How to Optimize a 2D Nonlinear Heat Conduction Solver in MATLAB?

Dirichlet boundary conditions. He is open to any suggestions or code from others who may have experience with this type of problem. In summary, Chetan is seeking help with optimizing his code for a non-linear heat conduction equation in 2 dimensions.
  • #1
range.rover
16
0
Hi friends,

i have developed an code for a non linear heat conduction in 2 dimensions with dirichlet boundary condition by finite difference method in Matlab. my code is running slow to give output.
If anybody has any idea of solving this equation or have written any Code for this equation, please share it with me.
Any body who has worked on this can share the idea with me.

(d2t/dx2 + d2t/dy2)(K(t)) = Q
K(t)= (a - b*t) ; a>>b.
 
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  • #2
If K represents the thermal conductivity, then this formulation is incorrect. It should read:
[tex]\frac{\partial}{\partial x}\left(K(T)\frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(K(T)\frac{\partial T}{\partial y}\right)=Q[/tex]
Chet
 

FAQ: How to Optimize a 2D Nonlinear Heat Conduction Solver in MATLAB?

1. What is the Poisson 2D non linear equation?

The Poisson 2D non linear equation is a partial differential equation that describes the behavior of a non linear system. It is often used in physics, engineering, and mathematics to model phenomena such as heat conduction, fluid flow, and electrostatics.

2. How is the Poisson 2D non linear equation solved?

The Poisson 2D non linear equation is typically solved using numerical methods, such as the Finite Difference Method (FDM). This involves discretizing the equation and solving it iteratively to approximate the solution.

3. What is the Finite Difference Method (FDM)?

The Finite Difference Method (FDM) is a numerical method used to solve partial differential equations. It involves approximating the derivatives in the equation using finite differences and solving the resulting system of equations iteratively.

4. What are the advantages of using FDM to solve the Poisson 2D non linear equation?

Some advantages of using FDM to solve the Poisson 2D non linear equation include its simplicity, efficiency, and versatility. FDM can handle a wide range of boundary conditions and can be easily implemented on a computer.

5. What are the limitations of using FDM to solve the Poisson 2D non linear equation?

One limitation of using FDM to solve the Poisson 2D non linear equation is that it can be computationally expensive for large and complex systems. Additionally, FDM may not always provide accurate solutions for highly non linear systems and may require careful selection of grid size and time step for convergence.

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