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# Question 33 & dz= 2Lefl end (1-0) of a copper rod of length ]OOmm is kept constant lemperalure 0f Temp = 10+d2 degrees and the right end and sides are insulated...

## Question

###### Question 33 & dz= 2Lefl end (1-0) of a copper rod of length ]OOmm is kept constant lemperalure 0f Temp = 10+d2 degrees and the right end and sides are insulated, so that the temperature in the Ou 3 u rod, u(x,t) obeys - the heat partial DE; where D = H mm-/s for copper: 8x'Write the boundary conditions for U(x,t) of the problem above: Note that for the left end the condition is not zero, which presents problem for the separation of variable method. Use u(x,t) = Const + ((x,t) and select

Question 3 3 & dz= 2 Lefl end (1-0) of a copper rod of length ]OOmm is kept constant lemperalure 0f Temp = 10+d2 degrees and the right end and sides are insulated, so that the temperature in the Ou 3 u rod, u(x,t) obeys - the heat partial DE; where D = H mm-/s for copper: 8x' Write the boundary conditions for U(x,t) of the problem above: Note that for the left end the condition is not zero, which presents problem for the separation of variable method. Use u(x,t) = Const + ((x,t) and select Const appropriately to have the zero boundary condition for ((x,t) atx 0. Check that if o(x,t) is solution to the heat equation; u(x,t) = Const + ((x,t) is also solution. Find the boundary condition for ((x,t) al the right end of the rod_ (b) Find the general solution to heat equation for ((x, satislying the boundary conditions found in (a) and then delermine the temperature in the rod, u(x,t) Using the solution in (b) find u(x,t) that satisfies the initial conditions: 3T 5t u(x,0) =10+dz+sin d, sin +dz sin 200 200 200 (d) Using the solution in (c) determine the temperature in the middle of the rod at t60, record your answer t0 significant figures (this is not three decimal places)

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