Heat transfer by natural convection and radiation in three dimensional differentially heated tall cavities

Abstract

Natural convection coupled with radiation is numerically studied in a tall rectangular parallelepiped cavity filled with air and constant differentially heated opposite vertical walls. This type of tall cavity is found in walls built with hollow blocks. Three dimensional steady state numerical simulations are performed. Numerical models for pure natural convection and natural convection coupled with radiation are validated with experimental results. In this work, the tall cavity studied has a 0.06 m width, 0.155 m depth and a 2.56 m height, giving a vertical aspect ratio of A=42.7 and a horizontal aspect ratio of A′=2.6. The cold wall temperature, Tc, is fixed. The hot wall temperature, Th, is varied, obtaining the Rayleigh numbers: RaW, 1.01×104, 1.07×105 and 7.20×105. The emissivity, ϵ, varies from 0.0 to 1.0. The results show that with a given Th, the convective Nusselt number, Nuc, depends on ϵ. For the emissivity value of hollow block materials (ϵ=0.8) the radiative heat transfer represents 83% for the lowest Th. For pure natural convection, a Nuc correlation as a function of RaW is obtained. A simplified calculation of the total heat transfer, Nut, is proposed.