Numerical solution of partial differential equations for lid-driven fluid flow and heat transfer analysis with no-slip and free-slip effects / Wong Hon Fei - Wong , Hon Fei (2021)
Thermal fluid is a branch of science and engineering that covers the application of experimental research and mathematical modeling based on fundamental laws from physics, heat transfer and fluid dynamics. The great significance of thermal fluids can be seen in phase transition and chemical reactions. Perhaps two-dimensional lid-driven model is the simplest model to demonstrate the study of the thermal fluids. The behavior of fluid that filled inside the lid-driven cavity when subject to different boundary conditions (free-slip and no-slip), different aspect ratios and different steady-state criteria are studied extensively. The partial differential equations of time-dependent vorticity-stream function and thermal energy equation are discretized and solved using finite difference method. All the codes were written and solved inside Matlab® environment and the results were verified using commercial engineering simulation software named Ansys Fluent®. For the first study, an analysis of time dependent stream-function of fluid to identify patterns of forming, merging and unmerging of additional eddy is presented when steady-state condition with different criteria are achieved. Due to numerical error, it is also observed that the value of stream function begins to drop and streamline distribution changes shape after achieving steady-state criterion of . Also, damage of merging and formation of additional eddy happens until the free-slip boundary condition effect passes the threshold value. For the second study, the iteration process focuses on dissipation of viscous-heating through a transient conduction process of the entire liquid filled inside the lid-driven 6 10  e cavity. The time–dependent fluid flow and heat transfer with viscous heating process are depicted by contour plot and image plot inside Matlab® environment. For the third study, Robin boundary condition is adopted rather than Neumann boundary condition which employed in the second study. Moreover, heat transfer analysis is extended to cooling process in the third study. The effects of viscous heating coupled with several other physical parameters, namely Reynolds, Prandtl, Peclet and other numbers are examined. Finally, a simple graphical user interface is developed using Matlab® to facilitate the end user in analyzing the fluid flow.