FULLY-DEVELOPED FLOW AND HEAT-TRANSFER IN SEMIELLIPTIC DUCTS

A control volume-based numerical solution is described for the fully developed laminar flaw and heat transfer in ducts of semi-elliptical cross section. Both an isothermal and a uniform axial heat flux condition on the duct walls have been considered. Numerical results for velocity and temperature profiles, friction factor, pressure defect, and Nusselt number are presented for a wide range of duct aspect ratios from 0.1 to 0.999. Comparison with earlier numerical results for the limiting case of semicircular duct and with analytical solution for fully elliptical ducts is excellent. For ducts in which the baseplate is on the major axis, friction factor and Nusselt number for the uniform heat flux condition increase as the aspect ratio decreases, with values for the lowest aspect ratio of 0.1 being about 25 percent larger than those for a semicircular duct. For ducts with the baseplate on the minor axis, all characteristics exhibit a nonmonotonic behavior with respect to the aspect ratio. While the maximum velocity and pressure defect exhibit a mild maximum for aspect ratio of 0.6, the friction factor and Nusselt number exhibit a minimum at the same aspect ratio. The ratio of Nusselt number to friction factor is higher for semi-elliptical ducts in comparison to that for other ducts, such as sinusoidal,circular segmental, and isosceles triangular ducts.