A fluid-like element for flow and heat convection problems

Application of mixed order finite element method to solve the laminar flow and heat convection problems is presented in this study. Solutions in primitive variables are obtained using the T4/C3 mini element on unstructured grids. The T4/C3 element is an element with the fewest degrees of freedom which also meets the LBB condition. Meanwhile, with one extra node in the triangle element, the T4/C3 element is more capable to represent the realistic phenomena of flow and heat transfer by taking the central physical behavior of triangle into consideration. This numerical approach has been validated by the applications of two test cases: natural convection in a differentially heated square cavity and forced convection in a sudden expansion. The approach is then applied to predict the flow over a heated channel with the opposite walls roughened by three pairs of repeated transverse ribs. Based on the numerical validations and experiments, the good numerical performance of applying the developed model in T4/C3 elements is verified.