Optimization of Heat Transfer Model Based on Greedy Algorithm
Authors: Jiang Min Hao , Chen Yu Fan , Gu Yu Jie , Song HaoZe 
Published: June 2021

Abstract
Aiming at the problem of furnace temperature curve, this paper uses Fourier’s law of heat conduction and Newton’s law of cooling to establish a heat transfer model to obtain the temperature changing law of the welding area and the furnace temperature curve; uses the single-objective optimization model to establish the maximum conveyor belt passing speed and find out the optimal temperature for each temperature zone; the greedy algorithm and traversal search are used to obtain the undetermined parameters of the dual-objective model through local optimization. In response to question 1, it is required to study the temperature change in the center of the welding area. First, we set the heat transfer model from heat conduction law and convection heat transfer law. The interface of the reflow furnace is two-dimensional: the conveyor belt direction is the x-axis and the vertical direction of the reflow furnace is the y-axis. The energy balance method is used to find the relationship between the x and y-axis heat conduction to establish a differential equation, after then we use Newton Cooling Law and the temperature distribution in the reflow furnace and establish the difference equation of the welding zone temperature. This paper uses the numerical calculation to solve the differential equation sets, obtaining the statistics of the temperatures at intervals of 0.5s. The theoretical furnace temperature curve is drawn as well. The second problem requires the maximum furnace passing speed of the conveyor belt after the temperature of each zone was determined and the constraints of the process limit must be met. A single-objective optimization model was established in this paper and the maximum conveyor belt speed was taken as the objective function. Without exceeding the constraints of the problem, the maximum conveyor belt passing speed was 92.6cm/min after the computer finished the programme. For problem three, it is required to find out the suitable temperature of each zone and the belt-speed, making the area minimized which is covered by the temperature curve exceeding 217°C and under the peak point. This paper establishes a single-objective optimization model, where the objective function is the minimum coverage area; the constraints are the same as the five constraints above in question 2. We use the programming software to search the feasible solution: the temperature of the preheating zone is 167 °C, the temperature of the constant temperature zone 6 is 185.1°C, the temperature of the constant temperature zone 7 is 225°C, the temperature of the reflow zone is 259.2°C, and the passing speed of the conveyor belt is 91.2cm/min. For question four, it is required to make the furnace temperature curve as symmetrical to the peak value as possible while considering the coverage area. This paper defines the symmetry coefficient to quantify the peak symmetry. On this basis, a dual-objective optimization model is first established, and then the coverage area in the objective is converted into constraint conditions, which is transformed into a single-objective optimization problem, and the unknown parameters are finally determined. The full traversal search needs to determine 5 parameters so the calculation is time-consuming. Therefore, we first use the greedy algorithm to solve some of the local optimal parameters, and then use the full traversal search to simplify the calculation. The final result: the temperature of the preheating zone is 169.5°C, the temperature of the constant temperature zone 6 is 185°C, the temperature of the constant temperature zone 7 is 225°C, the temperature of the reflow zone is 258.7°C, the furnace passing speed of the conveyor belt is 90.4cm/min. Finally, the model established in this paper is discussed and analyzed, the model established is comprehensively evaluated, and the conclusion is made.