Mixed convection in a lid-driven cavity filled with single and multiple-walled carbon nanotubes nanofluid having an inner elliptic obstacle

Fatih Selimefendigil

Mechanical Engineering Department, Celal Bayar University, Manisa 45140, Turkey

Abstract: In this study, numerical analysis and optimization in a single and multiple walled carbon nanotube-water nanofluid filled lid driven cavity having an inner elliptic obstacle were performed by using finite element method and COBYLA optimization solver. The top wall is moving with constant speed and vertical walls are kept at constant temperatures. An optimal size of the inner elliptic obstacle was determined by using an optimization study to maximize the average heat transfer along the hot wall of the cavity. Numerical simulation was performed by for various values of Richardson numbers (between 0.05 and 50) and various solid particle volume fraction (between 0 and 0.06) for single and multiple-walled carbon nanotubes water nanofluid. A larger obstacle (higher values of radii in the major and minor axis) with lower values of Richardson number results in higher heat transfer rates. The average Nusselt number versus solid particle volume fraction shows a linear trend and the discrepancy between the average Nusselt number for the cavity with the optimized obstacle and other obstacles becomes higher with higher particle volume fraction. The average heat transfer enhances significantly which is about 120.20% for single wall carbon nanotube -water nanofluid at solid volume fraction of 0.06 when compared to pure water.  The discrepancy between the average Nusselt number for single and multiple walled carbon nanotubes becomes higher for higher values of Richardson number and solid particle volume fraction. A polynomial type correlation was proposed for the average Nusselt number along the hot wall which is fifth order for Richardson number an first order for nanoparticle volume fraction.  

Keywords: Lid-driven cavity; Carbon nanotubes; Optimization; Finite element method