2-D Unsteady State Heat Conductivity

In summary, the conversation is about using finite element analysis for solid materials, specifically for time-dependent heat conductivity in 2-D. The speaker is a computer scientist seeking assistance in translating a 2-D steady-state heat conductivity code to an unsteady-state version using explicit Euler time marching. They also mention using a preconditioned conjugate gradient solver and their interest in Gaussian quadrature in relation to time-marching algorithms for FE solutions. They are seeking a simple 2-D unsteady state algorithm and any assistance or explanation would be greatly appreciated.
  • #1
dinaharchery
24
0
Hello all,

I am not an engineer but am trying to learn finite element analysis for solid materials - in particular heat conductivity for time dependent problems in 2-D for a single material. I am interested in the explicit Euler time marching, thus I believe I need a lumped capacity matrix?

I have finished a C++ program using 2-D Steady state heat conductivity, it is very simple (as I said I am not an engineer). Can anyone assist me in translating a 2-D code for steady state heat conductivity to a unsteady state (time dependent) version? Small words please :smile: , I am a computer scientist.

Thanks for any help.
 
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  • #2
Any idea at all? A simple 2-D unsteady state algorithm?

Thanks again
 
  • #3
How exactly does your steady-state code compute the solution? Many solvers like this use some sort of pseudo-time, whether you want to call it iterations, or time-steps or whatever.
 
  • #4
The steady-state code uses a preconditioned conjugate gradient solver, so the solver itself is iterative. I would like to use the explicit euler time marching algorithm but I currently do not have a lumped capacity matrix.
 
  • #5
I have been doing some research into the unsteady state heat for finite element analysis and have run across Gaussian quadrature. Can anyone explain how this relates to a time-marching algorithm for the FE solution to a simple 2-D (x and y) heat conductivity problem:confused:?

Thanks.
 

What is 2-D unsteady state heat conductivity?

2-D unsteady state heat conductivity refers to the transfer of heat through a two-dimensional object or system that is not in thermal equilibrium. This means that the temperature of the object or system is changing over time, resulting in a flow of heat from areas of higher temperature to areas of lower temperature.

How is 2-D unsteady state heat conductivity different from 1-D unsteady state heat conductivity?

The main difference between 2-D and 1-D unsteady state heat conductivity is the number of dimensions involved. 1-D refers to heat transfer in a single dimension, while 2-D involves transfer in two dimensions. This means that 2-D heat conductivity takes into account not only the temperature gradient in one direction, but also in the perpendicular direction.

What factors affect 2-D unsteady state heat conductivity?

The factors that affect 2-D unsteady state heat conductivity include the material properties of the object or system, such as thermal conductivity and specific heat capacity, as well as the boundary conditions, such as temperature at the boundaries and the rate of heat transfer at the surface. The geometry and shape of the object or system also play a role.

How is 2-D unsteady state heat conductivity calculated?

The calculation of 2-D unsteady state heat conductivity involves solving the heat equation, which takes into account the material properties, boundary conditions, and geometry of the object or system. This can be done analytically or numerically using mathematical methods and computer simulations.

What are some real-world applications of 2-D unsteady state heat conductivity?

2-D unsteady state heat conductivity has many practical applications, such as in the design and optimization of building insulation, the cooling of electronic devices, and the study of heat transfer in the Earth's atmosphere and oceans. It is also used in various engineering and manufacturing processes, such as in the production of semiconductors and in thermal management systems for vehicles.

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