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Helical force with a two-phase Cattaneo LTNE model on hyper-chaotic convection in the presence of magnetic field

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Abstract

An extensive and precise computational evaluation of Cattaneo local thermal nonequilibrium (LTNE) impacts through the chaotic convective dynamical behavior in a two-phase porous medium with a helical force of magnetic field has been accomplished by using the double-Fourier mode techniques. Meanwhile embracing the Darcy–Brinkman model for base fluid flow and the Cattaneo heat flux law-derived hyperbolic-type heat transport equation in solid is being assessed. The energy equations are derived using the LTNE, which establishes different temperature profiles for both the fluid and solid phases. As a result of the Cattaneo LTNE effect, the system also exhibits exceptional topological properties, with regular patches enclosed within chaotic domains. The recently proposed perspective is in favor of the discovery of an analytical description for the critical Darcy–Rayleigh numbers that signify the commencement of steady and oscillate convection, respectively. The novel perspective of chaotic convection provides the most comprehensive explanation for the transition from Cattaneo heat flow, magnetic field, helical force, thermal relaxation parameter, and Darcy effect. The flow features of behavior in response to the stimulating individual and combination factors are investigated visually in great depth. At its most acute, the combination of heat flux conductivity and interphase thermal transfer destabilizes the system, whereas the magnetic field, helical force, Darcy effect, and thermal relaxation parameter coefficient have the opposite effect.

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Data Availability Statement

No Data associated in the manuscript. This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during the current study are available from the corresponding author on reasonable request.]

Abbreviations

c :

Specific heat at constant pressure

\({\tilde{\textrm{D}}}\textrm{a}\) :

Modified Darcy number

\({\tilde{g}}\) :

Gravitational acceleration

\(\phi \) :

Interphase heat flow

K :

Permeability

\(k_{\textrm{f}}\) :

Fluid thermal conductivity

\(k_{\textrm{s}}\) :

Solid thermal conductivity

Pr\(_{\textrm{D}}\) :

Darcy–Prandtl number

R\(_D\) :

Rayleigh number

\(\vec {v}\) :

Velocity vector

\({\tilde{T}}\) :

Temperature

\(\alpha \) :

Thermal diffusivity of the fluid in (\(\textrm{m}^{2}\,\textrm{s}^{-1}\))

\(\alpha _{\textrm{t}}\) :

Coefficient of thermal expansion in (K\(^{-1}\))

\(\mu _f\) :

Dynamic viscosity in (Kg m\(^{-1}\,\textrm{s}^{-1}\))

\(\epsilon \) :

Porosity of the medium

\({\tilde{\rho }}\) :

Density in (\(\mathrm{Kg\,m}^{-3}\))

\({\tilde{\rho }}_{\textrm{f}}\) :

Fluid density

\({\tilde{\rho }}_{\textrm{s}}\) :

Solid density

\({\tilde{\mu }}_f\) :

Effective viscosity

\(\chi _{\textrm{s}}\) :

Solid thermal relaxation time

\({\tilde{\chi }}\) :

Nondimensional solid thermal relaxation parameter

\('\) :

Dimensionless

c:

Critical

f:

Base fluid

s:

Solid

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Authors and Affiliations

  1. Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Ramapuram, Tamil Nadu, 600 089, India

    R. Surendar

  2. Department of Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, 641 046, India

    M. Muthtamilselvan

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  1. R. Surendar
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Surendar, R., Muthtamilselvan, M. Helical force with a two-phase Cattaneo LTNE model on hyper-chaotic convection in the presence of magnetic field. Eur. Phys. J. Plus 138, 658 (2023). https://doi.org/10.1140/epjp/s13360-023-04297-3

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