# Questions tagged [heat-transfer]

For questions about modeling heat transfer, often through the use of heat (differential) equation.

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### Thermo Hydraulic Mechanical modeling of energy wall slab in camsol multiphysics

I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
1 vote
112 views

### How to handle non bilinear weak form?

I solved the 2D heat equation using the finite element method. It all went well first with the adiabatic case, however problems occured when I introduced cooling with the enviroment. I modeled the ...
319 views

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1 vote
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### How to solve heat equation in spherical coordinates with finite differences?

I have a problem dealing with heat transfer which is spherically symmetrical. I was thinking it should be possible to solve this as a 1d problem in spherical coordinates using the radius only. ...
• 111
132 views

### Solving geodesics on triangular meshes gives negative distances

I have implemented the heat method for geodesics: https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf When I run it I am getting a solution that, visually, seems correct: In this image, ...
• 263
203 views

### Incorporating heat flux into Laplace Equation

I need to find the temperature distribution of a square plate using the Laplace equation by using FDM: $$\frac{d^2T}{dx^2} + \frac{d^2T}{dy^2} = 0$$ But there is a heat flux entering from the top ...
• 145
399 views

### Two-dimensional heat equation with Neumann boundary conditions: any hope to find an analytical solution?

I am looking for references showing how to analytically solve the heat equation with Neumann boundary conditions in two dimensions. So far, I have found the problem solved analytically in one ...
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Starting from $$c_p \frac{\partial u }{\partial t} = k \nabla^2 u$$ in a one dimensional domain [0,1] where $c_p$ and $k$ are modeling two different materials: $$k = \begin{cases} 1 ~\text{if} ~x &... • 601 1 vote 2 answers 738 views ### How to use the Thomas-Algorithm to the Heat-diffusion-equation correctly My post is structured in four parts: I give you some information about the context my principal questions refer to. I will tell you what I believe to know about the Thomas Algorithm. If I am wrong ... 2 votes 3 answers 488 views ### Flux sign and face normal confusion in finite volume method I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) \nabla. (k\nabla T) = 0, using finite volume method, however, I am having some ... • 304 1 vote 0 answers 404 views ### Incorporating radiation boundary condition at the edge in finite difference I am trying to solve the 2-d heat equation on a rectangle using finite difference method. I am confused as to how to incorporate non linear radiation boundary condition at the edge. -k\frac{\partial ... • 19 3 votes 0 answers 103 views ### Correct approach for thermal finite element simulation of layered assembly I would like to optimise the heat transfer on a PCB. Several dies are on the top and cooling air is going through the fins in heat sink on the bottom. The assembly consists of several layers like ... • 570 2 votes 1 answer 372 views ### Solution method of nonlinear heat transfer analysis The governing equation of transient heat transfer analysis is described as follows:$$C \frac{dT}{dt}+K T = Q$$When using backward difference scheme for the discretization of the time we get the ... • 840 0 votes 1 answer 47 views ### Produce vertex displacements from volumetric shrinkage data on unstructured meshes I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh? ... • 1,403 2 votes 1 answer 276 views ### Lumped matrices in thermal analysis using finite elements The governing equation of the transient heat transfer problem is$$C \frac{dT}{dt}+K T = Q$$C is the heat capacity matrix. K is the thermal conductivity matrix. T is the temperature vector. ... • 840 1 vote 2 answers 180 views ### Simulating the heat equation with insulating material My plan is to solve the heat equation in the right half portion of the domain, while having the left half completely isolated with constant temperature. To do so, I model the left half with a very low ... • 601 0 votes 2 answers 1k views ### (FEM) 1D time-dependent heat equation convergence problem I'm simulating a simple 3-node bar with convection BCs at the edges to validate my FEM code. The following data was used: Initial temperature = 25 ºC Temperature surrounding the rod = 10 ºC Thermal ... 0 votes 1 answer 575 views ### Heat diffusion - Is this the correct approach to include Newmann boundary conditions? Thank you for looking at this problem. Is this the correct approach to include neumann boundary conditions? With this solution temperature is not correct, and there´s no diffusion. The model seems ... 1 vote 1 answer 14k views ### Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression Hello all, I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ... 0 votes 1 answer 65 views ### Modeling Diodes in Autodesk CFD I'm extremely new to Autodesk CFD, and I'm working on a project that deals with diodes heating up and cooling down based on a fixed temperature regulated by a temperature switch. Basically, I have a ... 2 votes 1 answer 632 views ### Solve 3-D Heat equation with Neumann boundaries I want to solve the Poisson PDE for heat flow in a 3-D solid cube with given dimensions x, y, and z:$$\rho C\frac{\partial T}{\partial t} = k \Delta T$$The cube is irradiated with a constant ... • 21 1 vote 1 answer 372 views ### Analytical testcase for 2D/3D anisotropic Diffusion (Heat Kernel) I want to verify and compare different Discretizations of the anisotropic diffusion equation in 2D / 3D. In order to both test the timestepping and the spatial discretisations I had a look at using ... • 11 8 votes 1 answer 525 views ### Computing geodesic distances with diffusion I am trying to solve an APSP (All-Pair Shortest Path) problem on a weighted graph. This graph is actually a 1, 2 or 3 dimensional grid, and the weights on each edge represent the distance between its ... • 131 0 votes 1 answer 80 views ### Solving the diffusion/heat equation for a randomly distributed set of points in 3D In this problem I am trying to solve, I have a messy set of points distributed in 3D space, each with a defined temperature. If I would want to calculate the heat transfer scenario in this system, how ... 1 vote 0 answers 897 views ### 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 vote 0 answers 203 views ### 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 ... 1 vote 2 answers 389 views ### V-cycle Multigrid for 2D transient heat transfer on a square plate using finite difference I'm currently developing a program to solve 2D transient state heat conduction on a square plate using the V-cycle multigrid. Althought my program is able to reach the steady state solution, it's ... 1 vote 2 answers 2k views ### Finite Difference Grid Spacing and Scaling I have been exploring finite differences and heat transfer using the 2D heat equation to further expand my knowledge. So far I think it is going well. I am running into some confusion around grid ... • 11 0 votes 1 answer 813 views ### 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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For the heat equation $$u_t(t,x) = \nu u_{xx}(t,x)$$ for $x \in [0,1]$ with boundary conditions $u(t,0) = u(t,1) = 0$ and initial value $u(0,x) = u_0(x)$ it is easy to ...