# Questions tagged [heat]

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8 questions
38 views

### Finite difference coupled PDE solution to 1D heat-reaction equation

I am trying to solve a coupled PDE for a thermal runaway reaction using finite difference method. I have 2 variables, temperature (T) and concentration (c) that vary as a function of time (t) and ...
35 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 ...
153 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 ...
201 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 ...
205 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 ...
370 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 ...
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\,,...
For the heat equation $$u_t(t,x) = \nu u_{xx}(t,x)$$ 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 ...