Consider the conceptual model presented in the attached image, of heat conduction in a bar.
There is a heat source at left side and heat is observed at point Ho after a distance L from the source. If we consider only heat transfer through conduction then this problem can be modeled by diffusion/heat conduction equation.
If I have developed a new semi-analytical or numerical solution (and eventually code) of this problem, then how can I validate my code?. For simplicity, suppose the source to be sinusoidal. Is there a standard solution for such an ideal case with sine input source, so that I can compare my code and then apply it to real field conditions?
I agree with Luis that you should validate your code with well-known problems that have a solution first. However, I suggest that you do not try to compare yourself to experimental data or other simulation results, but that you look for theoretical problems that have a known analytical solution. When comparing to experiments or other simulations you will never know for sure who is wrong in case your simulation does not match. Certainly, it will not match exactly. With an analytical solution you will have an absolute reference.
I am not sure if there is an analytical solution to your sinusoidal problem. However, I see phases of heating and cooling. So, I would suggest one heating and one cooling simulation (constant heating/cooling, no sine wave). Your best friend is energy conservation. In any simulation you can check if the initial energy + energy input (heating/cooling) over time equals your current total energy. Based on the heat conductivity you should be able to compute for the heating and cooling scenarios how long it takes for the pipe to completely heat up or cool down. Then, you can check if your simulation matches this time.
The solution is given in Wikipedia "Heat equation#Solving the heat equation using Fourier series".
Hello Ather,
I think that the majority of the answer is already given. It is worth mentioning to validate your model with a constant heat supply. First, it is easy to find an analytical solution for this case. Second, a steady-state solution can allow you easily to verify energy conservation. As such, you can verify the correctness of your numerical method. Finally, you can use whatever boundary condition and follow the previous suggestions.
There are many cases deals with yours, and many numerical and experimental works had the same results. Compare your results with the others.
Best Wishes
Dear Mr. Abbas,
I can add to the previous answers the attached file where if I well understood the case, it is a 1-D transient heat conduction. I assume the sinusoidal source is function of time and not space. Hence, by looking at the first couple of pages of this chapter, you can deduce the general solution for the 1-D Transient heat conduction. And by applying your boundary conditions, you should be able to determine the constants in the equation. this way you have an analytical solution for your problem and hence you can compare your code to it. otherwise, in the attached file you have the exact analytical solution for a well know case.
I hope this is helpful to you.
Kind regards
A simple test for a transient load would be a step function at the entry either in temperature or in thermal flux. Such problems are trated in the litterature and you canfind several approaches to compare with.
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