Numerical analysis of the most appropriate heat transfer correlations for free ventilated double skin photovoltaic façades

Double skin façades with photovoltaic integrated systems are building components which combine functions of the building envelope with electricity and thermal energy generation. The heat transfer modelling of these components, especially under free convection situations, raises a high complexity and is one of the main drawbacks for a massive dissemination of this technology. Many attempts to fill this gap have been undertaken and some mathematical correlations allowing evaluating average Nusselt numbers and air mass flow rate have been obtained in the last decades. However, very few studies faced a detailed analysis of the valid range of these mathematical expressions and of the restrictions entailed. This paper introduces a methodology to analyse the valid range of the existing mathematical correlations for the convective heat transfer coefficients and for the air mass flow rate in laminar and transition to turbulent free convection, and provides an evaluation of the effect of the asymmetry of the wall boundary conditions. A specific numerical code, based on a stabilized finite element formulation (FEM), is used to solve the incompressible Navier-Stokes equations within the air gap and to determine the accuracy of the existing heat transfer correlations. This evaluation was preceded by an extensive bibliographic research as well as a detailed validation of the physical and numerical hypothesis adopted in the finite element code.