https://doi.org/10.1140/epjs/s11734-025-01744-3
Regular Article
Stability analysis of Rayleigh–Benard convection on an inclined plane with an operative usage of solar energy in a biviscous Bingham fluid
1
Department of Mathematics, Bharathiar University, 641 046, Coimbatore, Tamil Nadu, India
2
Department of Mechanical Engineering, Keimyung University, Daegu, South Korea
3
Centre for Nonlinear Systems, Chennai Institute of Technology, 600069, Chennai, India
a
muthtamil1@buc.edu.in
b
kimih@kmu.ac.kr
Received:
23
August
2024
Accepted:
6
June
2025
Published online:
25
June
2025
Understanding Rayleigh–Bénard convection is crucial in various scientific and engineering disciplines, such as meteorology, geophysics, and material sciences. The present study focuses on the two-dimensional Rayleigh–Bénard convection of biviscous Bingham fluid with inclined parallel planes. The thermal instability of double-diffusive convection with a temperature-dependent internal heat source is also addressed. The linear instability of small-amplitude disturbances to the system is analyzed in terms of transverse and longitudinal rolls. The resulting eigenvalue problem is numerically addressed using the Ginzburg–Landau technique under appropriate initial conditions. Our investigation revealed that the system experiences increased instability when the thermal diffusivity surpasses the biviscous parameter, and similarly, when the strength of the internal heat source rises. We observed that adjusting the angle of inclination serves to stabilize the system.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
