传热学v4-第四章导热数值解法

ShanghaiJiaoTong

Heat SJTU-ShanghaiJiaoTong

Heat 数值计算方法的优点 SJTU-ShanghaiJiaoTong

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HeatSJTU-ShanghaiJiaoTong

Heat对相邻节点写出温度t对内节点(m,nxx:(m,n)的相邻节点为(m+1,nm-y:(m,n)的相邻节点为(m,n+1m,n-X方x2 2xx2 2xtm1,ntm,nxSJTU-ShanghaiJiaoTong

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Heat＝从所有方向流入控制体的总热量从所有方向流入控制体的总热量SJTU-ShanghaiJiaoTong

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对控制体每个界面线（图中虚线）SJTU-ShanghaiJiaoTong

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Heat为什么要建立边界节点为什么要建立边界节点SJTU-ShanghaiJiaoTong边界节点离散方程的推导（热平衡法

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xy m,ntm1,n2xwSJTU-ShanghaiJiaoTong边界节点离散方程的推导（热平衡法

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Heat SJTU-ShanghaiJiaoTongStep-5:（代数）

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......anntn直接解法SJTU-HeatShanghaiJiaoTong SJTU-ShanghaiJiaoTong

HeatStep-5:节点离散（代数）方程的求 k

tt(k1)t(k1)a11t(k)a12t(k)......1121nt(k)b(k1t(k1)221t(k1)22t(k)......2nt(k)b(k2tt(k1t3nt(k)b(k3t(k1)an1t(k1)an2t(k1)......ann1t(k1)annt(k)b(kn12nn在计算后面的节点温度时应采 SJTU-ShanghaiJiaoTong maxt(k1)t(k tt(k1)t(kiit(ki

Heatε为允许的偏差，一般取10-3～10-t(k)

maxtt(k1)t(kiit(k计算域温度存在近于0 计算域温度存在近于0SJTU-ShanghaiJiaoTong

Heat 绝对值的代数和(参 例题4-Step-6:解的分析数值计算中偏差ε总是存在的，增加节点数目可以减小误差。SJTU-ShanghaiJiaoTong

Heat4-4稳态项（扩散项SJTU-ShanghaiJiaoTong

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Heat4-4非稳态导热问题的数值解 Δx为空间步长Δτ

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点 扩散项中心差点SJTU-ShanghaiJiaoTong

Heat4-4非稳态导热问题的数值解 x t(i t(inxt(i)tn t(i1)t(innE SJTU-ShanghaiJiaoTong

Heat4-4非稳态导热问题的数值解 tt1

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Heat4-4非稳态导热问题的数值解 NN NN

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Heat4-4 22iii+112a

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Heat4-4 SJTU-ShanghaiJiaoTong附加一、稳态、常物性(导热系数λ),条件下的导热问题为例，进h, h h,SJTU-ShanghaiJiaoTong附加二给出不同迭代方法下，最大相对误差ε的变化历程，并绘图。1）计算可以采用、C等语言（推荐-方便 A=[100123;110224116.811;0018.22;12309.4];% %e1-迭代过程的误差结forx0=[1111whi