A numerical study of the natural convection of laminar heat transfer in the stationary state in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder was investigated. This annular space is traversed by a Newtonian and incompressible fluid. The Prandtl number is set to 0.71 (air case) for different Rayleigh numbers. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The inner and outer surfaces are isothermal. The study was performed for Rayleigh numbers ranging from 1.3 × 10 3 to 5.5× 10 5. Particularly, we have studied the effects of different thermal Rayleigh numbers on natural phenomenon convection. The results were presented in the form of isotherms, streamlines, and local and average Nusselt numbers. The purpose of this study is to observe the influence of the thermal Rayleigh number on the structure of the flow and distribution of the temperature.

A numerical study of the natural convection of laminar heat transfers in the stationary state in a half-elliptic inclined cavity, which represents a continuation of the work done, we studied the influence of the tilt of the cavity by varying the angle — entered 0 degrees, which corresponds to the horizontal cavity, up to 15 degrees. For each value of δ we varied the Rayleigh number from 2.13 103 to 106. The system of equations governing the problem solved numerically by the fluent calculation code based on the finite volume method. Based on the Boussinesq approximation. Both bottom and upper walls maintained at a constant temperature. The interest of this study is to see the influence of the tilt of the half-elliptic cavity on the structure of the flow and the distribution of temperature. These results can exploited in semi-elliptic agricultural greenhouses that rest on sloping soils. We chose a Prandtl number 0.71 that corresponds to the air. Keywords: Heat transfer; half-elliptical; Natural convection; Laminar flow; Multicellular; CFD simulation

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A NaCeP2O7 compound was successfully synthesized by a high-temperature reaction with the solid-state method.

This paper is the first part of a two-part study, and it presented numerical research of double-diffusive natural convection within an annulus area, situated in two horizontal confocal elliptic solids charged by a Newtonian fluid. The elliptical coordinates were used to transform the physical domain into a rectangular one. To resolve the governing equations and the boundary layer conditions, a calculator code based on the finite volume approach was developed. The details of the influences of thermal Rayleigh number on heat and mass transfer were investigated. Results obtained were compared with those existing in other reasearch works. K E Y W O R D S double-diffusive, elliptical cylinders, natural convection, Rayleigh number, stream function formulation