基于热传导方程的最优速度模型

The Optimal Velocity Model Based on the Heat Conduction Equation

摘要: 本文主要研究回焊炉内的热传导问题。我们将回焊炉简化为一维热传导模型进行分析，建立基于差分方程的热传导模型，从而得到焊接区域中心温度变化情况。根据约束条件通过变步长搜索方法、离散化、五重循环遍历算法方法，对目标优化模型进行求解。以温度分布模型为基础，我们建立以允许的最大传送带过炉速度为目标的单变量优化模型。在一维非稳态热传导模型基础上，我们改变初始条件和边界条件，用变步长搜索进行求解。运用MATLAB编程，我们得到满足此优化模型里的全部约束条件的最大传送带过炉速度为96 cm/min。

Abstract: In this paper, we mainly research on the problem of heat conduction in a reflow furnace .We simplify the reflow furnace into a one-dimensional heat conduction model to analyze and establish heat conduction model based on difference equation, then we obtain the variation of the central temperature of the welding zone. According to the constraints condition, we solve the objective optimization model using the variable step-size search method, discretization, five-loop traversal algorithm. Based on the temperature distribution model, we set up the single variable optimization model with the maximum allowable convey or pass rate as a goat. Based on a one-dimensional unsteady heat conduction model, we change the initial and boundary conditions, use variable step size search to solve. Through Matlab program, we obtain the maximum passing velocity of the conveyor belt is 96 cm/min, which satisfies all the constraints in the optimization model.