Finite Difference Method using Matlab

[semeer.s]

I am curious to know if anyone has a program that will solve for 2-D Transient finite difference I have an assignment in a heat transfer class and I am supposed to use Matlab to solve for this. The governing equation given here is to solve using finite difference method using matlab.



In this problem we know the heat generated (Q) as 11×10^6 W/m^2.

The material using for this study is aluminum having following material properties

ρ = 2700 kg/m3,
k = 180 W/m-K,
c=896 J/kg-K.


In this study maximum time is allowed as for generated heat (Q) is 0.5 seconds.

The line diagram is enclosed in the attached file..

My assignment is to find out the temperature distribution of the sheet at the end of 0.5 Seconds.
Any help would be appreciated.

 

[Aaron Bex]

There are several different programs available that can be used to solve 2-D transient finite difference problems. Some of the most popular programs include MATLAB, COMSOL, and ANSYS. Each of these programs has a number of tutorials and examples that can help you get started with your problem. Additionally, there are several online resources and forums where you can ask questions or seek assistance from other users.

 

[tacman]

The finite difference method is a numerical technique used to solve partial differential equations, such as the heat transfer equation in this case. This method involves discretizing the domain into a grid and approximating the derivatives in the governing equation using finite difference formulas. Matlab is a powerful tool for solving such problems as it provides a wide range of built-in functions and capabilities for numerical computations.

To solve for the 2-D transient heat transfer problem using the finite difference method in Matlab, you can follow these steps:

1. Define the grid: Define the number of grid points in the x and y directions, and the grid spacing. This will determine the size and resolution of your solution domain.

2. Set boundary conditions: Specify the boundary conditions for your problem, such as temperature or heat flux values at the boundaries. These will be used to solve for the unknown temperatures in the domain.

3. Formulate the finite difference equations: Using the governing equation for heat transfer, discretize the equation using finite difference approximations for the spatial and temporal derivatives. This will result in a set of algebraic equations that can be solved for the unknown temperatures at each grid point.

4. Solve the equations: Use the built-in functions in Matlab, such as "solve" or "fsolve", to solve the set of equations obtained in the previous step. These functions use numerical methods to find a solution for the unknown temperatures at each grid point.

5. Plot the results: Once the solution is obtained, you can use the "contour" or "surf" functions in Matlab to visualize the temperature distribution on the 2-D grid at the end of 0.5 seconds. You can also plot the temperature profiles at different time steps to see the transient behavior of the system.

Overall, solving this problem using the finite difference method in Matlab will involve a combination of coding, using built-in functions, and visualizing the results. I would recommend looking into examples and tutorials on finite difference methods and using Matlab for numerical computations to get a better understanding of the process. Good luck with your assignment!