3. (25 points) Consider the heat equation 2004 on the interval [0, L] for a rod constructed from two different materials

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3 25 Points Consider The Heat Equation 2004 On The Interval 0 L For A Rod Constructed From Two Different Materials 1 (109.74 KiB) Viewed 62 times

3. (25 points) Consider the heat equation 2004 on the interval [0, L] for a rod constructed from two different materials so that the diffusivity constant c is given by ={ K 0<<< K2 <x< 1 Assume that the ends of the rod are held at fixed temperatures so that u(0,t) = T, and u(L,t) = T,. Find the steady state solution v(x). (Hint: Assume the temperature at x = { is T; and work the problem separately in each half of the rod and find a boundary condition at x = { that states that the heat flowing out of the one half is equal to the heat flowing into the other half and use it to find T;.)