Example: Heat Flow on a Square Plate

Functions > Solving and Optimization > Differential Equation Solvers > Example: Heat Flow on a Square Plate - I

Example: Heat Flow on a Square Plate - I

Solve for the steady-state temperature distribution of a square plate using the partial differential equation solver multigrid.

Solving Laplace's Equation

Find the temperature T(x,y) of a square plate with a constant internal heat source. The boundary of the source is pinned at zero degrees.

1. Define the dimension of the square plate:

2. Write a Laplace equation, in two variables, to represent points on the plate that are free of the heat source:

3. Set the dimensions of the heat source ρ:

4. Define the position of the heat source:

5. Define the strength of the heat source:

6. Set the number of cycles at each level of multigrid iteration:

7. Use function multigrid to find the solution:

8. Create a 3D plot to show the heat distribution over the square plate:

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9. Create a contour plot to show the lines of constant temperature:

10. Define a different configuration of heat sources positioned at different locations:

11. Set the number of cycles at each level of the multigrid iteration:

12. Use function multigrid to find the solution:

13. Create a 3D plot to show the heat distribution over the square plate:

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14. Create a contour plot to show the lines of constant temperature: