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

Abstract

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 in constant surface heat flux, while the outer wall is isothermally cooled. Equations of continuity, momentum, and energy were formulated using the dimensionless form in elliptic coordinates for two-dimensional, laminar, and incompressible flow under a steady-state condition, and expressed in terms of vorticity and stream function. The governing equations were discretized by the control volume method. For the thermophysical properties of CNTs, empirical correlations were used in terms of the volume fraction of nanoparticles. For the effective thermal conductivity of CNTs, a new model was used. Modified Rayleigh number (103 R a m 106 ) and volume fraction of nanoparticles (0 0.12). The eccentricity of the inner and outer ellipses and the angle of orientation were fixed at 0.9, 0.6, and 0°, respectively. Results were presented in the form of streamlines, isotherm contours, and distribution of temperature and local and average Nusselt numbers on solid boundaries. The results were also discussed in detail, demonstrating that very good agreement exists between the present results and those from the literature.