Natural convection of CNT-water nanofluid in an annular space between confocal elliptic cylinders with constant heat flux on inner wall

In this paper, free convection heat transfer in an annulus between confocal elliptic cylinders filled with CNT-water nanofluid is investigated numerically. The inner cylinder is at constant surface heat flux while the outer wall is isothermally cooled. Equations of continuity, momentum and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional, laminar and incompressible flow under steady state condition, which is expressed in terms of vorticity and stream function. The governing equations are discretized using the control volume method. For the thermo-physical properties of CNTs, empirical correlations are used in terms of the volume fraction of nanoparticles. For the effective thermal conductivity of CNTs, a new model has been used. The study is performed for modified Rayleigh number (103≤ Ram ≤106), volume fraction of nanoparticles (0≤ f ≤0.12). The eccentricity of the inner and outer ellipses and the angle of orientation are fixed at 0.9, 0.6 and 0°, respectively. Results are presented in the form of streamlines, isotherm contours, and distribution of temperature and local and average Nusselt numbers on solid boundaries. The results are also discussed in detail and a very good agreement exists between the present results and those from the literature.