Low-order models for transitional forced convective flow and heat transfer

Present study focuses on developing low-dimensional models for transitional forced convective flow and heat transfer in a periodically grooved channel. The full governing partial differential equations with appropriate boundary conditions are solved by a spectral element method. Proper orthogonal decomposition is used to extract the empirical eigenfunctions at Re=430. Using the empirical eigenfunctions as basis functions in a truncated series expansion and applying Galerkin's method, a low-dimensional system of non-linear ordinary differential equations is obtained. Expansion coefficients computed based on the low-order model and by direct projection of the full model data are found to be in very good agreement. Four modes for both velocity and temperature are the smallest set capable of predicting stable, self-sustained oscillations with correct amplitude. It is found that keeping more modes than necessary in the expansion may reduce the accuracy and restrict the validity of the low-order models due to the noise introduced by the low energy level higher modes.