Cant solve heat equation on semi infiniate solid

In summary, the speaker is struggling with a task given by their employer regarding a semi-infinite solid at a constant temperature. They are asking for help with setting up the problem, not solving it. The main points of the conversation include the problem scenario, the requested help, and the misunderstanding about the task.
  • #1
kieranzas
2
0
Hi All,

I am having issues trying to work out a task my employer has given me and was wondering if there is someone who could help. Question:

A Semi-infiniate solid (L=3M) x>0, is initially at temperature zero. At time t=0, a constant temperature Uo>0 is applied and maintained at the face x=0. Find:

1. The boundary conditions,
2. Laplace transforms for the both sides of the formula.
3. The equation constants.
4. The temperature at any point of the solid at any later time t>0.
5. Sketch the heat equation.

I really need help on this my maths was never much good.

Please and thankyou
 
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  • #2
You titled this "Can't solve heat equation on semi-infinite solid" but you are not asked to solve it. You are only asked to set the problem up. Do you know what the "heat equation" is?
 
  • #3
right i think i might know where your going with that. yes i know what the general heat equation is shall have a look into it a bit further i think. i thought it had to be solved did not realize i was only having to set up the question.
 

1. How do I define the boundary conditions for a semi-infinite solid in the heat equation?

In order to solve the heat equation for a semi-infinite solid, you must specify the boundary conditions at the end of the solid that extends to infinity. These boundary conditions could include the temperature at the boundary, the heat flux at the boundary, or a combination of both. It is important to carefully consider the physical properties of the solid and its surroundings in order to determine the appropriate boundary conditions.

2. Can the heat equation be solved analytically for a semi-infinite solid?

In most cases, it is not possible to find an exact analytical solution for the heat equation on a semi-infinite solid. This is because the boundary conditions at infinity are typically unknown or difficult to define. However, approximate solutions can be obtained using numerical methods or by making simplifying assumptions.

3. What is the importance of the initial conditions in solving the heat equation for a semi-infinite solid?

The initial conditions, or the temperature distribution at the beginning of the simulation, play a crucial role in solving the heat equation for a semi-infinite solid. These initial conditions determine the starting point for the temperature evolution and can greatly affect the final solution. It is important to carefully consider and accurately define the initial conditions for an accurate simulation.

4. How does the thermal conductivity of the solid affect the solution of the heat equation on a semi-infinite solid?

The thermal conductivity of the solid plays a significant role in determining the temperature distribution within the solid. A higher thermal conductivity will result in a faster diffusion of heat throughout the solid, leading to a more uniform temperature distribution. On the other hand, a lower thermal conductivity will result in a slower diffusion of heat and a larger temperature gradient within the solid.

5. Can the heat equation on a semi-infinite solid be used to model real-world scenarios?

Yes, the heat equation on a semi-infinite solid can be used to model a variety of real-world scenarios, such as heat transfer in materials, buildings, and geological processes. However, it is important to carefully consider the boundary and initial conditions, as well as the material properties, in order to accurately simulate real-world situations.

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