The natural convection fluid flow and heat transfer in an annulus of two differentially heated confocal elliptic cylinders filled with the Cu–water nanofluid are investigated numerically. The outer cylinder is maintained at a constant temperature Tc while the inner cylinder is kept at a differentially higher constant temperature Th. Equations of continuity, momentum, and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional steady, laminar, and incompressible flow, which is expressed in terms of stream function, vorticity, and temperature. The basic equations are discretized using the finite-volume method. Using a developed code, calculations were performed for Rayleigh number (103 ≤ Ra ≤ 3 × 105), volume fraction of nanoparticles (0 ≤ ϕ  ≤ 0.12), and eccentricity of the inner ellipse, ε1 = 0.7, 0.8, and 0.9. The eccentricity of outer ellipse and the angle of orientation are fixed at 0.6 deg and 0 deg, respectively. Results are presented in the form of stream lines, isotherm plots, and local and average Nusselt numbers. The results discussed in this present work show the existence of a very good agreement between the present results and those from the previous researches.

In this paper, free convection heat transfer in an annulus between confocal elliptic cylinders lled with CNT-water nano uid is investigated numerically. The inner cylinder is in constant surface heat ux, 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 ow 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 e ective thermal conductivity of CNTs, a new model was used. Modi ed Rayleigh number (10 3 Ra m 10 6 ) and volume fraction of nanoparticles (0 0:12). The eccentricity of the inner and outer ellipses and the angle of orientation were xed 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.

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In this research, a numerical study was carried out on heat transfer by natural convection, in a closed tunnel greenhouse, in the range of the Rayleigh number (10 3 ≤Ra≤10 6 ). Were considered in the study, the number of heating tubes used (1≤Nt≤7), which were equidistant inside the greenhouse volume, when the bottom at an average temperature and cold Roof. The governing equations written in a bicylindrical coordinates were discretized using the finite volume method and vorticity-stream function formulation; the resulting algebraic equations were solved using successive over relaxation method (S.O.R). First, the effect of the Rayleigh number on heat transfer was examined for a fixed number of tubes as reference (Nt = 3) and the number of tubes was varied to investigate the influence on heat transfer in the greenhouse. Finally, the results obtained were summarized in the form of isotherms and streamlines, and for the average Nusselt number profile; in addition to the horizontal and vertical velocities and temperatures. However, in the reference case, for low Rayleigh numbers, the heat transfer is dominated by pure conduction.With the increase of the Rayleigh number and the number of tubes Nt, the natural convection becomes more dominant and the heat transfer increases, and in general the heat transfer increase with the increasing number of tubes.