Bifurcations and chaos in convection taking non-Fourier heat-flux

Layek, G. C.; Pati, Nivedita

doi:10.1016/j.physleta.2017.09.020

Cited by 22 publications

(15 citation statements)

References 15 publications

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“…Thermal relaxation time can be interpreted physically as the time needed for accumulating the thermal energy essential for generating heat flux [6] [7]. The inclusion of the thermal inertial in heat prorogation has effects in the heat transport in nano-material, nanofluids and many areas of ballistics and astrophysics [8] [9] [10].…”

Section: Introductionmentioning

confidence: 99%

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

Karim¹,

Samad²

2020

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The present study deals with the analysis of heat transfer of the unsteady Maxwell nanofluid flow in a squeezed rotating channel of a porous extensile surface subject to the velocity and thermal slip effects incorporating the theory of heat flow intensity of Cattaneo-Christov model for the expression of the energy distribution in preference to the classical Fourier's law. A set of transformations is occupied to renovate the current model in a system of nonlinear ordinary differential equations that are numerically decoded with the help of MATLAB integrated function bvp4c. The effects of various flow control parameters are investigated for the momentum, temperature and diffusion profiles, as well as for the wall shearing stress and the heat and mass transfer. The results are finally described from the material point of view. A comparison of heat flux models of Cattaneo-Christov and Fourier is also performed. An important result from the present work is that the squeezing parameter is strong enough in the middle of the channel to retard the fluid flow. How to cite this paper: Karim, M.E. and Samad, M.A. (2020) Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect. Applied Mathematics, 11, 277-291.

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Section: Introductionmentioning

confidence: 99%

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

Karim¹,

Samad²

2020

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“…To know about the physical meaning of variables and parameters, we suggest consulting Layek and Pati [1] where system (1) was derived and first investigated. In addition to obtaining the five-dimensional nonlinear system (1), Layek and Pati [1] report on analytical results related with equilibrium points, linear stability analysis, and bifurcations.…”

Section: Introductionmentioning

confidence: 99%

Hyperchaos in convection with the Cattaneo-Christov heat-flux model

Daumann

Rech

2019

Eur. Phys. J. B

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In this paper, we report on the nonlinear dynamics of a five-variable, four-parameter system, which models the effects of thermal relaxation time on Rayleigh-Bénard convection of Boussinesq fluid layer heated underneath. Six cross-sections of the four-dimensional parameter-space are considered. By using Lyapunov exponents spectra to characterize the dynamical behavior at each point of each these diagrams, we show that different parameter regions are allowed, from equilibrium points to chaos and hyperchaos regions.

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“…Recently, Layek and Pati reported on the influences of thermal time-lag on the onset of convection, and obtained a five-dimensional nonlinear system from a loworder Galerkin expansion of velocity and temperature variables [6]:…”

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confidence: 99%

“…Here σ is the Prandtl number, r is the normalized Rayleigh number, b = 4π 2 /Λ is the geometrical parameter, δ = 1/(2ΛC) and C is the Cattaneo number. Layek and Pati include some numerical results including bifurcation transition diagrams, plots of the largest Lyapunov exponents, phase-space portraits, and routes to chaos via period-doubling bifurcations for r > 10 [6]. In 2019, Daumann and Rech used Lyapunov exponents spectra to characterize the dynamical behavior of system (1), and found numerically the existence of chaos in different parameter regions [2] (see the attractors in the phasespace of system (1) in Fig.…”

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confidence: 99%

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Codimension one and two bifurcations in Cattaneo-Christov heat flux model

Wei¹,

Zhang²,

Moroz³

et al. 2021

DCDS-B

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Layek and Pati (Phys. Lett. A, 2017) studied a nonlinear system of five coupled equations, which describe thermal relaxation in Rayleigh-Benard convection of a Boussinesq fluid layer, heated from below. Here we return to that paper and use techniques from dynamical systems theory to analyse the codimension-one Hopf bifurcation and codimension-two double-zero Bogdanov-Takens bifurcation. We determine the stability of the bifurcating limit cycle, and produce an unfolding of the normal form for codimension-two bifurcation for the Layek and Pati's model.

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Bifurcations and chaos in convection taking non-Fourier heat-flux

Cited by 22 publications

References 15 publications

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

Hyperchaos in convection with the Cattaneo-Christov heat-flux model

Codimension one and two bifurcations in Cattaneo-Christov heat flux model

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