Questions tagged [heat-equation]

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2 votes
1 answer
95 views

How to solve PDEs for function $\Psi(z,\bar{z})$ dependent on independent variables $z,\bar{z}$? (Wirtinger derivatives)

For the past few days, I have been struggling to convey to mathematica to solve a PDE that is in terms of the independent variables $(z,\bar{z})$. I know mathematica supports solving PDEs with respect ...
0 votes
1 answer
76 views

How to solve this initial boundary value problem for heat conduction equation?

I want to solve the following PDE: heqn=D[u[x,t],t]==D[u[x,t],{x,2}]-D[u[x,t],{x,1}]; with the initial conditions: ...
3 votes
1 answer
149 views

Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder

I want to symbolically solve the following boundary value problem in my textbook. It's steady-state heat conduction equation i.e. Laplace equation inside a cylinder $$ \left\{\begin{array}{l} \Delta u=...
0 votes
1 answer
139 views

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,...
  • 125
0 votes
1 answer
103 views

Is there any alternative for Manipulate or Animate?

I have a project to animate heat equation in 3D. I have the following problem $$u_t=u_{xx},\qquad 0\leq x\leq 1 \land t>0$$ $$u(0,t)=u(1,t)=0$$ $$u(x,0)=\begin{cases} 2x, & 0\leq x<\frac{1}{...
1 vote
0 answers
53 views

Neumann Boundary Condition for thermal radiation between two bodies

I'm trying to formulate and solve a pde which models thermal radiation between two bodies using a Neumann boundary condition. I've created a mesh and want to capture the thermal radiation heat ...
3 votes
1 answer
126 views

Speeding up Boussinesq equations solving?

I am working on Boussinesq equation. The notebook can run perfectly for only 0.6 steps and then the calculation starts running slowly after 0.7. All boundary conditions seemed fine. I am unsure if I ...
1 vote
1 answer
66 views

Why do I see Part::partw error when using NDSolveValue?

Bug introduced in version 12.0 (or earlier) and fixed in version 13.0 (or earlier) I am using Mathematica 12.0. The present calculation is a simple "test case" to prove efficacy, but I am ...
  • 11
2 votes
1 answer
174 views

Coupled heat transfer equations using collocation method

Using the collocation method proposed here, recently this problem has been solved. I am trying to solve a similar problem described by the equations given below. My attempt in Mathematica is ...
  • 143
5 votes
2 answers
198 views

question on documentation convention for heat PDE used by Finite Elements methods in Mathematica

Why FEM documentation says heat PDE is second order in time? This makes it looking same as the wave PDE. Is this meant to be that $m=0$ for the heat pde? But this looks confusing. Could this be just ...
  • 115k
3 votes
1 answer
117 views

FEM nonlinear anisotropic heat transfer with element markers

I'm trying to model a 2D nonlinear anisotropic heat transfer using FEM with element markers. I got stuck with errors and have no idea what to do to make it work... I have simple toy-model: two ...
  • 33
1 vote
0 answers
122 views

Boundary Value of Function Disagrees with Neumann Boundary Heat Equation

I'm trying to solve a time-dependent 2D heat equation with a source, initial specified heat distribution and heat flux loss at the boundary which goes with the temperature difference. Thus far, I've ...
1 vote
1 answer
76 views

how we can extract the value of the solution of a PDE in a point x? (NDSolve) [closed]

Please I need your help, I calculate the solution of heat equation using methode of line This is my code: ...
5 votes
2 answers
248 views

Modified Heat Transfer in Fluid Flow

I am trying to simulate Modified Heat Transfer in Fluid Flow (based on Buoyancy-Driven Flow in a Square Cavity ). The modified heat transfer takes the form: with the solid volume fraction: The ...
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4 votes
1 answer
225 views

Different answer between HeatTransferPDEComponent and Matlab

I've been working on a 2-layer HeatTransferPDE Model. The diagram of the model is The two materials have an initial temperature of 37℃, and the outside is 75℃. The model is for heat insulation so it ...
7 votes
2 answers
237 views

NDSolve coupled PDE Grad function in source term error

I am working on a multiphysics problem involving heat transfer and electrostatics. I have been messing around with the Joule Heating Tutorial Case and got stuck with the heat source term not working. ...
  • 563
1 vote
1 answer
179 views

Adding maximum value for function within diffusion equation

I have a function that I want to max out at a certain value, say 1 for simplicity. There is a pump that will heat in a certain area, but once its reaches the cap, it no longer heats past this (as if ...
  • 115
2 votes
1 answer
125 views

Mathematica heat transfer tutorial problem

I want to solve some heat transfer problems with Mathematica. I am trying to run the heat transfer tutorial cases but I am always getting the error "NDSolveValue: Equation or list of equations ...
  • 563
1 vote
1 answer
161 views

1D Nonlinear Diffusion Equation with NDSolve Graphs

I am trying to model/solve a specific instance of a 1D diffusion equation in which I have a nonlinear Neumann boundary condition at x=1 (length of unit 1). My equations that I have are: D[u[x,t],t] == ...
0 votes
0 answers
71 views

Setting Up to Solve the Diffusion Equation with Nonlinear Neumann [duplicate]

I am really new to Mathematica, so please bear with me if I ask any relatively easy questions. I am trying to model/solve a specific instance of a 1D diffusion equation in which I have a nonlinear ...
2 votes
1 answer
122 views

How we can solve heat equation with this particular boundary conditions (error NDsolve)?

Please I need help to solve this heat equation with this particular boundary conditions: This the Code I tried in Mathematica: ...
1 vote
1 answer
150 views

How can I solve this system please?

I need to solve the following impulsive heat equation: $$ \left\{\begin{array}{ll} \partial_{t} \psi(x,t)-\partial_{xx} \psi(x,t)=0, & (x,t)\in (0,1) \times((0, 2) \backslash\{1\}) \\ \...
-1 votes
1 answer
154 views

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\}) \\ ...
12 votes
2 answers
405 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 ...
  • 435
6 votes
1 answer
308 views

Heat transfer with functions defined on different domains

I'm attempting to model a situation in which a polymer initially at a higher temperature is sandwiched between two cooler metallic mold pieces with conductive boundary conditions in between the ...
  • 239
10 votes
3 answers
736 views

Laplace's equation in spherical coordinates with Neumann b.c

I am trying to find the temperature field in a semi-infinite solid on whose surface there is an isotherm spherical cap sunken by a length p. For example: ...
  • 435
2 votes
2 answers
166 views

Heat balance in layer coupled via BC

I am trying to solve the heat balance in a 3 layer system in Mathematica 12.0.0. Each layer has different thermal properties. The layers are coupled via the boundary conditions (Neumann type) to ...
  • 1,087
1 vote
0 answers
98 views

2D transient heat equation resolution

I'm writing a code to get the analytical solution mentioned in Sun et al., 2013. I will copy here the passages needed to solve the equation. The 2D transient heat equation is: First of all, I set the ...
0 votes
1 answer
180 views

Including point heat sources in a 2D transient PDE heat equation

I want to be sure that I included the point heat sources correctly in my PDE. The result should be: I wrote: ...
4 votes
0 answers
124 views

Heat balance multilayer with heat flux continuity

I am solving the heat equation (diffusion only) over a 3-layer system (physical properties varying from layer to layer). ...
  • 1,087
1 vote
1 answer
104 views

Graphing Heat Equation

I was able to solve the heat equation, but am unsure of how to graph the partial sums of the solution. The problem: a.) Solve the heat equation subject to ...
7 votes
2 answers
850 views

Solving a 2D heat equation on a square with Dirichlet boundary conditions

I am trying to solve the following heat equation problem on the square [0,1]x[0,1]. \begin{equation*} \begin{gathered} u_t = u_{xx} + u_{yy} + f(x,y,t), \qquad u(x,y,0) = 0, \qquad u=0 \text{ on ...
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1 vote
1 answer
102 views

Solving a Heat Equation

I'm new to Mathematica and am a little lost as to how to code this heat equation: u(0, t) = 0, u(L, t)=0, t>0 u(x, 0)= 1, 0<x<L/2 = 0, L/2<x<L How would I go about solving this?
2 votes
1 answer
283 views

Discontinuity problem with 3D cylindrical heat equation (possibly due to a conversion between Cartesian to Cylindrical coordinates)

I have been working a certain type of 3D cylindrical diffusion equation for a bit now. I am trying to simulate a longitudinal diffusion process in a cylinder with a dislocation defect that will make ...
5 votes
2 answers
281 views

Solving a heat equation on a finite interval with Neuman boundary conditions

I am new to Mathematica and need to verify my numerical result. Can anyone please show me how to solve the following heat equation problem $$ u_t = u_{xx}$$ on the interval $ x \in [0,1]$. The initial ...
  • 225
0 votes
1 answer
105 views

Trying to find values of two parameters that match the boundary conditions defined

I have been trying to solve for the values of two parameters that satisfy the boundary conditions set for a set of equations set. The below is the code. ...
  • 3
0 votes
1 answer
130 views

Solve complex heat transfer equation

I am trying to solve a heat transfer problem related to calculating the cooling rate after quenching a sample. The equations (and explanations) are taken from this paper: https://sci-hub.se/10.1029/...
  • 1,531
4 votes
1 answer
144 views

How to convert a Piecewise function in a HeavisideTheta function?

I want to convert a Piecewise function in a HeavisideTheta function in order to correctly evaluate its derivatives at the point of abrupt change and then integrate the result along the axis. How can I ...
3 votes
2 answers
149 views

Super Slow Manipulate with Heat Equation - - Assumption, and Interpolate

Aim: solve coupled heat equation with cubic source, use DensityPlot and observe how system will react to changes in parameter(like kand ...
  • 191
1 vote
1 answer
110 views

How to solve a 3D permanent conjugate heat transfer problem?

I want to solve this conjugate heat transfer problem on NDSolve but Mathematica always quits the Kernel. Can you help me? I do not know exactly how to use the numerical methods that are NDSolve method ...
0 votes
0 answers
208 views

NDSOLVE-Error ("For the method \!\(\"IDA\"\), only machine real code is available. "

I am trying to solve mass transfer equations in an adsorption column to obtain the breakthrough curves. Previously, I asked a question on this and received great help:NDSolve for system of PDEs -Error:...
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2 votes
1 answer
253 views

Solving a PDE (2D Laplacian) coupled with an ODE

I have asked this question before, but this is my new attempt and so instead of cluttering the previous one, I am making a new post. I am trying to analytically solve a PDE ($\nabla^2 T(x,y)=0$) ...
  • 143
3 votes
1 answer
204 views

NDSolve Inconsistent equation dimensions

I am getting an error while trying to solve for a differential equation. It is saying "NDSolveValue::femper: PDE parsing error... Inconsistant equation dimensions." I was wondering if anyone ...
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1 vote
0 answers
104 views

Why is there no heat being transfered in my program?

I have been working on this code and am new to this coding language. I have been trying to model the transfer of heat through a hot plastic being cooled in a water bath. For some reason I have not ...
  • 91
1 vote
0 answers
161 views

Can this boundary value problem leading to a partio-integral DE be solved using finite Fourier or any integral transform?

I asked the three-dimensional version of this problem here which lead to a trivial solution. I have now tried it in 2-D $$\frac{\partial \theta_h}{\partial x} + b_h (\theta_h - \theta_w) = 0, \tag 1\\\...
  • 143
5 votes
2 answers
293 views

Mesh Generation help

I am having trouble generating a mesh of a rectangle inside another rectangle. I have been following the steps on this article: https://reference.wolfram.com/language/PDEModels/tutorial/HeatTransfer/...
  • 91
10 votes
3 answers
2k views

Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)

I have the three dimensional Laplacian $\nabla^2 T(x,y,z)=0$ representing temperature distribution in a cuboid shaped wall which is exposed to two fluids flowing perpendicular to each other on either ...
  • 143
8 votes
2 answers
322 views

Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)

I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
  • 143
3 votes
1 answer
610 views

Problem with NDSolveValue : "The function value {$Failed} is not a list of numbers with \ dimensions..."

I was having fun modifying a code given to me as an answer to a previous problem here, courtesy of user Alex Trounev (Thank you again), when I encountered a certain error which I had never seen before....
1 vote
0 answers
91 views

Need help with IVP for Heat Equation [closed]

I'm trying to solve the heat equation on a torus and am running into a problem... Mathematica keeps running, but never finishes/ends. Even after leaving it running overnight, I still got nada. ...