This study aims to develop a numerical model that can simulate the heat transfer in spherical coordinates and predict the temperature of olive fruit during the thermal process. The first step was to measure or estimate the thermophysical properties of olive fruit. The fixed grid finite difference method with an explicit scheme was used to solve the heat transfer equation. The product had an average geometric diameter of 18.18 mm, a bulk density of 556 kg/m3, a porosity of 48% and a specific heat of 3180 kJ/kg. The inverse method was used to determine the thermal conductivity of olive fruit, which was 0.44 W/m°C. The model was validated by comparing the predicted values with the experimental temperature profiles obtained during the thermal process of the fruit (correlation coefficient higher than 0.99 and mean squared error lower than 1.8°C). The sensitivity coefficient results indicated that the surrounding temperature and the diameter of the product were the most influential parameters on the heat transfer of the product. The model was effective in simulating the thermal processing of olive fruit. The research results can be applied to optimize the pasteurization process of olive fruit.

The main objective of this study is to present a mathematical model for frictional forces in orthodontic tooth movements. In order to produce lighter and more efficient sliding movement, good estimation of frictional forces must be determined. For the purpose of analysis, a typical bracket with a circular cross section arch wire is considered with a view to examine the effect of ligation technique (shape), geometry and properties of ligature, and arch wire on the friction forces between ligature and arch wire. Both uniform and non-uniform distributions of contact forces are considered. The result presented herein indicated that, for circular orthodontic arch wires, friction force between ligature and wire is proportional to tensile force in elastomeric ligature. This force is depended on the shape of ligation, material properties and geometries of wire, bracket and ligature.

Background and Aim: As central incisors have a prominent role in esthetics, appropriate preparation, considering natural tooth anatomy and proper planes have always been considered. The aim of this study was to determine the number of planes in labial surface of maxillary central incisors using image processing and mathematical analysis.Materials and Methods: This pilot study was performed on 32 intact maxillary central incisors in dental students of Tehran University of medical sciences. Photographs were taken from profile view of each tooth by a digital camera. Images were processed and number of planes was obtained using Sigma Scan Pro. Version 5.00 software and a customized program. Data were analyzed by t-test and regression tests with p<0.05 as the level of significance.Results: 96.9% of central incisors had three planes and 3.1% had two planes in labial surface. The angle between middle-cervical and middle-incisal planes showed statistically significant difference (p< 0.01).Conclusion: Based on the results of this study, a few percentages of maxillary central incisors had two planes and most of them had three planes in their labial surfaces. Thus, considering three planes for restoring maxillary central teeth is closer to principles of tooth preparation and esthetics.