Abstract:
The mixed convection between two concentric horizontal cylinders with physical properties which depend on temperature is presented in this three-dimensional numerical study of laminar, viscous and incompressible flow. The fluid considered is water with a Prandtl number equal to 8.082 and its viscosity and thermal conductivity are considered variable functions of the temperature. The thermal conditions are as follows: a uniform volume heating produced by an internal source of energy in the thickness of the outer cylinder, while the inner cylinder is adiabatic. The mixed convection generated in the fluid, and the thermal conduction in the wall of the outer cylinder are at the origin of a conjugated thermal transfer. The thermal losses by radiation and convection towards the ambient are considered. The flow and thermal fields are modeled by the continuity equation, momentum and energy equations with appropriate initial and boundary conditions using a cylindrical coordinate system. The system of nonlinear partial differential equations is solved by a finite volume numerical method with second order accurate spatiotemporal discretizations. The mesh used in this study is 26 × 44 × 162 in the radial, azimuth and axial directions respectively. In this study, two adimensional control parameters are fixed: the Reynolds numbers, which indicates the flow dynamics, and the Prandtl number which is a physical characteristic of the fluid, are equal respectively, 373.28 and 8.082. While the geometric aspect ratio equal 277.77. By varying the number of Grashof, which indicate the effect of, buoyancy forces on the flow. We study its effects on the two modes of convection, forced and mixed. For geometric, dynamic and thermal control parameters considered, the results of the flows and thermal fields of forced convection and mixed convection with varying physical properties were presented and compared. The passage from forced convection to mixed convection completely changes the axisymmetric structure of thermal and dynamic fields; this change becomes more and more important by increasing the number of Grashof. For the Grashofs numbers studied, a secondary flow develops in the polar plane in the form of two contrarotating vortices, is always the cause of the circumferential variation of the temperature and in consequence, the physical properties of the fluid. The phenomenon of stratification of temperature is highlighted and the vortices obtained lead to an improvement of the heat transfer quantified by the increase of the number of Nusselt. The thermo-dependence of the properties is well evidenced with a stratified behavior in any polar plane and an axial variation more important for the viscosity than for the conductivity.
