Cant solve heat equation on semi infiniate solid

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SUMMARY

The discussion focuses on setting up the heat equation for a semi-infinite solid with a length of 3 meters, initially at zero temperature. The task requires defining boundary conditions, applying Laplace transforms, determining equation constants, and finding the temperature distribution over time. The participants clarify that the objective is to establish the problem rather than solve it, emphasizing the importance of understanding the general heat equation.

PREREQUISITES
  • Understanding of the heat equation and its applications in thermal analysis.
  • Knowledge of boundary conditions in partial differential equations.
  • Familiarity with Laplace transforms and their use in solving differential equations.
  • Basic concepts of temperature distribution in solid materials.
NEXT STEPS
  • Study the general heat equation and its derivation.
  • Learn about boundary conditions specific to semi-infinite domains.
  • Explore Laplace transform techniques for solving partial differential equations.
  • Investigate methods for visualizing temperature distribution in solids over time.
USEFUL FOR

Students, engineers, and researchers in thermal dynamics, particularly those working with heat transfer in solid materials and seeking to understand the setup of heat equations.

kieranzas
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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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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?
 
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.
 

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