东南大学传热学二维稳态差分接点计算论文

1、二维稳态计算实验报告 王# 能源与环境学院 03012#一、题目要求二、各节点离散化代数方程取研究节点为，其上部节点温度用T表示，下部节点温度用B表示，左侧节点温度用L表示，右侧节点温度用R表示。该题目各节点离散化代数方程可分为四个区域：区域一：=区域二：=区域三：=区域四：=三、源程序Jacobi迭代计算代码（C#）：for (int n = 0; n 6; n+) mg0m, n = newButton();mg0m, n.Text = mgm, n.Text.ToString (); for (int m = 1; m 4; m+) int n = 1;double t = Conver

2、t.ToDouble(mg0m - 1, n.Text.ToString();double b = Convert.ToDouble(mg0m + 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();double r = Convert.ToDouble(mg0m, n + 1.Text.ToString();double center = (200 + t + 2*r + b) / 24;mgm, n.Text =center.ToString();mgm, n.BackColor = Co

3、lor.LightBlue; for (int m = 1; m 4; m+) for (int n = 2; n 5; n+) double t = Convert.ToDouble(mg0m - 1,n.Text.ToString();double b = Convert.ToDouble(mg0m + 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();double r = Convert.ToDouble(mg0m, n + 1.Text.ToString();double cente

4、r = (l + t + r + b) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 4; m 5; m+) int n = 1;double t = Convert.ToDouble(mg0m - 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();double r = Convert.ToDouble(mg0m, n + 1.Text.ToString();double

5、 center = (100 + t + r) / 12;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int n = 2; n 5; n+) int m = 4;double t = Convert.ToDouble(mg0m - 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();double r = Convert.ToDouble(mg0m, n + 1.Text.ToString();d

6、ouble center = (2*t + r + l) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; j = Convert.ToDouble(mg1, 1.Text.ToString();for (int m = 0; m 6; m+) for (int n = 0; n 6; n+) mg0m, n = newButton();mg0m, n.Text = mgm, n.Text.ToString(); 高斯（Gauss）-赛德尔（Seidel）迭代计算代码（C#）：for (int m =

7、1; m 4; m+) int n = 1;double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double b = Convert.ToDouble(mgm + 1, n.Text.ToString();double l = Convert.ToDouble(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mgm, n + 1.Text.ToString();double center = (200 + t + 2*r + b) / 24;mgm, n.Text =cent

8、er.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 1; m 4; m+) for (int n = 2; n 5; n+) double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double b = Convert.ToDouble(mgm + 1, n.Text.ToString();double l = Convert.ToDouble(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mgm, n

9、+ 1.Text.ToString();double center = (l + t + r + b) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 4; m 5; m+) int n = 1;double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double l = Convert.ToDouble(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mgm,

10、 n + 1.Text.ToString();double center = (100 + t + r) / 12;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int n = 2; n 5; n+) int m = 4;double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double l = Convert.ToDouble(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mg

11、m, n + 1.Text.ToString();double center = (2 * t + r + l) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; 四、不同初值时的收敛快慢将从0100的不同初值代入，均已绝对误差小于等于0.001为收敛条件。以迭代次数为纵坐标，初值为横坐标作图。1.采用Jacobi迭代计算时的最佳初值可看到当初值=77时，最小迭代次数为7次。2.高斯（Gauss）-赛德尔（Seidel）迭代计算时的最佳初值可看到当初值=88时，最小迭代次数为7次。五、上下边界的热流量上

12、边界热流量：=解得，=358.99W。下边界热流量：下边界绝热 =0。六、计算结果的等温图七、计算小结本次实验的目的是研究二维稳态导热问题计算效率的影响因素，运用MATLAB，C#等计算工具，从迭代方法，初值设置等方面研究计算效率。得出以下结论：1.迭代计算方法G-S迭代计算方法优于Jacobi迭代计算方法。因为G-S迭代方法在每次计算中都用到周围节点的最新计算值，该值比初值更接近于稳态值，所以一定程度上减少了计算步骤。2.初值设置通过将不同初值代入并比较运算次数，结合图线我们可以找到迭代计算的最佳初值，在该初值下迭代计算最少的次数便可达到收敛条件。G-S迭代法与Jacobi的最佳初值不同。研究最佳初值的设置可以帮助我们在工程中提高实际传热问题的计算效率。3.稳态温度等值线由稳态温度等值线我们可以发现