Quantification of free convection in a quarter-spherical innovative Trombe wall design

Objective of this work is to quantify the natural convective heat transfer occurring in an innovative Trombe wall whose design consists of two concentric quarter spheres. The exterior glazing is maintained isothermal while the internal one is the wall of the system, subjected to a solar heat flux determined in some sites located between the 28.56 degrees and 53.31 degrees North latitudes on the four specific days of solstices and equinoxes. Calculations show that the quarter-spherical shape of the proposed Trombe wall allows to collect an average solar irradiation higher than that of a traditional vertical plane Trombe wall. Its overall thermal performance is improved without changing its simple dynamic operation since it does not require any complex sun tracking systems. The free convective heat transfer occurring in its channel is quantified by means of the Nusselt number determined in a wide range of the Rayleigh number varying between 9.22 x 10(7) and 6.76 x 10(11), based on the distance between the active walls of the enclosure. New correlations of the Nusselt-Rayleigh type are proposed in this work, determined by means of a 3D numerical approach using the volume control method based on the SIMPLE algorithm. They constitute a necessary tool for the thermal sizing of this original Trombe wall that Engineers and Architects can integrate into existing and new constructions, thus contributing to improve the building's energy performance.