# Questions tagged [heat-transfer]

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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: $$k = \begin{cases} 1 ~\text{if} ~x &... 2answers 117 views ### How to use the Thomas-Algorithm to the Heat-diffusion-equation correctly My post is structured in four parts: I give you some information about the context my principal questions refer to. I will tell you what I believe to know about the Thomas Algorithm. If I am wrong ... 3answers 146 views ### Flux sign and face normal confusion in finite volume method I implemented a solver for the 2D steady-state heat equation (without heat generation and homogeneous material) \nabla. (k\nabla T) = 0, using finite volume method, however, I am having some ... 0answers 67 views ### Incorporating radiation boundary condition at the edge in finite difference I am trying to solve the 2-d heat equation on a rectangle using finite difference method. I am confused as to how to incorporate non linear radiation boundary condition at the edge. -k\frac{\partial ... 0answers 79 views ### Correct approach for thermal finite element simulation of layered assembly I would like to optimise the heat transfer on a PCB. Several dies are on the top and cooling air is going through the fins in heat sink on the bottom. The assembly consists of several layers like ... 1answer 60 views ### Solution method of nonlinear heat transfer analysis The governing equation of transient heat transfer analysis is described as follows:$$C \frac{dT}{dt}+K T = Q$$When using backward difference scheme for the discretization of the time we get the ... 1answer 37 views ### Produce vertex displacements from volumetric shrinkage data on unstructured meshes I was wondering what would be an efficient way to produce compatible displacements for mesh nodes/vertices if the computed data is volume shrinkage of each element/cell in the unstructured mesh? ... 1answer 96 views ### Lumped matrices in thermal analysis using finite elements The governing equation of the transient heat transfer problem is$$C \frac{dT}{dt}+K T = Q$$C is the heat capacity matrix. K is the thermal conductivity matrix. T is the temperature vector. ... 2answers 93 views ### Simulating the heat equation with insulating material My plan is to solve the heat equation in the right half portion of the domain, while having the left half completely isolated with constant temperature. To do so, I model the left half with a very low ... 2answers 562 views ### (FEM) 1D time-dependent heat equation convergence problem I'm simulating a simple 3-node bar with convection BCs at the edges to validate my FEM code. The following data was used: Initial temperature = 25 ºC Temperature surrounding the rod = 10 ºC Thermal ... 1answer 220 views ### Heat diffusion - Is this the correct approach to include Newmann boundary conditions? Thank you for looking at this problem. Is this the correct approach to include neumann boundary conditions? With this solution temperature is not correct, and there´s no diffusion. The model seems ... 1answer 5k views ### Python Finite Difference Schemes for 1D Heat Equation: How to express for loop using numpy expression Hello all, I've recently been introduced to Python and Numpy, and am still a beginner in applying it for numerical methods. I've been performing simple 1D diffusion computations. I suppose my ... 1answer 45 views ### Modeling Diodes in Autodesk CFD I'm extremely new to Autodesk CFD, and I'm working on a project that deals with diodes heating up and cooling down based on a fixed temperature regulated by a temperature switch. Basically, I have a ... 1answer 220 views ### Solve 3-D Heat equation with Neumann boundaries I want to solve the Poisson PDE for heat flow in a 3-D solid cube with given dimensions x, y, and z:$$\rho C\frac{\partial T}{\partial t} = k \Delta T$$The cube is irradiated with a constant ... 1answer 140 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 ... 1answer 366 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 ... 1answer 42 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 ... 0answers 556 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 ... 0answers 125 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 ... 2answers 271 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 ... 2answers 684 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 ... 1answer 630 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\,,...
For the heat equation \begin{equation} u_t(t,x) = \nu u_{xx}(t,x) \end{equation} 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 ...