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## 1D Heat Conduction using explicit Finite Difference Method

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### Implicit Finite difference 2D Heat

Fahad Pervaiz on 31 Aug Vote 0. Answered: michio on 14 Sep Accepted Answer: michio. Cancel Copy to Clipboard. Details paprameters, varaiables, typical values? Accepted Answer. I think pdepe function will work for your problem.Sign in to comment.

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### 2D heat conduction using Matlab

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Travis on 22 Apr Vote 1. Commented: Walter Roberson on 24 Dec I struggle with Matlab and need help on a Numerical Analysis project. The code I've developed so far for the first part is:. I'm having trouble assigning the temperature reference to each node. Once this is complete I will use a matrix method with corresponding boundary conditions.

I'm also required to calculate an exact solution for comparison. My exact solution code so far is as follows. Currently this code doesn't work, causing a matlab error that says "the cell can not be evaluated be cause it contains an incomplete statement. Also, I'm not sure that my code will accurately find a temperature at each node.

Ideally, I will construct 3D plots for each code for comparison.Sign in to comment. Sign in to answer this question. Unable to complete the action because of changes made to the page. Reload the page to see its updated state. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Suchen Answers Clear Filters.

Answers Support MathWorks. Search Support Clear Filters. Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Heat conduction through 2D surface using Finite Difference Equation.

Travis on 22 Apr Vote 1. Commented: Walter Roberson on 24 Dec I struggle with Matlab and need help on a Numerical Analysis project. The code I've developed so far for the first part is:. I'm having trouble assigning the temperature reference to each node.

Once this is complete I will use a matrix method with corresponding boundary conditions. I'm also required to calculate an exact solution for comparison. My exact solution code so far is as follows. Currently this code doesn't work, causing a matlab error that says "the cell can not be evaluated be cause it contains an incomplete statement.

Also, I'm not sure that my code will accurately find a temperature at each node. Ideally, I will construct 3D plots for each code for comparison. Answers 2. Walter Roberson on 22 Apr Vote 0. Cancel Copy to Clipboard.For steady state analysis, comparison of Jacobi, Gauss-Seidel and Successive Over-Relaxation methods was done to study the convergence speed.

The transient case was solved using both implicit and explicit methods and both methods were compared for stability and convergence. The temperaure profile is shown below. Among the three methods, the SOR method was the fastest. The number of iterations till convergence for each case is given in below table. Applying Central Differencing for spacial derivatives, and forward differencing for time derivative.

For transient condition, timestep of 0. SOR of 1. Both implicit and explicit methods were solved and both gave same results. But implicit was slightly faster compared to explicit method. For an end time of 50, implicit took iteration whereas explicit took The temperature profile after 5, 50,and time units let's assume seconds is shown below.

We can see that atit has almost reached steady state. The stabiltiy of explicit and implicit schemes were studied for different CFL numbers. It was found that implicit solution is always stable and gives the same solution for varying CFL. Implicit is independent of CFL, and Von-Neuman stability criterion applies only for explicit schemes.

Therfore, it must become unstable when CFL is greater than 0. In this problem, dt for unstable solution must be 6. But here it becomes unstable when CFL reaches 0. Introduction Adiabatic Flame Temperature is the final temperature of products when one mole of a particular fuel is burnt using the exact stoichiometric amount of air in an insulated box. This is the temperature obtained when the heat of combustion is used to heat u Read more.

In the modern world, diesel engines are used more commonly in trucks, heavy-duty equipment, marine vehicles, and also as backup generators for electricity. It is a challenge to design engines which have a fewer environmental impact, and also good torque-power characteri Read more.

We have been using Internal Combustion IC engines for more than a century now. The engines we use today are much better in performance, efficiency and emit a lot lesser pollutants. There is still a lot more to improvise, and industries are working on new technologies Read more. In this project the Prandtl-Meyer expansion fan was simulated to study compressible flow.Sign in to comment.

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You may receive emails, depending on your notification preferences. Derek Shaw on 15 Dec Vote 1. Answered: youssef aider on 12 Feb Accepted Answer: michio.

Hello I am trying to write a program to plot the temperature distribution in a insulated rod using the explicit Finite Central Difference Method and 1D Heat equation. The rod is heated on one end at k and exposed to ambient temperature on the right end at k. I am using a time of 1s, 11 grid points and a.

When I plot it gives me a crazy curve which isn't right. I think I am messing up my initial and boundary conditions. Here is my code. KSSV on 15 Dec Cancel Copy to Clipboard.

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First place, it is not giving any curve. Please recheck your code once. I am not sure I understand correctly. In the above I wrote this equation to be iterated.

With Boundary conditions. I am not sure how to set these boundary conditions in the code. Or if there is a curve I need to derive before doing the iterations. Accepted Answer.Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance.

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**Transient Conduction, Numerical Method**

Search Support Clear Filters. Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. Heat conduction through 2D surface using Finite Difference Equation. Travis 22 Apr I struggle with Matlab and need help on a Numerical Analysis project. The code I've developed so far for the first part is:. I'm having trouble assigning the temperature reference to each node.

Once this is complete I will use a matrix method with corresponding boundary conditions. I'm also required to calculate an exact solution for comparison. My exact solution code so far is as follows. Currently this code doesn't work, causing a matlab error that says "the cell can not be evaluated be cause it contains an incomplete statement.

Also, I'm not sure that my code will accurately find a temperature at each node. Ideally, I will construct 3D plots for each code for comparison.Finite Difference Equations shown in table 5. Results Transient conduction the origin of the plot is the top left corner of the cross section Transient conduction the origin of the plot is the top left corner of the cross section 1.

Frank P.

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