对于2-D稳态热模型，计算节点位置和指定点的热流gydF4y2BaxgydF4y2Ba而且gydF4y2BaygydF4y2Ba坐标。gydF4y2Ba

创建稳态分析的热模型。gydF4y2Ba

Thermalmodel = createpde(gydF4y2Ba“热”gydF4y2Ba）;gydF4y2Ba

创建几何图形并将其包含在模型中。gydF4y2Ba

R1 = [3,4，-1,1,1，-1,1,1, 1,1，-1]';g = decsg(R1，gydF4y2BaR1的gydF4y2Ba，（gydF4y2BaR1的gydF4y2Ba) ');geometryFromEdges (thermalmodel g);pdegplot (thermalmodelgydF4y2Ba“EdgeLabels”gydF4y2Ba，gydF4y2Ba“上”gydF4y2Ba) xlim([-1.5 1.5]gydF4y2Ba平等的gydF4y2Ba

假设这个几何图形代表一个铁板，热导率为gydF4y2Ba $$\mathrm{7gydF4y2Ba}\mathrm{9gydF4y2Ba}．gydF4y2Ba\mathrm{5gydF4y2Ba}\mathrm{WgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba\mathrm{米gydF4y2Ba}\mathrm{KgydF4y2Ba}）gydF4y2Ba$$．gydF4y2Ba

thermalProperties (thermalmodelgydF4y2Ba“ThermalConductivity”gydF4y2Ba, 79.5,gydF4y2Ba“脸”gydF4y2Ba1);gydF4y2Ba

在板的底部(边缘3)施加500k的恒定温度。同时，假设板的顶部(边缘1)是绝缘的，并在板的两侧(边缘2和边缘4)施加对流。gydF4y2Ba

thermalBC (thermalmodelgydF4y2Ba“边缘”gydF4y2Ba3,gydF4y2Ba“温度”gydF4y2Ba, 500);thermalBC (thermalmodelgydF4y2Ba“边缘”gydF4y2Ba, 1gydF4y2Ba“HeatFlux”gydF4y2Ba, 0);thermalBC (thermalmodelgydF4y2Ba“边缘”gydF4y2Ba(2 - 4),gydF4y2Ba.．.gydF4y2Ba“ConvectionCoefficient”gydF4y2Ba25岁的gydF4y2Ba.．.gydF4y2Ba“AmbientTemperature”gydF4y2Ba, 50);gydF4y2Ba

网格的几何和解决问题。gydF4y2Ba

generateMesh (thermalmodel);结果= solve(热模型)gydF4y2Ba

results = SteadyStateThermalResults with properties: Temperature: [1541x1 double] XGradients: [1541x1 double] YGradients: [1541x1 double] ZGradients: [] Mesh: [1x1 FEMesh]gydF4y2Ba

评估节点位置的热流。gydF4y2Ba

[qx,qy] = evaluateHeatFlux(results);图pdeplot (thermalmodel,gydF4y2Ba“FlowData”gydF4y2Ba(qx qy))gydF4y2Ba

创建指定的网格gydF4y2BaxgydF4y2Ba而且gydF4y2BaygydF4y2Ba坐标，并评估到电网的热流。gydF4y2Ba

V = linspace(-0.5,0.5,11);[X,Y] = meshgrid(v);[qx,qy] = evaluateHeatFlux(results,X,Y);gydF4y2Ba

重塑gydF4y2BaqTxgydF4y2Ba而且gydF4y2Ba数量gydF4y2Ba向量，并绘制出结果的热通量。gydF4y2Ba

qx =重塑(qx，大小(X));qy =重塑(qy，大小(Y));图颤抖(X, Y, qx、qy)gydF4y2Ba

或者，您可以使用查询点矩阵来指定网格。gydF4y2Ba

querypoints = [X(:) Y(:)]';[qx,qy] = evaluateHeatFlux(结果，查询点);qx =重塑(qx，大小(X));qy =重塑(qy，大小(Y));图颤抖(X, Y, qx、qy)gydF4y2Ba

对于三维稳态热模型，计算节点位置和指定点的热流gydF4y2BaxgydF4y2Ba，gydF4y2BaygydF4y2Ba,gydF4y2BazgydF4y2Ba坐标。gydF4y2Ba

创建稳态分析的热模型。gydF4y2Ba

Thermalmodel = createpde(gydF4y2Ba“热”gydF4y2Ba）;gydF4y2Ba

创建以下3-D几何图形，并将其包含在模型中。gydF4y2Ba

importGeometry (thermalmodelgydF4y2Ba“Block.stl”gydF4y2Ba）;pdegplot (thermalmodelgydF4y2Ba“FaceLabels”gydF4y2Ba，gydF4y2Ba“上”gydF4y2Ba，gydF4y2Ba“FaceAlpha”gydF4y2Ba, 0.5)标题(gydF4y2Ba“铜块，厘米”gydF4y2Ba)轴gydF4y2Ba平等的gydF4y2Ba

假设这是一个铜块，块的热导率约为gydF4y2Ba $$\mathrm{4gydF4y2Ba}\mathrm{WgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba\mathrm{cgydF4y2Ba}\mathrm{米gydF4y2Ba}\mathrm{KgydF4y2Ba}）gydF4y2Ba$$．gydF4y2Ba

thermalProperties (thermalmodelgydF4y2Ba“ThermalConductivity”gydF4y2Ba4);gydF4y2Ba

在砌块的左侧(面1)施加373 K的恒温，在砌块的右侧(面3)施加573 K的恒温。gydF4y2Ba

thermalBC (thermalmodelgydF4y2Ba“面子”gydF4y2Ba, 1gydF4y2Ba“温度”gydF4y2Ba, 373);thermalBC (thermalmodelgydF4y2Ba“面子”gydF4y2Ba3,gydF4y2Ba“温度”gydF4y2Ba, 573);gydF4y2Ba

在块的底部应用热流边界条件。gydF4y2Ba

thermalBC (thermalmodelgydF4y2Ba“面子”gydF4y2Ba4gydF4y2Ba“HeatFlux”gydF4y2Ba, -20);gydF4y2Ba

网格的几何和解决问题。gydF4y2Ba

generateMesh (thermalmodel);热结果=解决(热模型)gydF4y2Ba

thermalresults = SteadyStateThermalResults with properties: Temperature: [12691x1 double] XGradients: [12691x1 double] YGradients: [12691x1 double] ZGradients: [12691x1 double] Mesh: [1x1 FEMesh]gydF4y2Ba

评估节点位置的热流。gydF4y2Ba

[qx,qy,qz] = evaluateHeatFlux(热流结果);图pdeplot3D (thermalmodel,gydF4y2Ba“FlowData”gydF4y2Ba，[qx qy qz])gydF4y2Ba

创建指定的网格gydF4y2BaxgydF4y2Ba，gydF4y2BaygydF4y2Ba,gydF4y2BazgydF4y2Ba坐标，并评估到电网的热流。gydF4y2Ba

[X,Y,Z] =网格(1:26:100,1:6:20,1:11:50);[qx,qy,qz] = evaluateHeatFlux(热流结果，X,Y,Z);gydF4y2Ba

重塑gydF4y2Baqx、gydF4y2Ba，gydF4y2BaqygydF4y2Ba,gydF4y2Ba求出gydF4y2Ba向量，并绘制出结果的热通量。gydF4y2Ba

qx =重塑(qx，大小(X));qy =重塑(qy，大小(Y));qz =重塑(qz，大小(Z));图quiver3 (X, Y, Z, qx, qy,求出)gydF4y2Ba

或者，您可以使用查询点矩阵来指定网格。gydF4y2Ba

querypoints = [X(:) Y(:) Z(:)]';[qx,qy,qz] = evaluateHeatFlux(热流结果，查询点);qx =重塑(qx，大小(X));qy =重塑(qy，大小(Y));qz =重塑(qz，大小(Z));图quiver3 (X, Y, Z, qx, qy,求出)gydF4y2Ba

在一个方形区域上求解二维瞬态换热问题，并计算通过对流边界的热流。gydF4y2Ba

为这个问题建立一个热模型。gydF4y2Ba

Thermalmodel = createpde(gydF4y2Ba“热”gydF4y2Ba，gydF4y2Ba瞬态的gydF4y2Ba）;gydF4y2Ba

创建几何图形并将其包含在模型中。gydF4y2Ba

G = @squareg;geometryFromEdges (thermalmodel g);pdegplot (thermalmodelgydF4y2Ba“EdgeLabels”gydF4y2Ba，gydF4y2Ba“上”gydF4y2Baxlim([-1.2 1.2]) ylim([-1.2 1.2]gydF4y2Ba平等的gydF4y2Ba

指定以下热特性:热导率为gydF4y2Ba $$\mathrm{1gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{WgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}）gydF4y2Ba$$，质量密度为gydF4y2Ba $$\mathrm{7gydF4y2Ba}\mathrm{8gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{kgydF4y2Ba}\mathrm{ggydF4y2Ba}/gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\mathrm{3.gydF4y2Ba}}$$，比热为gydF4y2Ba $$\mathrm{5gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{JgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba\mathrm{kgydF4y2Ba}{\mathrm{ggydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}）gydF4y2Ba$$．gydF4y2Ba

thermalProperties (thermalmodelgydF4y2Ba“ThermalConductivity”gydF4y2Ba, 100,gydF4y2Ba.．.gydF4y2Ba“MassDensity”gydF4y2Ba, 7800,gydF4y2Ba.．.gydF4y2Ba“SpecificHeat”gydF4y2Ba, 500);gydF4y2Ba

在三棱处应用绝缘边界条件，在右棱处应用自由对流边界条件。gydF4y2Ba

thermalBC (thermalmodelgydF4y2Ba“边缘”gydF4y2Ba，[1 3 4]，gydF4y2Ba“HeatFlux”gydF4y2Ba, 0);thermalBC (thermalmodelgydF4y2Ba“边缘”gydF4y2Ba2,gydF4y2Ba.．.gydF4y2Ba“ConvectionCoefficient”gydF4y2Ba, 5000,gydF4y2Ba.．.gydF4y2Ba“AmbientTemperature”gydF4y2Ba25);gydF4y2Ba

设置初始条件:均匀的室温跨域和较高的温度在顶部边缘。gydF4y2Ba

thermalIC (thermalmodel 25);thermalIC (thermalmodel, 100,gydF4y2Ba“边缘”gydF4y2Ba1);gydF4y2Ba

生成一个网格并解决问题gydF4y2Ba0:1000:200000gydF4y2Ba作为时间的向量。gydF4y2Ba

generateMesh (thermalmodel);Tlist = 0:1000:200000;Thermalresults = solve(thermalmodel,tlist);gydF4y2Ba

创建指定的网格gydF4y2BaxgydF4y2Ba而且gydF4y2BaygydF4y2Ba坐标，并评估到电网的热流。gydF4y2Ba

V = linspace(-1,1,11);[X,Y] = meshgrid(v);[qx,qy] = evaluateHeatFlux(热流结果，X,Y,1:长度(tlist));gydF4y2Ba

重塑gydF4y2Baqx、gydF4y2Ba而且gydF4y2BaqygydF4y2Ba，并绘制出第25步溶液的热通量。gydF4y2Ba

tlist (25)gydF4y2Ba

Ans = 24000gydF4y2Ba

图颤抖(X (:), Y (:), qx (:, 25) qy (:, 25));xlim([1])轴gydF4y2Ba平等的gydF4y2Ba

求解下面由不同材料制成的正方形和菱形组成的二维几何图形的传热问题。计算热通量，并把它画成一个矢量场。gydF4y2Ba

为瞬态分析创建热模型。gydF4y2Ba

Thermalmodel = createpde(gydF4y2Ba“热”gydF4y2Ba，gydF4y2Ba瞬态的gydF4y2Ba）;gydF4y2Ba

创建几何图形并将其包含在模型中。gydF4y2Ba

Sq1 = [3;4;0;3;3;0;0;0;3;3); D1 = [2; 4; 0.5; 1.5; 2.5; 1.5; 1.5; 0.5; 1.5; 2.5]; gd = [SQ1 D1]; sf =“于SQ1 + D1”gydF4y2Ba；Ns = char(gydF4y2Ba“于SQ1”gydF4y2Ba，gydF4y2Ba“D1”gydF4y2Ba）;Ns = Ns ';Dl = decsg(gd,sf,ns);geometryFromEdges (thermalmodel dl);pdegplot (thermalmodelgydF4y2Ba“EdgeLabels”gydF4y2Ba，gydF4y2Ba“上”gydF4y2Ba，gydF4y2Ba“FaceLabels”gydF4y2Ba，gydF4y2Ba“上”gydF4y2Ba) xlim([-1.5 4.5]) ylim([-0.5 3.5]gydF4y2Ba平等的gydF4y2Ba

对于正方形区域，分配以下热特性:热导率为gydF4y2Ba $$\mathrm{1gydF4y2Ba}\mathrm{0gydF4y2Ba}\mathrm{WgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}）gydF4y2Ba$$，质量密度为gydF4y2Ba $$\mathrm{2gydF4y2Ba}\mathrm{kgydF4y2Ba}\mathrm{ggydF4y2Ba}/gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\mathrm{3.gydF4y2Ba}}$$，比热为gydF4y2Ba $$\mathrm{0gydF4y2Ba}．gydF4y2Ba\mathrm{1gydF4y2Ba}\mathrm{JgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba\mathrm{kgydF4y2Ba}{\mathrm{ggydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}）gydF4y2Ba$$．gydF4y2Ba

thermalProperties (thermalmodelgydF4y2Ba“ThermalConductivity”gydF4y2Ba10gydF4y2Ba.．.gydF4y2Ba“MassDensity”gydF4y2Ba2,gydF4y2Ba.．.gydF4y2Ba“SpecificHeat”gydF4y2Ba, 0.1,gydF4y2Ba.．.gydF4y2Ba“脸”gydF4y2Ba1);gydF4y2Ba

对于菱形区域，分配如下热特性:热导率为gydF4y2Ba $$\mathrm{2gydF4y2Ba}\mathrm{WgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}）gydF4y2Ba$$，质量密度为gydF4y2Ba $$\mathrm{1gydF4y2Ba}\mathrm{kgydF4y2Ba}\mathrm{ggydF4y2Ba}/gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\mathrm{3.gydF4y2Ba}}$$，比热为gydF4y2Ba $$\mathrm{0gydF4y2Ba}．gydF4y2Ba\mathrm{1gydF4y2Ba}\mathrm{JgydF4y2Ba}/gydF4y2Ba（gydF4y2Ba\mathrm{kgydF4y2Ba}{\mathrm{ggydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}）gydF4y2Ba$$．gydF4y2Ba

thermalProperties (thermalmodelgydF4y2Ba“ThermalConductivity”gydF4y2Ba2,gydF4y2Ba.．.gydF4y2Ba“MassDensity”gydF4y2Ba, 1gydF4y2Ba.．.gydF4y2Ba“SpecificHeat”gydF4y2Ba, 0.1,gydF4y2Ba.．.gydF4y2Ba“脸”gydF4y2Ba2);gydF4y2Ba

假设该菱形区域是一个密度为的热源gydF4y2Ba $$\mathrm{4gydF4y2Ba}\mathrm{WgydF4y2Ba}/gydF4y2Ba{\mathrm{米gydF4y2Ba}}^{\mathrm{3.gydF4y2Ba}}$$．gydF4y2Ba

internalHeatSource (thermalmodel 4gydF4y2Ba“脸”gydF4y2Ba2);gydF4y2Ba

涂上恒温的gydF4y2Ba $${\mathrm{0gydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}$$在方板的两侧。gydF4y2Ba

thermalBC (thermalmodelgydF4y2Ba“温度”gydF4y2Ba，0,gydF4y2Ba“边缘”gydF4y2Ba，[1 2 7 8]);gydF4y2Ba

设置初始温度为gydF4y2Ba $${\mathrm{0gydF4y2Ba}}^{\circ gydF4y2Ba}\mathrm{CgydF4y2Ba}$$．gydF4y2Ba

thermalIC (thermalmodel 0);gydF4y2Ba

网格的几何和解决问题。gydF4y2Ba

generateMesh (thermalmodel);gydF4y2Ba

这个问题的动态过程非常快:温度在大约0.1秒内达到稳定状态。要捕获动态中有趣的部分，请将解决方案时间设置为gydF4y2Balogspace (2, 1, 10)gydF4y2Ba．这给出了10个对数间隔的解时间，介于0.01和0.1之间。解这个方程。gydF4y2Ba

Tlist = logspace(-2，-1,10);Thermalresults = solve(thermalmodel,tlist);温度=热结果。gydF4y2Ba

计算热流密度。使用等高线绘制解的等温线，并使用箭头绘制热通量矢量场。gydF4y2Ba

[qTx,qTy] = evaluateHeatFlux(热流结果);图pdeplot (thermalmodel,gydF4y2Ba“XYData”gydF4y2Ba临时(:10),gydF4y2Ba“轮廓”gydF4y2Ba，gydF4y2Ba“上”gydF4y2Ba，gydF4y2Ba.．.gydF4y2Ba“FlowData”gydF4y2Ba[qTx(: 10)数量(:,10)),gydF4y2Ba.．.gydF4y2Ba“ColorMap”gydF4y2Ba，gydF4y2Ba“热”gydF4y2Ba）gydF4y2Ba