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How does the temperature vary along the length of the rod if its both ends are at different temperature. As an example, consider the problem:

20 cm long rod has rod at one end 100 ºC and another end at 0 ºC. Find the temperature at the center of the rod when it's in thermal steady state.

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closed as off-topic by Waffle's Crazy Peanut, Nathaniel, Qmechanic Jul 21 '13 at 4:54

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It is a quite basic problem driven by a one-dimensional second order ordinary differential equation with two boundary conditions, the temperature prescribed at the two ends, known as the Heat Equation. Do not forget to express the temperature in Kelvin and remove the time-dependent term since you are only interested in the final steady-state solution.

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