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.

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This paper proposes an algorithm for phase demodulating fringe patterns using a two-dimensional continuous wavelet transform (2D-CWT). This algorithm exploits the isotropy property of the fan mother wavelet conjugated to Shannon entropy to perform the ridge extraction process by using only 2D-CWT arguments. The proposed algorithm’s performance is shown through simulated fringe patterns corrupted by speckle noise. Also, to evaluate the accuracy of the ridge extracted from the modulus to that obtained from the arguments of 2D-CWT, the developed algorithm is compared to the maximum ridge extraction algorithm for 2D-CWT and cost function ridge extraction algorithm for 2D-CWT, which extract the ridge from the 2D-CWT modulus. Furthermore, we demonstrate the ability of the proposed algorithm to demodulate real fringe patterns derived from optical metrology for temperature measurement. The most important result of the proposed method is that it is provably optimal in estimating the 2D-CWT ridge of oriented fringes. The added strength of the algorithm is that it is simpler and has better resistance to speckle noise than previous methods because it employs scalograms of arguments, which are the origin of the definition of the ridge.

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