COMPUTATION OF HEAT AND FLUID FLOW IN DUCTS OF ARBITRARY CROSS SECTION

Abstract

This paper reports on connective heat transfer in irregular ducts maintained under a constant wall temperature. In particular, due to the complexity of the geometry, the paper investigates in detail the fluid flow and convective heat transfer in right-triangular and semicircular ducts. The hydrodynamically fully developed flow and the developing temperature in these geometries are obtained analytically/numerically from the solution of the energy equation employing the method of lines. The energy equation is reformulated by a system of a first-order differential equation controlling the temperature along each line. It was found that reliable closed-form solutions for the temperature distribution in the thermal entrance region can be obtained utilizing 21 lines, or less, displayed in the cross-stream direction of the duct. The grid pattern chosen provides: drastic savings in computing time. Results for the thermal entry region flow heat transfer are presented in tabular and graphical forms. The representative curves illustrating the variation of bulk temperature and Nusselt numbers with pertinent parameters in the entire thermal entry region are plotted. The computed results are compared against some analytical/numerical findings reported in the literature. In all cases, satisfactory comparison is obtained. The asymptotic Nusselt numbers are 1.90, 2.25, and 2.29 for 15°, 30°, and 45° right-triangular ducts, respectively, and 6.030 for semicircular ducts