Modified Fourier heat flux impact on heat transfer of magnetic nano-encapsulated phase change materials inside a chamber with microorganisms

Purpose This study aims to offer a numerical examination of natural convection in a porous cavity filled with nano-encapsulated phase change materials (NEPCMs), where engine oil and N-eicosane serve as the base fluid–core combination, and polyvinyl alcohol forms the encapsulating shell. Design/methodology/approach The governing nonlinear partial differential equations, together with applicable boundary conditions, are elucidated using the finite element method. The effects of key controlling parameters – nanoparticle volume fraction (ϕ), magnetic number (M), porosity parameter (k1), thermal relaxation time (γ), Rayleigh number (Ra), radiation parameter (R), Peclet number (Pe), fusion parameter (θf), Stefan number (Ste) and bioconvection Rayleigh number (Rb) – are systematically analyzed to evaluate their influence on isotherms, streamlines, heat capacity ratio, microorganisms and solute isoconcentration distributions. Findings The results reveal that increasing (ϕ) enhances thermal conductivity and heat transfer, while larger (M) values suppress convective circulation. The parameter (γ) significantly affects thermal relaxation, and (Ste) governs the balance between latent and sensible heat storage. In addition, bioconvection strongly modifies the spatial distribution of microorganisms within the cavity. Originality/value The work carried out in this analysis is original and no part is copied.