The thermal dynamic behavior of buildings represents an important aspect of the energy efficiency and thermal comfort of the indoor environment. For this, phase change material (PCM) wallboards integrated into building envelopes play an important role in stabilizing the temperature of the human comfort condition. This article provides an assessment of the thermal behavior of a “bi-zone” building cell, which was built based on high-energy performance (HEP) standards and heated by a solar water heater system through a hydronic circuit. The current study is based on studying the dynamic thermal behavior, with and without implantation of PCMs on envelope structure, using a simplified modeling approach. The evolution of the average air temperature was first evaluated as a major indicator of thermal comfort. Then, an evaluation of the thermal behavior’s dynamic profile was carried out in this study, which allowed for the determination of the PCM rate anticipation in the thermal comfort of the building cell.

The thermo convective instability of the Darcy-Benard problem (DB) using Robin (third-kind) thermal conditions is investigated here. We consider a viscous Newtonian fluid saturating a porous layer in which the layer is sandwiched between two impermeable boundaries. The upper and the lower walls are modelled in the form of the Neumann (second-kind) and the Robin (third-kind) thermal conditions, respectively. The difference in the temperature distribution between both phases allows the lack of a local thermal equilibrium model to be present. As a consequence, the third kind of thermal condition brings about one extra dimensionless parameter of the Biot number to the usual one of the inter-heat transfer coefficient and the thermal conductivity ratio. The normal modes method adopted in a linear stability analysis gives rise to perturbed governing equations. The eigenvalue problem is handled numerically as a result of the perturbed governing equations leading to the marginal stability condition.