This thesis, large eddy simulation of turbulent heat transfer in stationary and rotating square ducts, is a record of some research work done by Zhaohui Qin in Iowa State University from 2002 to 2007 for his Ph.D. degree.;Five major studies are described in detail after an introduction of the large eddy simulation methodology. These five studies are: incorporating the Navier-Stokes characteristic boundary conditions (NSCBC) into the lower-upper symmetric Gauss-Seidel (LU-SGS) scheme; investigating the thermally developing turbulent flow through stationary square ducts under strong heating with large eddy simulation; studying the turbulent heat transfer in rotating square ducts with large eddy simulation; analyzing the velocity field and instability of rotating duct flow and computing rotating nano-scale channel flow with molecular dynamics simulation.;The incorporation of the NSCBC with LU-SGS enables us to simulate developing flow and flows in complex geometries, which cannot be handled by conventional periodic boundary conditions. This method is used in the large eddy simulations in this thesis. From the simulations of turbulent heat transfer through stationary square ducts, it can be concluded that strong heating causes the flow to become laminar-like. Also heat transfer is found to have obvious impact on the secondary flows, which in turn have major effects on the distributions of wall shear stress and wall heat flux. Another influence of heat transfer on the flow is that heating tends to decrease the magnitude of turbulent Prandtl number and make its distribution more uniform.;In the turbulent flow in a heated rotating duct, buoyancy changes the streamwise velocity and secondary flow pattern through a delicate force balance. And these changes influence the Nusselt number and mean shear stress distributions. Buoyancy also affects turbulent kinetic energy and temperature fluctuation distributions through its contributions to the corresponding production terms.;By combining the solutions of linear Stewartson layer, non-linear Ekman layer and a local-similarity assumption, the flow field inside a fully developed rotating square duct is given analytically. By using linear stability analysis, the onset of the instabilities of the Stewartson layer, the Ekman layer and the abrupt changes of the drag curves are investigated and good agreements are reached between the present theory and experiments. Many different features are discovered for instabilities of the non-linear Ekman layer from its linear counterpart.;Molecular dynamics simulation is employed to investigate a liquid flow in rotating nano-scale channels. Couette flow and Poiseuille flow are used to verify the code. Then flow through two rotating geometries, a rectangular box and a cubic box, are simulated. As the rotation number increases, the streamwise velocity profile becomes more unsymmetrical and the number density gradient increases. It is also observed the multi-layer structures become more obvious at one wall while contrary trend shows at another wall as rotation number increases.