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.

中文翻译：

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铸模异质系统温度分布的解析方法

目的

本文的主要目的是计算异质铸模系统中温度分布的解析解或闭合解。

设计/方法/方法

首先，作者制定并分析了异质铸模系统中热传导方程的数学公式，并任意假设了铸模接触点的理想接触。然后，基于变分迭代法（VIM）、拉普拉斯变换和同伦摄动法（HPM），利用He-Laplace法详细阐述了该系统的解析解。He-Laplace 方法的主要重点是通过一种简单的方法找到拉格朗日乘子，这使得 HPM 的实现非常顺利，并提供了非常接近精确解的级数解。

发现

一个例子表明He-Laplace方法为计算铸模异质系统中的温度分布提供了有效的结果。图形表示和误差分布表明He-Laplace方法实现起来非常简单，对铸模异质系统有效。

原创性/价值

本文的工作具有原创性和先进性。特别是，这项工作的文献中没有报道铸模系统的拉格朗日乘数的计算。