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We describe an Abel inversion method for tomographic reconstruction of an axisymmetric medium. The essence of this method is the approximation of data by Chebyshev wavelets. A numerical method and operational matrices are proposed. The accuracy of the method is tested in terms of the noise coefficient. The studied method is compared with the Legendre wavelets method. The results show that the proposed method is less sensitive to noise. We also demonstrate the efficiency of the developed method by obtaining good and expected results for the inversion of interferometric data.

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

This paper summarizes a numerical and experimental investigation of free convective heat transfer in an open‐ended cavity between two horizontal parallel circular plates. The upper plate is maintained at an ambient temperature and the lower one is heated. Air is used as the heat transfer medium. The numerical model equations are solved using a control volume‐based finite differences method, and the experimental study was performed using holographic interferometry. Streamlines and isotherm patterns are presented and discussed for different aspect ratios (A) and Rayleigh numbers (Ra). Heat transfer at the surface of the lower plate is thoroughly inspected in the ranges 0.1≤A≤1 and 102≤Ra≤5×106. Useful correlations of Nusselt numbers in terms of Ra and A are given with their validity ranges. Also, an investigation of both numerical and experimental results is performed. It shows similar temperature field aspect with some differences in the radial boundary layer thickness and a small deviation in the heat transfer.