All Questions
Tagged with heat-transfer pde
7 questions
0
votes
0
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128
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Heat Equation for fast source with FiPy
I'm trying to solve the following differential equation with FiPy, basically laser irradiation on a surface
$$
\rho_{s}C_{p,s}\frac{\partial T}{\partial t} = k_{s}\frac{\partial^{2}T}{\partial x^{2}} +...
- 11
1
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0
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50
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How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?
I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
- 11
1
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0
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115
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Accuracy of the Crank-Nicolson method for non-linear, inhomogeneous heat equation
I am currently coding a solution to the following PDE:
$\frac{\partial T }{\partial t} =\frac{\partial}{\partial \theta}(A(\theta ,\phi )\frac{\partial T }{\partial \theta}) +\frac{\partial }{\partial ...
- 11
1
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2
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811
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How to use the Thomas-Algorithm to the Heat-diffusion-equation correctly
My post is structured in four parts:
I give you some information about the context my principal questions refer to.
I will tell you what I believe to know about the Thomas Algorithm. If I am wrong ...
- 11
1
vote
0
answers
953
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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 ...
- 21
1
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0
answers
212
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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 ...
- 23
0
votes
1
answer
853
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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\,,...
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