https://doi.org/10.1140/epjp/s13360-026-07427-9
Regular Article
Gravity modulation-induced thermal stability analysis of Biviscous Bingham fluid saturating a porous medium with uniform internal heat generation
Department of Mathematics, Thapar Institute of Engineering and Technology, 147001, Patiala, Punjab, India
a
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Received:
28
December
2025
Accepted:
7
February
2026
Published online:
20
February
2026
Abstract
Motivated by diverse industrial applications involving viscoplastic fluids in porous media, this study examines the stability characteristics of convection driven by thermal buoyancy in a horizontal porous layer saturated with biviscous Bingham fluid. The analysis incorporates the effects of internal heating and gravity modulation, utilizing the Darcy–Brinkman model to describe fluid flow within the porous media. For linear stability analysis, the normal mode technique in conjunction with the Galerkin method is employed to determine the thermal Rayleigh number under different types of boundary conditions. A perturbation approach is utilized to investigate the weakly nonlinear regime in the vicinity of critical Rayleigh number, wherein the temporal evolution of heat transfer, characterized by the Nusselt number, is articulated by a non-autonomous Ginzburg–Landau equation. The study delineates the influence of various governing parameters (
) on heat transfer and overall stability of the system with the findings indicating that the elevated values of internal heating parameter (Hs) result in an increase in the Nusselt number and destabilize the system while gravity field modulation yields enhancements of up to 9% in heat transfer relative to the unmodulated case. Additionally, it is found that the biviscous Bingham fluid exhibits elevated critical thresholds and enhanced resistance to the onset of convection relative to the Newtonian fluid, signifying a more stable system. The results provide a profound understanding of the interplay of Bingham rheology, gravitational modulation, and internal heating in regulating convective stability and heat transport in intricate porous systems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
