An empirical solution to turbulent natural convection and radiation heat transfer in square and rectangular enclosures

The effects of natural turbulent convection with the interaction of surface radiation in a rectangular enclosure have previously been numerically and theoretically studied. The analyses were carried out over a wide range of enclosure aspect ratios ranging from 0.0625 to 16, different enclosure sizes, with cold wall temperatures ranging from 283 to 373 K, and temperature ratios ranging from 1.02 to 2.61. The work was carried out using four fluids (Argon, Air, Helium and Hydrogen; whose properties vary with temperature). These can be used to calculate Nusselt number for pure natural convection and also to calculate the ratio between convection to radiation heat transfer for both square and rectangular enclosures. This work extends these results by providing an empirical solution for the case of radiation and natural convection in square and rectangular enclosures and also provides a correlation equation to calculate the total Nusselt number for these cases. This method allows the simple calculation of either the total heat transfer rate, given the fluid, the geometry and the temperatures of the hot and cold walls, or via a straightforward iterative technique, the temperature of one wall given the other wall temperature and the total heat transfer. ► Previous work has non-dimensionalised flow in enclosures with and without radiation. ► This extends the work by enabling a simple iterative technique to work out temperatures for total heat transfer rate. ► The provided solution has a maximum deviation of 7.7%. ► The method works for a variety of enclosures sizes, aspect ratios, temperatures and gases.