Questions tagged [heat-transfer-equation]

Questions on the symbolic (DSolve) and numerical (NDSolve) solutions of the heat transfer equation in Mathematica.

Filter by
Sorted by
Tagged with
1
vote
0answers
76 views

Multiphysics - Electrostatics and Heat Transfer - Joule Heating boundary conditions

I am working on a multiphysics problem involving electrostatics (direct current) and heat transfer. I was messing around with the Joule Heating tutorial case and need to answer some questions to apply ...
0
votes
0answers
50 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 ...
2
votes
1answer
65 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 ...
1
vote
1answer
101 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
0answers
58 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
1answer
75 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
1answer
138 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
1answer
143 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
2answers
312 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 ...
5
votes
1answer
132 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 ...
9
votes
3answers
431 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: ...
1
vote
2answers
121 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
vote
0answers
60 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
1answer
84 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: ...
3
votes
0answers
93 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
vote
1answer
71 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
2answers
564 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 ...
1
vote
1answer
68 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
1answer
202 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
2answers
202 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 ...
0
votes
1answer
88 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. ...
0
votes
1answer
98 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/...
3
votes
1answer
74 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
2answers
115 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 ...
1
vote
1answer
99 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
0answers
109 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:...
2
votes
1answer
225 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 ($\nabla^2 T(x,y)=0$) ...
3
votes
1answer
136 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 ...
1
vote
0answers
99 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 ...
1
vote
0answers
155 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\\\...
5
votes
2answers
270 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/...
8
votes
2answers
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 ...
8
votes
2answers
292 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 ...
3
votes
1answer
300 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
0answers
84 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. ...
1
vote
1answer
191 views

Plot time dependent 3D heat equation solution with functions like Plot3D +Manipulate (or Graph3D) but using cylindrical coordinates

I have a time dependant heat diffusion equation here and I would like to plot the result of NDSolveValue. Here is the code I am using : ...
0
votes
0answers
49 views
1
vote
0answers
107 views

Heat transfer FEM with nonlinear Cp

I would like to solve a 3D heat transfer problem with nonlinear heat capacity Cp (Cp=1*T[t,x,y,z]). My problem is very simple: a slab with the bottom surface insulated and the other five surfaces ...
0
votes
1answer
64 views

Blank plot is returned when trying to use Manipulate[Plot3D…] on the output function of NDSolve

I am currently trying to solve a transient cylindrical diffusion problem with space variable (r,z). Using NDSolve, I get a certain Interpolation function but I can't plot it no matter what I try. ...
6
votes
3answers
242 views

Incorrect Result from DSolve for Diffusion IBVP?

The result of DSolve for the following IBVP doesn't seem to satisfy the IBVP: \begin{cases} u_{t} - ku_{xx} = 0 &\mbox{} k>0,x>0,t>0 \\ u(0,t)=p(t) &...
3
votes
3answers
181 views

Inhomogeneous Heat Equation Formula Not Satisfying IVP

From Wikipedia, However, when I plug the formula of $u(x,t)$ into Mathematica 12.1, it doesn't seem to satisfy the PDE (does not give $0$): Here is the code: ...
4
votes
1answer
176 views

Solve free boundary problem for heat equation

How can I use Mathematica to compute/approximate and plot the solution of the following problem? $\min\{u_t - u_{xx} -1, u \} = 0 \text{ in } (0,T)\times (-1,1)$ $u(0,\cdot) = 0 \text{ in } (-1,1)$...
3
votes
0answers
230 views

Problem computing a cylindrical Heat equation with a parameter alpha

i have been struggling to compute a particular instance of cylindrical 3D heat equation. Here is my code : ...
7
votes
3answers
400 views

Wrong solution from multi materials FEM NDSolve

I'm quite new in Mathematica. I have a problem with obtaining the right solution for multi-layer 1D heat transfer problem. It seems that boundary condition not working. Could you advise something? I ...
3
votes
1answer
149 views

NDSolve 1D Heat equation with NeumannValue poorly satisfies boundary condition

Context I am trying to measure the slope of the stellar cuspide around our MilkyWay's central black hole using the observed distribution of S stars orbiting around it. Attempt Close to the ...
4
votes
1answer
286 views

A complicated boundary value problem leading to third order Eigen sytem [Help in continuing forward] [EDITED]

I have the following elliptic PDE (describing temperature in a plate, w in thermal contact with two fluids h and c): $$\lambda_h \frac{\partial^2 \theta_w}{\partial x^2} + \lambda_c V \frac{\partial^2 ...
4
votes
1answer
351 views

Approach to analytically solve a Coupled system of PDE in Mathematica [Heat transfer in cylindrical coordinates]

I have the following two PDEs, which describe steady-state coupled heat transport between a externally heated axi-symmetric solid body (Eq. 1, $T(r,z)$) and a fluid (Eq. 2, $t(z)$) flowing inside it $...
16
votes
4answers
794 views

How to model diffusion through a membrane?

This is a follow-up on How to handle discontinuity in diffusion coefficient? Consider diffusion of $u(t,x)$ on the domain $x \in [0,2]$ with some simple boundary conditions such as $u(0) = 2, u(2) = ...
9
votes
1answer
327 views

How to handle discontinuity in diffusion coefficient?

I am looking to solve the diffusion equation with a discontinuous jump in the diffusion coefficient. In 1D, the diffusion equation for $u(t,x)$ is: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
6
votes
3answers
296 views

How to define the boundary condition in 1D Heat transfer

I am trying to calculate the heat transfer among a 1-D rod, with one end insulated while the right end is immersed in constant temperature surface T=0. Assume that the initial temperature of the rod ...