Natural Convection in a Vertical Heated Tube Attached to a Thermally Insulated Chimney of a Different Diameter

Abstract

Natural convection is often a convenient and inexpensive mode of heat transfer. It is commonly employed in the cooling of electronic equipment and many other applications. Since the initial work by Bodoia and Osterle (1962) on finite difference solutions of natural convection between vertical isothermal plates, many other researchers have studied natural convection in vertical channels. Specifically Davis and Perona (1971) studied natural convection in vertical heated tubes. A thermally insulated chimney attached to a vertical heated channel induces an increase in the natural convection in the channel and leads to a higher heat transfer rate. This is the well-known chimney effect discussed in the paper by Haaland and Sparrow (1983). If the chimney diameter is larger than the heated tube diameter, the friction loss in the chimney region decreases with increasing chimney diameter. This induces an increase in the mass flow rate and leads to a higher heat transfer rate than the case for a chimney of the same diameter. However, from a geometric consideration it is evident that the chimney effect diminishes in the limiting case of an extremely large chimney diameter compared with its height. Therefore, there exists an optimum diameter where the heat transfer is maximum.more » To investigate the chimney effect computations are carried out for a Rayleigh number of 12.5, based on the heated tube radius, and for a Prandtl number of 0.7. The numerical results are based on a control volume finite difference method. The average Nusselt number results are compared with the numerical results obtained for a chimney attached to a tube of the same diameter.« less