Turbulent natural convection in an enclosure with localized heating from below

Abstract

This study reports the results of a numerical investigation of turbulent natural convection in a square enclosure with localized heating from below and symmetrical cooling from the vertical side walls. The present study simulates the case of an accidental heat generation due to fire in a typical isolated building of a nuclear reactor or electronic components cabin. The source of fire is considered to be centrally located at the bottom wall with different heated widths, which is assumed to be either isothermal or with isoflux. For the purpose of the analysis, the source length is varied from 20 to 80% of the total width of the bottom wall. The top wall and the unheated portion of the bottom wall are considered to be adiabatic, whereas sidewalls are isothermal. Steady as well as transient forms of two-dimensional Reynolds–Averaged-Navier–Stokes equations and conservation equations of mass and energy, coupled with the Boussinesq approximation, are solved by the control volume based discretisation method employing the SIMPLE algorithm for pressure–velocity coupling. Turbulence is modeled using the standard k – ε model. Rayleigh number, Ra, based on the enclosure height is varied from 10 8 to 10 12. Stream lines and isotherms are presented for various combinations of Ra and the heated width. A double cell flow pattern is observed with marginal loss in symmetry as Ra increases. The results are reported in the form of local and average Nusselt number on the heated floor. Correlations are developed to predict the heat transfer rates from the enclosure as a function of dimensionless heated width of the bottom wall and Ra, by least square linear regression analysis.