Heat generation effects in natural convection inside a porous annulus

The interplay between internal heat generation and externally driven natural convection inside a porous medium annulus is studied in detail using numerical methods. The axisymmetric domain is bounded with adiabatic top and bottom walls and differentially heated side walls sustaining steady natural convection of a fluid with Prandtl number, Pr = 5, through a porous matrix of volumetric porosity, ϕ = 0.4. The generalized momentum equation with Brinkman–Darcy–Forchheimer terms and the local thermal non-equilibrium based two-energy equation model are solved to determine the flow and the temperature distribution. Beyond a critical heat generation value defined using an internal Rayleigh number, RaI,cr⁎, the convection transits from unicellular to bicellular mode, as the annulus Tmax becomes higher than the fixed hot-wall temperature. The RaI,cr⁎ increases proportionately when the permeability based external Rayleigh number RaE⁎ and the solid–fluid thermal conductivity ratio γ are independently increased. A correlation is proposed to predict the overall annulus Nu as a function of RaE⁎, RaI⁎, Da and γ. It predicts the results within ± 20% accuracy.