Natural Convection Heat Transfer In Horizontal Elliptic Cavity With Eccentric Circular Inner Cylinder

The present work comprises a mathematical analysis of natural convection heat transfer in a horizontal elliptic cavity containing eccentric circular cylinder with different aspect ratios. The gap between two cylinders was full with Al2O3/water nanofluid. The external elliptic cavity was preserved at fixed temperature TC. Whereas, the circular cylinder was heated at fixed temperature Th. The stream function–vorticity method was employed to solve the governing equations. The governing equations are discretized utilizing the way of finite volume and resolved via code of FORTRAN. The aspect ratios between the two major axes were 0.3, 0.4, and 0.5. The values of Rayleigh number and volume fraction were (Ra = 104, 105, 𝑎𝑛𝑑 106) and (𝜙 = 0.0, 0.1, and 0.2); respectively, with Prandtl number equal to 6.2. Results show that the angular distribution of local Nusselt number for the inner and outer cylinders depends on Rayleigh number, aspect ratio, nanoparticles volume fraction, and eccentric of inner cylinder. It was concluded that, the average Nusselt numbers for case a (𝐸𝑥 = 0.2, 𝐸𝑦 = 0) and case b (𝐸𝑥 = 0, 𝐸𝑦 = 0.2) are close to each other with a slight increasing for case b relative to c. The higher Nusselt numbers were produced by case d (𝐸𝑥 = 𝐸𝑦 = 0.2), while the lower values occur at case a (𝐸𝑥 = 𝐸𝑦 = 0).