Given a rod of • length L diffusivity K • insulated along its length • initial conditions (x,0) = 0 • and boundary condi

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Given A Rod Of Length L Diffusivity K Insulated Along Its Length Initial Conditions X 0 0 And Boundary Condi 1 (80.34 KiB) Viewed 18 times

Given a rod of • length L diffusivity K • insulated along its length • initial conditions (x,0) = 0 • and boundary conditions (0,1)= (L,1) At time zero onward subject to a distributed heat source $(x) = S04x(L-x)/L? I remind you that the relevant one-dimensional heat equation is Ó = KO'+s(x,1) (0.1) (a) Calculate and write the full expression for Ⓡ(x,t) for this problem. You may leave your solution in terms of Bk and y, etc, so long as you have found/defined them previously. (b) Pull out the above the steady-state solution and write it. (c) You also can solve Equation 0.1 for the steady state solution by setting Ó = 0 and solving what is left. The solution is a polynomial; derive it for this problem. (d) Make a statement about the above two expressions. Possibly Useful: L" sin (1978) (4:42 4x(-x) L? 8L(1-cos(Ttn)) Ten L dx