R, S., M A, A., N, M., Al-Farhany, K., ., S., Kumar, V. (2026). Stability analysis of marangoni magneto-convective flow with heat generation: Effects of depth ratio and thermal boundaries. , 19(2), 231-240. doi: 10.30772/qjes.2026.166109.1780
Sumithra R; Archana M A; Manjunatha N; Khaled Al-Farhany; Shankara .; Vijaya Kumar. "Stability analysis of marangoni magneto-convective flow with heat generation: Effects of depth ratio and thermal boundaries". , 19, 2, 2026, 231-240. doi: 10.30772/qjes.2026.166109.1780
R, S., M A, A., N, M., Al-Farhany, K., ., S., Kumar, V. (2026). 'Stability analysis of marangoni magneto-convective flow with heat generation: Effects of depth ratio and thermal boundaries', , 19(2), pp. 231-240. doi: 10.30772/qjes.2026.166109.1780
R, S., M A, A., N, M., Al-Farhany, K., ., S., Kumar, V. Stability analysis of marangoni magneto-convective flow with heat generation: Effects of depth ratio and thermal boundaries. , 2026; 19(2): 231-240. doi: 10.30772/qjes.2026.166109.1780

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

Al-Qadisiyah Journal for Engineering Sciences
Article 10, Volume 19, Issue 2, June 2026, Pages 231-240    PDF (8.07 M)
Document Type: Research Paper
DOI: 10.30772/qjes.2026.166109.1780
Authors
Sumithra R1; Archana M A1; Manjunatha N* 2; Khaled Al-Farhany3; Shankara .4; Vijaya Kumar5
1Department of Mathematics, Nrupathunga University, Bengaluru, Karnataka, India.
2Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru, Karnataka, India.
3Department of Mechanical Engineering, College of Engineering, University of Al-Qadisiyah, Al-Qadisiyah, Iraq.
4Department of Civil Engineering, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, India.
5Department of Mathematics, M S Ramaiah Institute of Technology, Bengaluru, Karnataka, India.
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
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