Three-Dimensional Laminar Heat Transfer and Fluid Flow Characteristics in the Entrance Region of a Rhombic Duct

A solution methodology is developed to obtain three-dimensional fluid flow and heat transfer characteristics in the entrance region of a rhombic duct. Owing to the complexity of the geometry, the literature results are limited to the fully developed values. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for three-dimensional parabolic flows, which reduces the problem to a series of two-dimensional problems. The Nusselt number and friction factor results are obtained for boundary conditions of uniform wall heat flux and uniform wall temperature. The asymptotic values of the Nusselt numbers and friction factors approach the available fully developed results. The entry length results for the limiting case of φ = 90 deg are in perfect agreement with the available experimental and numerical results for a rectangular duct.