Derivation of heat conduction control partial differential equation:

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**Derivation of Partial Differential Equations for Heat Conduction Control in Rectangular Coordinate System**

**Derivation of Partial Differential Equations for Heat Conduction Control in Cartesian Coordinate System and Supplement to Cylindrical Coordinate System**

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Several small programs related to "Heat Transfer" are summarized as follows, and you can click to experience them on WeChat:

- Automatic mesh generation of finite element triangle element
- The first experience of Delaunay triangulation (theoretical poke this)
- Contour contour drawing (theoretical poke this)
- Finite Element Analysis of 2D Unsteady Temperature Field
- 1D steady-state heat conduction temperature field solution (source code stamp here)
- 1D non-steady-state heat conduction temperature field solver (source code stamp here)
- 2D steady-state heat conduction temperature field solution (source code stamp here)
- Planck blackbody monochromatic radiation

The demonstration animation of the related small program of "Heat Transfer" is as follows (the unsteady heat conduction calculation in Figure 1D below diverges, recalculate after reducing the time step, and the result converges!):

The monochromatic radiation power of a black body is shown in the figure below. It can be seen that the higher the temperature, the greater the radiation power of the same frequency:

Several small programs in "(Computational) Fluid Mechanics" can be clicked and experienced in WeChat:

- Blasius partial differential equation to solve the velocity boundary layer ( theory here )
- The potential flow of the ideal fluid in the pipeline ( source code poke this )
- Vorticity-flow function method to solve the top drive square cavity flow ( source code click here )
- SIMPLE algorithm to solve the top drive square cavity flow ( source code stamp here )
- Demonstration of calculation by Lattice Boltzmann Method ( reference source code )

The demonstration animations of several small programs related to "(Computational) Fluid Mechanics" are as follows:

Demonstration of the "Kaman Vortex Street" of the flow around a cylinder calculated by LBM (=Lattice Boltzmann Method) (due to the small number of grids and low resolution, the cylinder is almost square):

By the way, the simulation of PID controller in "(Thermal Process) Automatic Control" can click here to experience: PID control demonstration applet, (for PID control related videos, see: Basic/Tuning/Important Supplement ). The animation is as follows:

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Reference: https://cloud.tencent.com/developer/article/1549547 The derivation of partial differential equations for heat conduction control Edition2-云+社区-Tencent Cloud