Adiabatic means no heat exchange with the neighborhood, because the bar is completely insulated, also at the
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“Adiabatic” means no heat exchange with the neighborhood, because the bar is completely insulated, also at the ends. Physical Information: The heat flux at the ends is proportional to the value of ∂u/∂x there.
Show that for the completely insulated bar ux(0, t) = 0, ux(L, t) = 0, u(x, t) = f(x) and separation of variables gives the following solution, with An given by (2) in Sec. 11.3.
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Starting with the heat equation in 1D ux ut Assuming that uxt can be written as a product of functio...View the full answer
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