Questions tagged [heat-equation]
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148 questions
0 votes
0 answers
66 views
The heat conduction equation of solar cells can't be solved [duplicate]
The heat conduction equation of solar cells can't be solved. NDSolveValue::ndnum: Encountered non-numerical value for a derivative at x == 0. ...
- 61
2 votes
3 answers
248 views
Heat equation with b.c. at $+\infty$ and i.c. at $-\infty$
I am wondering what is the best way to solve numerically a initial-boundary value problem of heat equation like this (surely I've made a lot of mistakes in the code): ...
- 651
7 votes
1 answer
213 views
Heat equation, NeumannValue and RegionBoundary issues
Context I am interested in solving (no outgoing flux) heat equations on non trivial region with a specific boundary condition. For simplicity I assume here a Disk ...
- 23.4k
0 votes
1 answer
147 views
heat equation-second order partial differential equations
I am dealing with the following set of pde $\alpha(p,q)+2p\frac{\partial\alpha(p,q)}{\partial p}=0$, $\frac{3}{2}\alpha(p,q)+p\frac{\partial\beta(p,q)}{\partial q}=0$, $A\frac{\partial\alpha(p,q)}{\...
- 31
0 votes
0 answers
133 views
Solving the steady-state problem of a multilayer hollow sphere
I would like to reproduce the analytical solution for the steady state problem as described in the paper Singh2016(https://doi.org/10.1115/1.4033536). The additional conditions can be found in the ...
- 1
2 votes
0 answers
240 views
Problem with pdetoode for two coupled PDEs
I tried to adapt a code for a single equation to solve the following system using 'pdetoode' Updated answer ...
- 203
2 votes
1 answer
175 views
Need help solving cylindrical Laplacian
I'm trying to solve the cylindrical Laplacian for a heated disk in a large cylinder. The cylinder and disk have constant temperatures and I only care about the temperature field between the disk and ...
- 365
2 votes
2 answers
564 views
Spherical Heat Equation and Convection Boundary Conditions
I'm trying to solve transient heat conduction equation in spherical domain in Mathematica. I made the simplifying hypothesis that temperature varies only with time and radial coordinate. The code is: <...
3 votes
1 answer
600 views
Simulating the Conduction of Heat on a Metal Rod
Consider the one-dimensional heat equation $$ \frac{\partial u(x,t)}{\partial t}=\alpha\frac{\partial^2 u(x,t)}{\partial x^2}, \quad (x,t)\in (0,L)\times (0,\infty), $$ subject to the ...
- 415
1 vote
1 answer
125 views
Fitting Parameters to the Heat Equation [closed]
As part of my research, I have been trying to use a model of heat conduction through a 2D layer given an input steady-state Gaussian power profile and a heat loss term to the environment. All but one ...
- 11
1 vote
1 answer
186 views
Plot of non-homogeneous diffusion equation
Let the initial and boundary value problem for the diffusion heat equation \begin{align*} u_t(x,t)&=u_{xx}(x,t)-\alpha u_x(x,t), \quad 0<x<+\infty,t>0\\ u(x,0)&=f(x), \quad x\...
2 votes
2 answers
208 views
Solving 3D heat equation with an off-center boundary condition
So i have this code (albeit a simplified version but it'll do for this question)which solves a time dependant 3D heat equation on a cylinder. ...
1 vote
1 answer
446 views
2D transient heat equation solution
I want to calculate the time- and space- dependent temperature of a 2D system where there are 3 materials, with different thermal properties. The system can be described by the schematics: ...
- 1,303
2 votes
1 answer
83 views
Setting up a strategy delivering a smooth heat transfer solution
I have a polymeric film that undergoes a two-step cooling process. First, it spends time1 in air. Then it comes in contact with a piece of steel at a temperature <...
- 1,303
3 votes
2 answers
362 views
Stefan problem with mixed bc
I am trying to solve through Mathematica the classical Stefan problem $$ \left\{ \begin{array}{lll} \dot{v}(x,t)=v_{xx}(x,t) & x\in(0,s(t))\\ \dot{s}(t)=-v_x(s(t),t) & x = s(t)\\ v(0,t) = 0 &...
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