Abstract
Objectives: The purposes of this work are to investigate the free convective heat transfer in an axis-symmetric open-ended cavity heated from below and to propose useful correlations of Nusselt number. Methods: The governing equations that model the fluid flow and the temperature field are solved using a control volume-based finite differences method. Under steady state condition, the natural convective flow is considered to be laminar, incompressible and axisymmetric. The Boussinesq approximation with constant thermophysical properties is adopted. Numerical experimentations are performed to deduce the optimum sizes of the calculation domain and the mesh grid. Findings: the obtained results indicate that when Rayleigh number (Ra) and aspect ratio (A) are low the heat transfer is weak and mainly conductive. The increase of Ra and A enhances the convective heat transfer mode thereby the heat transfer is ameliorated. Unlike the Rayleigh Bénard convection, the transition from conduction to convection produces at critical value of Rayleigh number (Rac) that is variable dependent on A. Novelty: To the best of authors knowledge, the formula of (Rac) elaborated in this work for the studied cavity is the first attempt. As well, correlation of Nusselt numbers (Nu) for the cold upper plate in terms of Ra and A is performed. Comparisons between Nu at the lower plate given in previous work and Nusselt number at the upper plate is conducted. Keywords: free convection; circular plates; Nusselt number correlations; open ended cavity; critical Rayleigh number
Highlights
The natural convection heat transfer plays an important role in many applications and industrial processes such as electronics equipment, heat exchangers, and Chemical Vapor Deposition (CVD) reactors
The influence of Rayleigh number and aspect ratio on streamlines, isotherms and Nusselt number are explored for different values of Ra and A
The variation of the Nusselt number is periodic or pseudo-periodic in the radial direction with low values of Nu corresponding to the part of a vortex where the fluid is rising and vice versa for higher values of Nu. The amplitude of these oscillations increases while Rayleigh number increases
Summary
The natural convection heat transfer plays an important role in many applications and industrial processes such as electronics equipment, heat exchangers, and Chemical Vapor Deposition (CVD) reactors. Several challenges are imposed in its study due to the high thermal and hydro-dynamical coupling as well as the strong sensitivity to external disturbances These difficulties grow when flows are encountered in complex geometries such as open cavities. Boetcher and Sparrow(7) accomplished a numerical study of buoyancy induced flow in a horizontal open-ended cavity by means of ANSYS CFX 11.0 software. They discussed thoroughly the relevant numerical issues using enlarged calculation domain, appropriate boundary conditions on the surfaces of the extended domain and meshing to achieve high accuracy. Fu et al(11) conducted a numerical investigation of natural convection in three-dimensional horizontal parallel plates with a heated bottom surface without using Boussinesq approximation. Fu et al (12) concluded that more the space between the plates is narrow more the thermal field and the fluid flow are stable
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