Al-Qadisiyah Journal for Engineering Sciences

Stability analysis of marangoni magneto-convective flow with heat generation: Effects of depth ratio and thermal boundaries

Document Type : Research Paper

Authors

Sumithra R 1
Archana M A 1
Manjunatha N 2
Khaled Al farhany 3
Shankara . 4
Vijaya Kumar 5

1 Department of Mathematics, Nrupathunga University, Bengaluru, Karnataka, India.

2 Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru, Karnataka, India.

3 Department of Mechanical Engineering, College of Engineering, University of Al-Qadisiyah, Al-Qadisiyah, Iraq.

4 Department of Civil Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, India.

5 Department of Mathematics, M S Ramaiah Institute of Technology, Bengaluru, Karnataka, India.

https://doi.org/10.30772/qjes.2026.166109.1780
Abstract
The stability analysis of Marangoni magneto-convection (MMC) is investigated in a two-layer system consisting of an electrically conductive fluid-saturated porous layer overlain by an identical fluid layer, incorporating variable heat sources and a uniform magnetic field. The upper fluid surface is free, allowing surface-tension-driven convection, while the lower porous boundary is rigid. Two thermal boundary conditions are examined: (i) adiabatic–adiabatic (A–A) and (ii) adiabatic–isothermal (A–I). The governing equations are solved analytically using an exact method to obtain the thermal Marangoni number, an eigenvalue, as a function of depth ratio, Darcy number, Chandrasekhar number, internal Rayleigh numbers, wave number, and thermal diffusivity ratio. Graphical results show that the onset of MMC can be either advanced or delayed by appropriate choices of depth ratio and thermal boundary conditions. The novelty of the present work lies in deriving closed-form expressions for a composite fluid–porous system with simultaneous consideration of variable internal heat sources and magnetic effects under dual thermal boundary conditions, and demonstrating how depth ratio and thermal boundary conditions can be strategically tuned to either advance or delay the onset of instability.

Keywords

Marangoni convection
two-regions
heat source
magnetic field
Adiabatic and isothermal boundary
Crossmark
Subjects
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Al-Qadisiyah Journal for Engineering Sciences
Volume 19, Issue 2
Summer 2026
Pages 231-240

  • Receive Date 12 April 2025
  • Revise Date 02 February 2026
  • Accept Date 17 May 2026

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