To find the inner surface temperature of a wall undergoing transient heat conduction and subjected to a heat flux for 0.2 seconds, you can use the finite difference method in MATLAB.
Assuming a 1D heat transfer through a wall with thickness dx, and an initial uniform temperature Ti, the transient heat conduction equation can be written as:
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where
Using the finite difference approach, the equation can be discretized in both time and space. For example, the temperature at position i and time n can be represented as Ti,n. The finite difference method can be written as:
Ti,n+1 = Ti,n + (k * dt / (rho * cp * dx^2)) * (Ti+1,n - 2Ti,n + Ti-1,n) + (Q * dt / (rho * cp * A))
where dt is the time step.
To implement this in MATLAB, we can initialize the parameters of the problem and set up a loop to solve for the temperature at each time step. Here's an example code:
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This code will output a plot of the temperature profile at the final time. Note that this is a simplified example and does not account for certain effects, such as radiation heat transfer and temperature-dependent material properties.
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