Friction factors and nusselt numbers for laminar flow in ducts

Abstract

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable.