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 ow and heat transfer of al2o3-water nanouid inside polygonal ducts with round corners for the constant heat ux and uniform wall temperature boundary conditions. using the method, semi-analytical, closed-form solutions are obtained for the friction coecient and the nusselt number in terms of the radius of the round corners for the triangular, rectangular, hexagonal, and octagonal ducts. the eects of varying the radius of the round corners and the volume fraction of the nanoparticles on the friction coecient 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 ecient technique to obtain closed-form solutions for the ow and temperature elds in ducts with complex cross-sectional shapes.