Pressure drop in pipes can be calculated by using the Darcy-Weisbach formula. In order to use this formula, the Darcy friction factor should be known. The best approximation to the Darcy friction factor for turbulent flow is given by the Colebrook-White equation. This equation can only be solved by numerical root finding methods. There are several other approximate correlations to the Darcy friction factor with some relative error compared to the Colebrook-White equation. It was found that in some of these correlations, the percentage error is so small that they can be used directly in place of the Colebrook equation. In this study, a review of several friction factor correlations is performed. Relative error of these correlations is re-evaluated against the Reynolds number for a different value of relative pipe roughness. Also statistical analyses will be given for each correlation.

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In this study, a numerical analysis of the inward solidification of phase change material inside spherical capsule is carried out. The spherical capsule that is subjected to convection from the outside surface initially is not at its melting temperature. The control volume approach and temperature transforming method are applied to solve the dimensionless energy equation. The model solution results are validated through a comparison with published experimental data for similar case and it shows a considerably good agreement. The analysis results show that the larger diameter spherical capsules have significantly greater solidification time compared to those with smaller diameters of spherical capsules. In addition, the entropy generation inside spherical capsule is analyzed. It is found that the entropy generation increases with increasing sphere capsule diameter, attains a maximum and then decreases. Ó 2016 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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