heat transfer in block with cavity -凯发k8网页登录

create model with geometry

the first step in solving this heat transfer problem is to create an femodel object for thermal analysis with a geometry representing a block with a cavity.

model = femodel(analysistype="thermaltransient", ...
                geometry=@crackg);

plot geometry

plot the geometry with edge labels.

pdegplot(model,edgelabels="on");
xlim([-0.6,0.6])
ylim([-1,1])

specify thermal properties of material

specify the thermal conductivity, mass density, and specific heat of the material.

model.materialproperties = ...
            materialproperties(thermalconductivity=1, ...
                               massdensity=1, ...
                               specificheat=1);

apply boundary conditions

specify the temperature on the left edge as 100 and constant heat flow to the exterior through the right edge as -10. the toolbox uses the default insulating boundary condition for all other boundaries.

model.edgebc(6) = edgebc(temperature=100);
model.edgeload(1) = edgeload(heat=-10);

set initial conditions

set an initial value of 0 for the temperature.

model.faceic = faceic(temperature=0);

generate mesh

generate a mesh and assign the result to the model. this assignment updates the mesh stored in the geometry property of the model. plot the mesh.

model = generatemesh(model);
figure
pdemesh(model);
title("mesh with quadratic triangular elements")

specify solution times

set solution times to be 0 to 5 seconds in steps of 1/2.

tlist = 0:0.5:5;

calculate solution

calculate the solution by using the solve function.

results = solve(model,tlist)

results = 
  transientthermalresults with properties:
      temperature: [1320×11 double]
    solutiontimes: [0 0.5000 1 1.5000 2 2.5000 3 3.5000 4 4.5000 5]
       xgradients: [1320×11 double]
       ygradients: [1320×11 double]
       zgradients: []
             mesh: [1×1 femesh]

evaluate heat flux

compute the heat flux density.

[qx,qy] = evaluateheatflux(results);

plot temperature distribution and heat flux

plot the solution at the final time step, t = 5.0 seconds, with isothermal lines using a contour plot, and plot the heat flux vector field using arrows.

figure
pdeplot(results.mesh,xydata=results.temperature(:,end), ...
                     contour="on",...
                     flowdata=[qx(:,end),qy(:,end)], ...
                     colormap="hot")