2025 , Volume 30, № 6, p.37-55

The process of natural convection induced by internal heating, commonly referred to as penetrative convection, finds extensive applications across various industrial and engineering disciplines, so the objective of this article is to investigate the onset of penetrative convection in a horizontal dusty ferrofluid layer, heated from below and bounded by permeable boundaries. The study considers four distinct supply functions that induce either uniform or non-uniform internal heating within a dusty ferrofluid layer. The inclusion of permeable boundaries introduces a novel aspect to the analysis, which in turn provide its relevance across various fields. Using linear stability theory and normal mode analysis, an eigenvalue problem is derived and solved for stationary convection modes through the application of the single-term Galerkin method. Numer ical computations of the threshold convective instability parameters are carried out using MATLABR2023a, and the results are displayed graphically. The impact of key param eters on the onset of convection is analyzed for various combinations of hydrody namic boundary conditions, providing valuable insight into the stability characteristics of the system. The study reveals that the combined effect of heat sources and sinks increases the instability of the system compared to using only one type of source or sink. Also, the magnetic parameter (M₃) and dust particles parameters (h′) destabilize the system whereas the permeability parameters k′₀ and k′₁ are found to have a stabi lizing effect on the system. The findings from previous research are reconstructed as special cases from the results of the current study.