# Questions tagged [heat-equation]

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### 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
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### 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 ...
221 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: <...
211 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 ...
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1 vote
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### 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 ...
1 vote
78 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\...
113 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
262 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: ...
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### 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 <...
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### Heat Equation with Mobile Boundary

I am trying to use NDSolve to find the solution to a set of coupled diffEQs. They represent 1d (radial) heat balance in a spherical shell. The goal is to specify a heat flux into the base of the shell,...
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157 views

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### Please I need help, how can I solve this heat impulsive system? [closed]

Please I need your help!! I need to solve the following system:  \left\{\begin{array}{ll} \partial_{t} \psi(x,t)-\Delta \psi(x,t)=0, & (x,t)\in (0,1) \times((0, 2) \backslash\{1\}) \\ ...
470 views

### Total flux of the gradient of the numerical solution of a PDE through a surface

Trying to solve the following PDE with BC T==1 on a spherical cap of a unit sphere and T==0 at infinity (approximated as ...
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