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Appreciate help on the following

Hot water flows in an insulated copper pipe L long starting at temperature, T0

Need the temperature history, T(t,x).

T(0.x)=0

T(t,0)=T0

Heat transfer coefficient(conductance) water to pipe is U. Pipe heat capacity per unit length is C

I wrote the PDE equations but can't seem to get a solution in closed form.

Thank you

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# Closed form solution heat problem

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