleigh-type wave is obtained by considering a complex quantity wavenumber. The obtained result well agrees with the classical result and therefore validates the present study. The phase velocities and the attenuation coefficient for the Rayleigh-type wave propagation are numerically computed for the materials CdSe and LiNbO3; and the same are illustrated graphically. A significant effect of the affecting parameters on the propagation and the attenuation curves are depicted against the wavenumber. Comparative analysis of the influence of these parameters on the propagation and attenuation of Rayleigh-type waves is marked distinctly which serves as a salient feature of the present study. The techniques utilised the present problem and the obtained results may find potential application in various aspects. 2023, The Author(s), under exclusive licence to SocietItaliana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature. -
Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection
The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth- and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non-linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation. 2017, Shanghai University and Springer-Verlag Berlin Heidelberg. -
Nonlinear thermo-solutal convective flow of Casson fluid over an oscillating plate due to non-coaxial rotation with quadratic density fluctuation: Exact solutions
Purpose: The nonlinear density thermal/solutal fluctuations in the buoyancy force term cannot be ignored when the temperature/concentration difference between the surface and fluid is large. The purpose of this paper is to investigate the nonlinear density fluctuations across a flowing fluid with heat mass transfer effects on a non-axial rotating plate. Therefore, the impact of nonlinear convection in the flow of Casson fluid over an oscillating plate has been analytically investigated. Design/methodology/approach: The governing equations are modeled with the help of conservation equations of velocity, energy and concentration under the transient-state situation. The dimensional governing equations are non-dimensionalized by utilizing non-dimensional variables. Later, the subsequent non-dimensional problem has been solved analytically using Laplace transform method. Findings: The effects of thermal Grashof number, solute Grashof number, nonlinear convection parameters, Casson fluid parameter, unsteady parameter, Prandtl number as well as Schmidt number on hydrodynamic, thermal and solute characteristics have been quantified. The numeric data for skin friction coefficient, Nusselt number and Sherwood number are presented. It is established the nonlinear convection aspect has a significant influence on heat and mass transport characteristics. Originality/value: The effect of nonlinear convection in the dynamics of Casson fluid past an oscillating plate which is rotating non-axially is investigated for the first time. 2019, Emerald Publishing Limited. -
Nonlinear stability analysis of Rayleigh-Bard problem for a Navier-Stokes-Voigt fluid
The linear and nonlinear stability analyses of thermosolutal convection in a non-Newtonian Navier-Stokes-Voigt fluid, considering Soret and Ekman damping effects, are conducted analytically. Instability thresholds are determined for thermosolutal convection within a viscoelastic fluid of the Kelvin-Voigt type, wherein a dissolved salt field exists. Two scenarios are examined: one where the fluid layer is heated from the bottom and concurrently salted from the bottom, and the other where the fluid layer is heated from the bottom and concurrently salted from the top. The governing partial differential equations system includes conservation laws of mass, momentum, energy, and salt concentration. Using the energy method, the disturbances to the fluid system are shown to decay exponentially. Analytical expressions are developed for the eigenvalue as a function of Soret, Lewis, Prandtl, Kelvin-Voigt, and Rayleigh friction numbers. The study illustrates the shift from a stationary mode of convection to an oscillatory mode and provides thresholds that indicate these transitions. It is found that the viscoelastic property of the fluid acts as a stabilizing agent for oscillatory mode convection. Rayleigh friction substantially controls the convection threshold. Upon comparing threshold values between linear and nonlinear theories, a subcritical instability region is observed in the heating bottom-salting bottom case (case-1), whereas such a region is absent in the heating bottom-salting top case (case-2). 2024 Elsevier Ltd -
Nonlinear stability analysis of double-diffusive convection in KelvinVoigt fluid with chemical reaction
The influence of Rayleigh friction and chemical reaction on the onset of double-diffusive convection in a NavierStokesVoigt (NSV) fluid layer is investigatedby conducting linear instability and nonlinear stability analyses. The fluid layer is subjected to isothermal conditions and chemical equilibrium at the boundaries. The solubility of the dissolved component exhibits a linear dependency on temperature. The analysis is conducted for two distinct cases: the fluid layer is heated and salted from the bottom (case-1), and the fluid layer is heated from the bottom and salted from the top (case-2). Analytical expressions for the thermal Rayleigh number are obtained for both linear and nonlinear theories, and these expressions depend on KelvinVoigt, Rayleigh friction, solutal Rayleigh, Lewis, Prandtl, and Damkohler numbers. Including the Rayleigh friction term in the NSV fluid model improves the stability of the system and hence instabilityoccurs with less ease. For lower solutal Rayleigh numbers, convection commences in the stationary mode and subsequently transitions to the traveling wave mode occurred in case-1. The Damkohler number plays a significant role in the linear instability thresholds. It is also found that the KelvinVoigt number acts as a stabilizing factor for oscillatory mode convection. The comparison between linear and nonlinear thresholds unveils the region characterized by subcritical instability. 2024 John Wiley & Sons Ltd. -
Nonlinear Rayleigh-Bard magnetoconvection of a weakly electrically conducting Newtonian liquid in shallow cylindrical enclosures
A study of nonlinear axisymmetric Rayleigh-Bard magnetoconvection in a cylindrical enclosure filled with a dilute concentration of carbon-based nanotubes in a weakly electrically conducting Newtonian liquid heated from below for various aspect ratios is carried out. Cylindrical geometry is the prototype for heat storage devices and thermal coolant systems with a controlled environment. There is an analogy between porous media and magnetohydrodynamic problems and hence Rayleigh-Bard magnetoconvection problem is practically important. The solution of the velocity and the temperature is in terms of the Bessel functions of the first kind and hyperbolic functions that are further used to study the marginal stability curves, heat transport, and the dynamical system. Symmetric and asymmetric boundaries of the realistic-type are considered on the horizontal and vertical bounding surfaces. The results of these boundaries are compared with those of the idealistic-type which are symmetric. A unified analysis approach is adopted for all boundary combinations in deriving the Lorenz model and studying the nonlinear dynamics. The time-dependent Nusselt numbers incorporating the effect of the curvature of the cylinder accurately captures the enhanced heat transport situation in the regular convective regime. Further, the influence of various parameters on the indicators of chaos such as the rH-plots, Lorenz attractor, bifurcation diagram, and the time series plot is investigated. The rH-plots clearly point to the appearance of chaos and also assist in determining its intensity and periodicity. The trapping region of the solution of the Lorenz model having the shape like that of a rugby-ball is highlighted in the paper. The size of the ellipsoid shrinks with increase in the strength of the magnetic field and also depends on the boundary conditions. 2024 -
Nonlinear radiative flow of casson nanoliquid past a cone and wedge with magnetic dipole: Mathematical model of renewable energy /
Journal of Nanofluids, Vol.y, Issue 6, pp.1089-1100 -
Nonlinear radiative flow of casson nanoliquid past a cone and wedge with magnetic dipole: Mathematical model of renewable energy
Solar energy is an important source of energy for all the living things. Other sources of energy such as electricity and heat can be converted from solar radiation. The recent advanced technologies are utilized to convert solar energy into electricity. In this direction, nanoliquids are quite useful because they directly absorb or scatter solar radiation. Nanofluids are selected to be best aspirant for the development of renewable energy. They are successfully utilized in the processes of renewable energy. Due to such importance of nanofluids, we investigate the effects of nanoparticles on nonlinear convective and radiative flow of Casson liquid. Two cases are considered namely flow due to a cone and flow due to a wedge. In addition to traditional temperature dependent heat source aspect an exponential space dependent heat source effect is examined. Explicitly heat/mass transfer mechanism is analysed due to prescribed linear surface temperature/particles volume fraction. Problem formulation is presented using conservation laws of mass, momentum, energy and nanoparticles volume fraction under boundary layer approximations. The solutions to the dimensionless problem are computed via Runge-Kutta-Fehlberg based shooting method. Results are plotted and examined. The exponential space dependent and thermal dependent heat source aspects are dominates on thermal field. Further, heat and mass transfer rates are higher in case of flow created by cone than flow created by wedge. The liquid velocity is higher in the case of flow due to wedge than flow due to cone case. 2018 by American Scientific Publishers All rights reserved. -
Nonlinear radiation and cross-diffusion effects on the micropolar nanoliquid flow past a stretching sheet with an exponential heat source
Metallurgy, polymer and processing engineering, and petrochemical enterprises frequently encounter polar nanoliquid flows due to stretchable surfaces with radiative heat energy. Therefore, the radiative flow of a polar nanoliquid over a stretchable sheet is analyzed considering cross-diffusion and magnetic heat flux effects. The heat transport phenomenon is explored, including the characteristics of nonlinear radiation and exponential space-based heat generation. The highly nonlinear governing equations are converted to ordinary differential equations using apt transformations. These are, in turn, solved employing the finite difference method. The behavior of contributing parameters is presented using graphical visualizations. The interactive impacts of the pertinent constraints on the rate of heat transfer and skin friction are analyzed using three-dimensional surface plots. The enhancement of the temperature profile is observed by incrementing the radiation and exponential heat generation parameters. The magnetic field can be used to regulate the fluid flow as it decreases the flow field. Also, the heat generation factor has a predominant decreasing effect on the Nusselt number. 2020 Wiley Periodicals LLC -
Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition /
Physica B: Condensed Matter, Vol.537, pp.98-104, ISSN No: 0921-4526. -
Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition
This research is made to visualize the nonlinear radiated flow of hydromagnetic nano-fluid induced due to rotation of the disk. The considered nano-fluid is a mixture of water and Ti6Al4V or AA7072 nano-particles. The various shapes of nanoparticles like lamina, column, sphere, tetrahedron and hexahedron are chosen in the analysis. The irregular heat source and nonlinear radiative terms are accounted in the law of energy. We used the heat flux condition instead of constant surface temperature condition. Heat flux condition is more relativistic and according to physical nature of the problem. The problem is made dimensionless with the help of suitable similarity constraints. The Runge-Kutta-Fehlberg scheme is adopted to find the numerical solutions of governing nonlinear ordinary differential systems. The solutions are plotted by considering the various values of emerging physical constraints. The effects of various shapes of nanoparticles are drawn and discussed. 2018 Elsevier B.V. -
Nonlinear optical studies of sodium borate glasses embedded with gold nanoparticles
Optical glasses possessing large third-order optical nonlinear susceptibility and fast response times are promising materials for the development of advanced nonlinear photonic devices. In this context, gold nanoparticle (NP)-doped borate glasses were synthesized via the melt-quench method. The nonlinear optical (NLO) properties of thus prepared glasses were investigated at different wavelengths (i.e., at 532nm using nanosecond pulses, at 750nm, 800nm, and 850nm wavelengths using femtosecond, MHz pulses). At 532nm, open aperture (OA) Z-scan signatures of gold NP-doped borate glasses demonstrated reverse saturable absorption (RSA), attributed to mixed intra-band and interband transitions, while in the 750?850nm region, the OA Z-scan data revealed the presence of saturable absorption (SA), possibly due to intra-band transitions. The NLO coefficients were evaluated at all the spectral regions and further compared with some of the recently reported glasses. The magnitudes of obtained NLO coefficients clearly demonstrate that the investigated glasses are potential materials for photonic device applications. 2018, Springer-Verlag GmbH Germany, part of Springer Nature. -
Nonlinear Gravitational and Radiation Aspects in Nanoliquid with Exponential Space Dependent Heat Source and Variable Viscosity
The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquids temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity. 2018, Springer Science+Business Media B.V., part of Springer Nature. -
Nonlinear Dynamics in Distributed Ledger Blockchain and analysis using Statistical Perspective
More and more in healthcare is blockchain technology applied for safe and open data storage. Still, it is understudied how deeply regression analysis combined with nonlinear dynamics into distributed ledger systems performs. This kind of approach may help to increase data transfer efficiency and help storage management in blockchain systems. Data speed and storage efficiency restrictions make current blockchain systems difficult to handle for large amounts of healthcare data. Conventional methods find poor data retrieval and transfer due to the great complexity and nonlinear characteristics of healthcare data. Combining nonlinear dynamics with deep regression analysis, this paper proposes a fresh approach for maximizing data transfer and storage in blockchain systems. Inspired by nonlinear dynamics ideas, a deep regression model aimed at maximizing block storage and forecast data transmission requirements was assessed on a simulated healthcare dataset using a distributed ledger system with 1,000 blocks and a 500 GB total dataset size. Performance criteria covered transmission efficiency and storage consumption. The proposed technique improved data transmission efficiency by thirty percent over current techniques. Another clear improvement was using storage; block size needs fell 25%. The best model, according to numerical research, lowered an average transmission time from 120 to 84 minutes and storage overhead from 200 to 150 GB. 2024, International Publications. All rights reserved. -
Nonlinear convective and radiated flow of tangent hyperbolic liquid due to stretched surface with convective condition /
Results In Physics, Vol.7, pp.2404-2410, ISSN: 2211-3797. -
Nonlinear convective and radiated flow of tangent hyperbolic liquid due to stretched surface with convective condition
The current study compacts with effect of nonlinear convection and radiation on tangent hyperbolic fluid flow of through a convectively heated vertical surface. The converted set of boundary layer equations are solved numerically by Runge-Kutta-Fehlberg method. The effect of various pertinent parameters on flow and heat transfer characteristics are discussed with tabulated numerical values and deliberate figures. Additionally, the skin friction coefficient and Nusselt number are also presented. We noticed that, the skin friction factor and heat transfer rates are higher in presence of nonlinear convection than its absence. Further, velocity profile decreases by increasing power law index but establishes opposite results for skin friction. 2017 -
Nonlinear convection in nano Maxwell fluid with nonlinear thermal radiation: A three-dimensional study
The combined effects of nonlinear thermal convection and radiation in 3D boundary layer flow of non-Newtonian nanofluid are scrutinized numerically. The flow is induced by the stretching of a flat plate in two lateral directions. The mechanism of heat and mass transport under thermophoretic and Brownian motion is elaborated via implementation of the thermal convective condition. The prevailing two-point nonlinear boundary value problem is reduced to a two-point ordinary differential problem by employing suitable similarity transformations. The solutions are computed by the implementation of homotopic scheme. At the end, a comprehensive parametric study has been conducted to analyze the typical trend of the solutions. It is found that the nanoparticle volume fraction and temperature profiles are stronger for the case of solar radiation in comparison with problem without radiation. 2017 Faculty of Engineering, Alexandria University -
Nonlinear Boussinesq buoyancy driven flow and radiative heat transport of magnetohybrid nanoliquid in an annulus: A statistical framework
The effect of nonlinear Boussinesq buoyancy force on the flow of Cu-Al2O3-H2O hybrid nanoliquid in a vertical annulus, which is adjacent to the radial magnetic field and thermal radiation, is analyzed through a statistical approach. The phenomena of movement of annuli are taken into account. The aspect of nonlinear density temperature is also accounted based on nonlinear Boussinesq approximation (NBA). The exact solution is obtained for the two-point boundary value problem comprised dimensionless governing equations. The skin friction coefficient and Nusselt number expressions are also estimated. The impacts of various physical parameters on the velocity, temperature, skin friction coefficient, and Nusselt number distributions are analyzed. The statistical techniques, such as correlation coefficient, probable error, and a multivariate regression model, are employed for the detailed analysis. It is found that the NBA is favorable for the skin friction coefficient and the rate of heat transfer. The maximum heat transfer is found on the wall of the internal annuli. 2020 Wiley Periodicals LLC -
Nonlinear analysis of the effect of viscoelasticity on ferroconvection
Thispaper concerns a nonlinear analysis of the effects of viscoelasticity on convection in ferroliquids. We consider the Oldroyd model for the constitutive equation of the liquid. The linear stability analysis yields the critical value of the Rayleigh number for the onset of oscillatory convection in Maxwell and Jeffrey ferroliquids. The use of a minimal mode double Fourier series in the nonlinear perturbation equations yields a KhayatLorenz model for the ferromagnetic liquid, and that is scaled further to get the classical Lorenz model as a limiting case. The scaled KhayatLorenz model thus obtained is solved numerically and the solution is used to compute the time-dependent Nusselt number, which quantifies the heat transport. The results are analyzed for the dependence of the time-averaged Nusselt number on different parameters. 2021 Wiley Periodicals LLC -
Nonlinear 3D flow of Casson-Carreau fluids with homogeneousheterogeneous reactions: A comparative study
Nonlinear convective flow of magneto-Carreau-Casson liquids past a deformable surface under the aspects of heterogeneous and homogeneous reactions is investigated. The present phenomenon also included the interaction of nonlinear radiation, Ohmic and Joule dissipations. At moderate to high temperature, the nonlinear convection and radiation are significant. The governed nonlinear system is illustrated numerically via Runge-Kutta based shooting scheme in the domain [0,?). Role of significant parameters on flow fields as well as on the fiction factor, heat and mass transportation rates are determined and discussed in depth. Comparison is done for distinct flow fields of Carreau and Casson fluids. It is evaluated that the velocities of Casson liquid are higher in comparison to Carreau fluid model. However, liquid temperature for Casson fluid model is weaker in comparison to Carreau fluid. 2017