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Double-Diffusive Thermo-Solutal Hadley-Prats Flow: Stability Analysis

Rafeek, KVM; Reddy, G Janardhana; Matta, Anjanna; Basha, Hussain; Anwar Bég, O


KVM Rafeek

G Janardhana Reddy

Anjanna Matta

Hussain Basha



A mathematical model is developed to study the onset of double-diffusion fluid flow through an infinite permeable channel with internal heat source and viscous dissipation effects under the influence of convection conditions. Darcy's model is utilized for the considered isotropic and homogenous porous medium. A linear instability analysis is conducted and the longitudinal roll disturbances are examined. The dimensionless emerging eigenvalue problem is solved numerically using the fourth order Runge-Kutta scheme for longitudinal roll disturbances. Critical values of wave number and vertical thermal Rayleigh number are determined. A higher value of Gebhart number is observed to correlate significantly with the destabilizing phenomena in Hadley-Prats flow. Concentration based internal heat generation also strongly modifies the critical thermal Rayleigh number. Also, it is found that, the horizontal mass flow and viscous dissipation exert a substantial influence on the onset of instability in the flow regime. Linear instability analysis indicates that, greater values of Lewis number in the porous medium stabilize the convection process for both values of mass diffusion parameter (í µí° ¶ í µí± §). Enhancing í µí° ¶ í µí± § from negative to positive 2 2 values diminishes the critical thermal Rayleigh (í µí± í µí± §) value and consequently induces instability in the porous medium. Increased concentration-based internal heat generation generates the destabilisation process in the flow region. Extensive visualization and interpretation of the solutions relating to the onset of convection are provided. The study is relevant to geothermal, industrial manufacturing and chemical engineering transport processes.


Rafeek, K., Reddy, G. J., Matta, A., Basha, H., & Anwar Bég, O. (2024). Double-Diffusive Thermo-Solutal Hadley-Prats Flow: Stability Analysis. International Journal of Modelling and Simulation,

Journal Article Type Article
Acceptance Date Mar 7, 2024
Online Publication Date Mar 18, 2024
Publication Date Mar 18, 2024
Deposit Date Mar 8, 2024
Publicly Available Date Mar 19, 2025
Print ISSN 0228-6203
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Keywords Key-Words: Thermo-convective instability; eigenvalues; critical wave number; Gebhart number; Lewis number; Rayleigh number; concentration-based internal heat generation; mass diffusion; geothermic
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