Analytical approach for the temperature distribution in the casting-mould heterogeneous system

Abstract

Purpose The main purpose of this paper is to calculate the analytical solution or a closed-form solution for the temperature distribution in the heterogeneous casting-mould system. Design/methodology/approach First, the authors formulate and analyze the mathematical formulation of heat conduction equation in the heterogeneous casting-mould system, with an arbitrary assumption of the ideal contact at the cast-mould contact point. Then, He-Laplace method, based on variational iteration method (VIM), Laplace transform and homotopy perturbation method (HPM), is used to elaborate the analytical solution of this system. The main focus of He-Laplace method is to find the Lagrange multiplier with an easy approach which enables the implementation of HPM very smoothly and provides the series solution very close to the exact solution. Findings An example is considered to show that He-Laplace method provides the efficient results for calculating the temperature distribution in the casting-mould heterogeneous system. Graphical representation and error distribution represents that He-Laplace method is very simple to implement and effective for casting-mould heterogeneous system. Originality/value The work in this paper is original and advanced. Specially, calculation of Lagrange multiplier for casting-mould system has not been reported in the literature for this work.

Variational Iteration Method for Prediction of the Pull-In Instability Condition of Micro/Nanoelectromechanical Systems

“…Метод предполагает использование множителя Лагранжа для генерации подходящего оптимального корректирующего функционала с использованием вариационной теории и интегральных преобразований [40,41]. В последнее время вариационно-итерационный метод и его различные модификации [42,43], включая вариационно-итерационный метод Хе-Лапласа [21], применяют для решения различных задач [44][45][46], а также для исследования срабатывания в осцилляторах на основе М/НЭМС [7,21]. Однако многие авторы следуют стандартному процессу решения [34], но упрощенный алгоритм приводит к ошибкам.…”

Research Thermal Fields in the Crystallization Process of Steel Cast Parts

“…Balandinsummarized the information on previously conducted calculations and supplemented it with his own developments, on the basis of which he suggested analytical formulas for determining the duration of crystallization and cooling of castings in one-time (nonmetallic) foundry molds. Tese formulas are the basis of most modern analytical methods and software for foundry processes [18].…”