A decomposition solution of variable thickness absorber plate solar collectors with power law dependent thermal conductivity

We present a mathematical model of flat-plate solar collector whose thermal conductivity is a power law function of temperature, and non-dimensional length is governed by a profile index. The rectangular, convex and triangular shape absorber plates are obtained by changing the value of an index of non-dimensional length 0, ½ and 1, respectively. The energy equation governing the temperature of rectangular absorber plate is a non-singular-type equation, and convex and triangular cross-section absorber plate are two different singular type equations. One non-singular and two different singular value equations are solved separately by different operators, as explained separately in classical and modified Adomian decomposition method (ADM) theory respectively. The results obtained for the case of the rectangular, convex and triangular cross-section plate are validated by comparison with the exact analytical solution for special case as available in literature. The effects of various thermo-physical parameters such as power law thermal conductivity parameter, Biot number, aspect ratio, absorbed solar heat flux, overall heat transfer coefficient on the temperature distribution are analyzed.

Influence of the Geometrical Cross-Section Design on the Dynamic Cyclic Fatigue Resistance of NiTi Endodontic Rotary Files—An In Vitro Study

The aim of this study was to analyze and compare the influence of the geometrical cross-section design on the dynamic cyclic fatigue resistance of NiTi endodontic rotary files. Materials and Methods: Forty sterile endodontic rotary files were selected and distributed into the following study groups: A: 25.06 double S-shaped cross-section NiTi alloy endodontic rotary files (Mtwo) (n = 10); B: 20.04 rectangular cross-section NiTi alloy endodontic rotary files (T Pro E1) (n = 10); C: 25.04 convex triangular cross-section NiTi alloy endodontic rotary files (T Pro E2) (n = 10); and D: 25.06 triangular cross-section NiTi alloy endodontic rotary files (T Pro E4) (n = 10). A cyclic fatigue device was used to conduct the static cyclic fatigue tests with stainless steel artificial root canal systems with 200 µm and 250 µm apical diameter, 60° curvature angle, 3 mm radius of curvature, 20 mm length, and 4% and 8% taper. The results were analyzed using the ANOVA test and Weibull statistical analysis. Results: All the pairwise comparisons presented statistically significant differences between the time to failure and number of cycles to failure for the cross-section design study groups (p < 0.001). Conclusions: the double S-shaped cross-section of Mtwo NiTi endodontic files shows higher cyclic fatigue resistance than the rectangular cross-section of T Pro E1 NiTi endodontic files, the convex triangular cross-section of T Pro E2 NiTi endodontic files, and the triangular cross-section of T Pro E4 NiTi endodontic files.

Torsion of a growing prismatic bar with triangular cross-section made of a functional-graded material

В работе рассматривается задача о кручении растущего стержня треугольного сечения, изготовленного из вязкоупругого стареющего функционально-градиентного материала, с интегральными краевыми условиями на торцах. Изучается процесс непрерывного наращивания под действием крутящего момента. Предлагаются методы решения поставленных краевых задач путем приведения задач теории наращивания к задачам теории упругости с внутренним параметром. Приводятся формулы расшифровки для восстановления истинных параметров напряженно-деформированного состояния. Исследуется распределение интенсивности касательных напряжений на различных стадиях процесса наращивания. Приводятся расчеты задачи кручения призматического стержня с сечением в форме правильного треугольника. The paper considers the problem of torsion of a growing triangular cross-section bar made of a viscoelastic aging functionally-graded material with integral boundary conditions at the ends. The process of continuous growth under the influence of torque is studied. Methods for solving the set boundary value problems by reducing the problems of the growth theory to the problems of the theory of elasticity with an internal parameter are proposed. Deciphering formulas are given to restore the true parameters of the stress-strain state. The distribution of the shear stress intensity at different stages of the growth process is investigated. Calculations of the problem of torsion of a prismatic bar with a cross-section in the form of a regular triangle are presented.