Two-dimensional analysis of natural convection and radiation in utilidors

Abstract

Central heating plants are often used on large building complexes such as university campuses or military bases. Utilidors can be used to contain heat distribution lines and other utilities between a utility station and serviced buildings. Traditional thermal analysis of utilidors is one-dimensional, with heat transfer correlations used to estimate the effects of convection, radiation, and two-dimensional geometric effects. The expanding capabilities of computers and numerical methods suggest that more detailed analysis and possibly more energy-efficient designs could be obtained. This work examines current methods of estimating the convection and radiation that occur across an air space in square and rectangular enclosures and compares them with numerical and experimental data. A numerical model was developed that solves the energy, momentum, and continuity equations for the primitive variables in two dimensions; radiation between free surfaces was also included. Physical experiments were conducted with two 10-ft-long apparatuses; one had a 1-ft $\times$ 1-ft cross section, the other was 2 ft $\times$ 4 ft. Several pipe sizes and configurations were studied with the 1-ft $\times$ 1-ft apparatus. The 2-ft $\times$ 4-ft apparatus was limited to containing 4- and 8-inch insulated pipes. Corresponding numerical studies were conducted. Difficulties in modeling large enclosures or those with large temperature differences (Rayleigh numbers above 10$\sp7$) were encountered. Results showed good agreement between numerical and experimental average heat transfer rates, and for insulated pipe cases these results also compared well with rates obtained from one-dimensional analysis. A new effective conductivity correlation for air in a square enclosure was developed, and its use was demonstrated in numerical conduction solutions and compared with full numerical convection and radiation solutions and with experimental data. Reasonably good results were achieved when there was a small temperature difference across the air gap.