This paper explores the thermal behavior of a composite building element consisting of two air cavities inside a porous layer under isothermal heating of the side walls. The system presents a model of a thermal protection element or building envelope where heat transfer occurs through combined conduction in the porous medium and natural convection in the air gaps. The mathematical formulation is based on the Navier-Stokes equations and the Darcy-Brinkman formulation for the porous structure. The natural convection problem has been solved using the ψ–ω–θ formulation in dimensionless form (ψ—stream function, ω—vorticity, θ—temperature). The main heat transfer characteristics have been found to be strongly influenced by the governing parameters: Ra (the Rayleigh number), Da (Darcy number), ε (material porosity), and l_х, l_у (the size of the air gaps). Key findings: increasing the Rayleigh number from 10⁴ to 10⁶ enhances the mean Nusselt number from approximately 0.9 to 3.7 with intensification of convective heat transfer. Variations in the Darcy number over two orders of magnitude (10⁻⁴ to 10⁻²) result in a similar change in the mean Nusselt number. Increasing porosity from ε = 0.1 to ε = 0.8 reduces the Nusselt number by less than 6%. The analysis of air cavity geometry shows that enlarging cavity dimensions increases flow intensity but produces only a moderate enhancement in heat transfer. Practical implications: optimal thermal insulation is achieved with high-porosity foam concrete (ε ≥ 0.6) combined with low permeability (Da ≤ 10⁻⁴) and minimal air cavity dimensions. In this case, convective circulation is suppressed, and heat transfer remains conduction dominated with minimum values of the mean Nusselt number. The proposed model provides a physically consistent description of thermal transport in hybrid porous/fluid configurations and can serve as a basis for optimizing the thermal design of energy-efficient insulation structures and passive cooling devices.

A computational research of radiative-convective energy transport in large-scale enclosure with a heat-generating heater under normal room conditions has been conducted. The heater (underfloor heating system) is located at the bottom of the room. Employing the Boussinesq assumption, the control equations have been solved contemporaneously to receive both the velocity fields and temperature patterns. To generate the systems of linear equations using vorticity and stream function, the finite difference technique has been employed. The developed convective-radiative model has been validated through a comparison with several problems. The influence of heater size and location, internal surfaces emissivity from 0 to 1, Ostrogradsky number for a wide range from 0 to 5 on Nusselt numbers and both stream function and temperature distributions has been investigated. The results demonstrate that the influence of the thermal radiation on total heat transfer increases with surface emissivity of walls and heater surfaces.