# Tag Info

## Hot answers tagged heat-transfer

Accepted

### Flux sign and face normal confusion in finite volume method

When dealing with conservation laws like your case, you can often make use of the divergence theorem (as you did). You can then express the fact that the total mass within your integration region is ...
• 2,985
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### Solving geodesics on triangular meshes gives negative distances

The solution to the final Poisson equation is defined only up to an additive constant. So you just need to shift the solution vector so the smallest value is zero.
• 156
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### 2D Heat equation solved with finite element method converges in skewed way

The problem was that the LHS of the weak form was wrong, the correct one is: $$-\int u_{x} v_{x} + u_{y} v_{y} dxdy$$ Instead of $$-\int (u_{x}+u_{y}) (v_{x}+v_{y})dxdy$$ Thanks to whpowell96 for ...
Accepted

### Problem with my Octave code (unsteady heat equation with FEM)

Reading quickly through your code, it seems that you never update B. So the term $T^n$ of the previous step remains unchanged, hence you are effectively computing the same step over and over again... ...
• 1,943

### Two-dimensional heat equation with Neumann boundary conditions: any hope to find an analytical solution?

Expanding (sort of) on @MPIchael's answer, you can pick any smooth function you like and plug it into the heat equation to give a problem to then work the other way. In numerical methods, we call this ...
• 10.9k
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### Physical interpretation of L2 norm of heat equation solution

In these slide there are some comments about the energy. At pag 4 it focus on the fact that this energy is not a physical energy, but it is a mathematical tool. At pag 8 it observes that: From ...
• 1,340
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### Lumped matrices in thermal analysis using finite elements

No, you can't lump the $K$ matrix: that would not be a consistent approximation to the second-order differential operator it is supposed to represent. But if you're trying to be a bit more formal, ...
• 55.7k
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### Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?

The answer is quite simple: You have to set the Neumann boundary condition $u_x(-1,x)=0$ explicitly Add following line (fifth line): ...
• 1,379
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### Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression

numpy arrays and methods are incredibly helpful. They are usually optimized and much faster than looping in python. Always look for a way to use an existing numpy method for your application. ...
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### Finite Difference Grid Spacing and Scaling

Let's assume the following heat transient heat transfer equation in 1D : $$\frac{\partial T} {\partial t} = \alpha \frac{\partial^2 T}{\partial x^2}$$ If we take its finite difference ...
• 1,157
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### Heat equation with Neumann and Dirichlet conditions on same boundary

In the comments Christian directed me towards lateral Cauchy problems and the fact that this is a textbook example of an ill-posed problem. Following this lead, I found that this is more specifically ...
• 531

### (FEM) 1D time-dependent heat equation convergence problem

From the comments, I believe you are struggling with the FEM formulations and therefore fail to see what happens if the diffusion coefficient tends to zero. I don't have access to your book, but I ...
• 172

### Simulating the heat equation with insulating material

Why even bother to simulate the left half? Why not just simulate the right half with the left BC being the constant value? Seems simpler and more accurate to what you want to actually model, because ...
• 2,089

1 vote
Accepted

### Heat diffusion - Is this the correct approach to include Newmann boundary conditions?

The choice of the boundary conditions is dependent on the physics you want to model. If you're doing heat diffusion through a lake, and you want constant temp on top you'll have a different boundary ...
• 2,089
1 vote

### Modeling Diodes in Autodesk CFD

The natural convection of the oil shouldn't be an issue and can be solved without any 'assumptions' to be made. The challenge comes with the diodes temperature control. CFD doesn't currently have a ...

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