Questions tagged [heat-transfer]

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Produce vertex displacements from volumetric shrinkage data on unstructured meshes

I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh? ...
2
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1answer
66 views

Lumped matrices in thermal analysis using finite elements

The governing equation of the transient heat transfer problem is $$C \frac{dT}{dt}+K T = Q$$ $C$ is the heat capacity matrix. $K$ is the thermal conductivity matrix. $T$ is the temperature vector. $...
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2answers
83 views

Simulating the heat equation with insulating material

My plan is to solve the heat equation in the right half portion of the domain, while having the left half completely isolated with constant temperature. To do so, I model the left half with a very low ...
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2answers
337 views

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

I'm simulating a simple 3-node bar with convection BCs at the edges to validate my FEM code. The following data was used: Initial temperature = 25 ºC Temperature surrounding the rod = 10 ºC Thermal ...
0
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1answer
183 views

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

Thank you for looking at this problem. Is this the correct approach to include neumann boundary conditions? With this solution temperature is not correct, and there´s no diffusion. The model seems ...
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1answer
2k views

Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression

Hello all, I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ...
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1answer
41 views

Modeling Diodes in Autodesk CFD

I'm extremely new to Autodesk CFD, and I'm working on a project that deals with diodes heating up and cooling down based on a fixed temperature regulated by a temperature switch. Basically, I have a ...
2
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1answer
171 views

Solve 3-D Heat equation with Neumann boundaries

I want to solve the Poisson PDE for heat flow in a 3-D solid cube with given dimensions $x$, $y$, and $z$: $$\rho C\frac{\partial T}{\partial t} = k \Delta T$$ The cube is irradiated with a constant ...
1
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1answer
104 views

Analytical testcase for 2D/3D anisotropic Diffusion (Heat Kernel)

I want to verify and compare different Discretizations of the anisotropic diffusion equation in 2D / 3D. In order to both test the timestepping and the spatial discretisations I had a look at using ...
8
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1answer
275 views

Computing geodesic distances with diffusion

I am trying to solve an APSP (All-Pair Shortest Path) problem on a weighted graph. This graph is actually a 1, 2 or 3 dimensional grid, and the weights on each edge represent the distance between its ...
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1answer
40 views

Solving the diffusion/heat equation for a randomly distributed set of points in 3D

In this problem I am trying to solve, I have a messy set of points distributed in 3D space, each with a defined temperature. If I would want to calculate the heat transfer scenario in this system, how ...
1
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0answers
418 views

Methods and tools to solve the two-temperature model (TTM)

I would like to model heat diffusion at the gold / water interface after excitation of the metal surface by an ultrafast laser pulse (ca. 80 fs). An appropriate model to start with would be the "two ...
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0answers
107 views

BTCS-like method for heat conduction in unstructured triangular grid

I want to write a simple simulation for heat conduction in a unstructured triangular mesh. I already made it work for a structured rectangular grid with the ADI method, but now I need more complex ...
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2answers
239 views

V-cycle Multigrid for 2D transient heat transfer on a square plate using finite difference

I'm currently developing a program to solve 2D transient state heat conduction on a square plate using the V-cycle multigrid. Althought my program is able to reach the steady state solution, it's ...
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2answers
537 views

Finite Difference Grid Spacing and Scaling

I have been exploring finite differences and heat transfer using the 2D heat equation to further expand my knowledge. So far I think it is going well. I am running into some confusion around grid ...
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1answer
559 views

Heat equation with Neumann and Dirichlet conditions on same boundary

I am looking at numerical solutions to the heat equation with Dirichlet and Neumann conditions on the same boundary. That is $u(x,t)$ satisfying $$ u_t = u_{xx}\,, \quad x \in[0,1]\,, \quad t>0\,,...
0
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1answer
320 views

Physical interpretation of L2 norm of heat equation solution

For the heat equation \begin{equation} u_t(t,x) = \nu u_{xx}(t,x) \end{equation} for $x \in [0,1]$ with boundary conditions $u(t,0) = u(t,1) = 0$ and initial value $u(0,x) = u_0(x)$ it is easy to ...