Investigation of fully developed ow and heat transfer through n-sided polygonal ducts with round corners using the Galerkin weighted residual method

The Galerkin weighted residuals method is extended solve the laminar, fully developed flow and heat transfer of Al2O3-water nano fluid inside polygonal ducts with round corners for the constant heat flux and uniform wall temperature boundary conditions. Using the method, semi{analytical, closed{form solutions are obtained for the friction coefficient and the Nusselt number in terms of the radius of the round corners for the triangular, rectangular, hexagonal, and octagonal ducts. The effiects of varying the radius of the round corners and the volume fraction of the nanoparticles on the friction coefficient and the Nusselt number are analyzed. The results show that the friction factor and the average Nusselt number increase with increasing the radius of the round corners. The study indicates that the Galerkin weighted residuals method is an accurate and efficient technique to obtain closed{form solutions for the ow and temperature fields in ducts with complex cross{sectional shapes.