Computational Physics Project I started off by first deriving the algorithm needed for the 1Dimensional heat equation., which came from the Taylor expansion of This is a forward difference time algorithm since its increasing while the spatial part is a central difference, since it both increases and decreases. The K /Cp is a constant called thermal diffusivity and from now on will be eta (η). The algorithm yielded from the Taylor Series expansion is T[i][j+1] = T[i][j] + η(T[i+1][j]+T[i1][j] –2T[i][j]) We can then use to determine a solution to the heat equation. The first code is for a 1 dimensional bar, the graph has the thermal diffusivity of that material.
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Computational Physics Project
I started off by first deriving the algorithm needed for the 1-‐Dimensional heat equation., which came from the Taylor expansion of
This is a forward difference time algorithm since its increasing while the spatial part is a central difference, since it both increases and decreases.
The K /Cp is a constant called thermal diffusivity and from now on will be eta (η). The algorithm yielded from the Taylor Series expansion is T[i][j+1] = T[i][j] + η(T[i+1][j]+T[i-‐1][j] –2T[i][j]) We can then use to determine a solution to the heat equation. The first code is for a 1 dimensional bar, the graph has the thermal diffusivity of that material.
The next code was for a sinusoidal distribution., and I chose the b.c’s accordingly.
The next code was for two bars in contact with each other.
Finally this was Newtons law of cooling combined with the heat equation. I chose the environment temperature to be 70 degrees, and the heat source to be 100 degrees, this then leaves the( Te – To )to be 30 degrees. I then chose an arbitrary “h” value for the equations. Two dimensional heat equation:
You can expand this equation with the Taylor expansion as well, but this equation doesn’t have any thermal diffusivity as you can cancel it out, (since time =0). This then becomes a heated plate equation.
For an external source of heat centered on the plate, and the boundaries being zero.
Here the time derivative is zero, leaving the Laplacian, and an external heat source.