A dimensionless solution to radiation and turbulent natural convection in square and rectangular enclosures

The effects of natural convection with and without the interaction of surface radiation in square and rectangular enclosures have been studied, numerically and theoretically. The analyses were carried out over a wide range of enclosure aspect ratios ranging from 0.0625 to 16, including square enclosures in sizes from 40cm to 240cm, with cold wall temperatures ranging from 283 to 373 K, and hot to cold temperature ratios ranging from 1.02 to 2.61. The work was carried out using four different fluids whose properties are varying with temperature. FLUENT software was used to carry out the numerical study. Turbulence was modelled using the RNG k-ε model with a non-uniform grid. The Discrete Transfer Radiation Model (DTRM) was used for radiation simulation. A correlation equation for the new dimensionless group represented by the ratio of natural convection to radiation, as a function of Nusselt, Grashof, Prandtl numbers and temperature ratio also, the average Nusselt number without radiation as a function of Grashof and Prandtl numbers have been provided along with the constants needed to use them as a function of temperature ratio. This provides a generalised equation for heat transfer in square and rectangular enclosures both with and without radiation.