Need help for heat conduction problem with multiple BC

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SUMMARY

The discussion focuses on solving a heat conduction problem within a rectangular domain characterized by length L and width δ. The user is attempting to determine the temperature profile by applying energy balance to a differential cell of size dx by dy. Key parameters include thermal conductivity (λ) and a time-dependent heat transfer coefficient (α), which the user plans to simulate as a periodic function. The user expresses difficulty in solving the associated differential equations and boundary conditions.

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  • Understanding of heat conduction principles
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  • Knowledge of boundary conditions in thermal analysis
  • Experience with numerical simulation techniques
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  • Research methods for solving partial differential equations in heat conduction
  • Learn about numerical methods for simulating heat transfer, such as finite difference or finite element methods
  • Explore the implementation of periodic functions in heat transfer coefficient simulations
  • Study boundary condition applications in thermal analysis
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Engineers, physicists, and researchers working on thermal analysis and heat transfer problems, particularly those dealing with complex boundary conditions and numerical simulations.

bancux
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Dear all, I have difficulty in solving this problem (see the figure in attached thumbnails)

I have a rectangular shape with length/height of L and the thickness/width of \delta
Within the rectangular area, a heat conduction occurred. I would like to determine the temperature profile within the rectangular.

Based on the right hand side figure, I take a small cell with size of dx times dy. Applying the energy balance within the cell.

I have attached all the equation that I can think of, and also the boundary conditions. I have difficulty in solving the differential equation.

Thanks in advance.

note:

\lambda is thermal conductivity
\alpha is heat transfer coefficient, it is suppose to be dependent on x-location and time. I am going to simulate the heat transfer coefficient as a periodic function.
 

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Still no answer...
Hmmm...

:confused:
 

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