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06-05 Hot Wire

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    And now we come to a model that has way more compartments than the one before.
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    A model for heat conduction in a wire.
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    Let's draw imaginary lines after each millimeter of that wire
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    and treat each millimeter as one compartment.
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    Every single compartment is treated in the same way,
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    so we can just look at one single of them to get an idea of what happening, let's take no. 8.
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    Compartment no. 8 loses a specific percentage of its energy
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    per time to compartments no. 7 and no. 9.
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    To be specific, let's say it's going to lose 1%/ms to the left and 1%/ms to the right,
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    but there will also an energy flow from compartment no. 7 to no. 8 with the same
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    percentage of the energy of no. 7 and there will be an energy flow
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    from compartment no. 9 to compartment no. 8.
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    Again, the same percentage but of the energy content of compartment no. 9.
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    So after a short amount (h) of time, the temperature of the compartment no. 8
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    will be its initial temperature plus that amount of time
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    times 1%/ms to be gaining 1%/ms from compartment no. 7
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    and we are gaining 1%/ms from compartment no. 9 but we are losing 1%/ms to the left and to the right
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    so we're losing thrice that percentage.
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    One final thing to be doing to clean things up a little, let's get rid of this 1%/ms here.
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    If we work with seconds instead, 1 second amounts to 1000 ms, so we need 1000%/s.
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    1000% is 10--so now, we have an equation for the temperature
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    of the compartment no. 8 after one time step.
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    Of course, this works similarly for all other compartments.
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    We've just change the numbers. Its about the left neighbor, the right neighbor, and ourselves.
タイトル:
06-05 Hot Wire
Team:
Udacity
プロジェクト:
CS222 - Differential Equations
Duration:
01:59
Amara Bot edited 英語(米国) subtitles for 06-05 Hot Wire
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