Onset of Instability in Hadley-Prats Flow in an 
Anisotropic Porous Media with Viscous Dissipation

Badal Kumar; Ashalata keshri

doi:https://doi.org/10.14445/22315373/IJMTT-V70I11P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 70 | Issue 11 | Year 2024 | Article Id. IJMTT-V70I11P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I11P102

Onset of Instability in Hadley-Prats Flow in an Anisotropic Porous Media with Viscous Dissipation

Badal Kumar, Ashalata keshri

Received	Revised	Accepted	Published
16 Aug 2024	29 Sep 2024	15 Nov 2024	29 Nov 2024

Abstract

The stability of a Hadley-type flow in a horizontal porous medium under an inclined temperature gradient is investigated when a fundamental horizontal mass flow (Prats flow) is present. Consequently, the Hadley-prats flow is the name given to the basic flow. We consider anisotropic thermal diffusivity and weak vertical heterogeneity in permeability. It is believed that viscous dissipation has a significant impact. The Rayleigh number associated with the vertical thermal gradient Ra is one of the eigenvalues. The other parameters include the thermal diffusivity (𝜉), the Gebhart number (𝐺𝑒) for viscous dissipation, the horizontal Rayleigh number (Rah) for the horizontal through flow, and the parameter 𝜆 for changes in permeability. A linear stability analysis is executed, wherein the governing equations are numerically solved to determine the critical Rayleigh and wave numbers. The discussion pertains to longitudinal and transverse rolls. Longitudinal rolls are generally considered the most effective means of characterizing instability in most scenarios.

Keywords

Porous medium, Thermal diffusivity, Anisotropy, Permeability.

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Citation :

Badal Kumar, Ashalata keshri, "Onset of Instability in Hadley-Prats Flow in an Anisotropic Porous Media with Viscous Dissipation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 11, pp. 5-15, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I11P102