Simplified analytical model for thermal transfer in vertical hollow brick

A modern building envelope has a lot of little cavities. Most of them are vertical with a high height to thickness ratio. We present here the conception of a software to determine heat transfer through terra-cotta bricks full of large vertical cavities. After a bibliographic study on convective heat transfer in such cavities, we made an analytical model based on Karman-Polhausenʹs method for convection and on the radiosity method for radiative heat transfer. We used a test apparatus of a single cavity to determine the temperature field inside the cavity. Using these experimental results, we showed that the exchange was two-dimensional. We also realised heat flux measurements. Then we expose our theoretical study: we propose relations between central core temperatures and active face temperatures, then between outside and inside active face temperatures. We calculate convective superficial heat transfer because we noticed we have boundary layers along the active faces. We realise a heat flux balance between convective plus radiative heat transfer and conductive heat transfer, so we propose an algorithm to calculate global heat transfer through a single cavity. Finally, we extend our model to a whole hollow brick with lined-up cavities and propose an algorithm to calculate heat flux and thermal resistance with a good accuracy (≈ 7.5%) compared to previous experimental results.