I have attached some notes to the question please show steps Problem 13.3.5: Suppose heat is lost from the lateral surface of a thin rod oflength L into a surrounding medium at temperature zero. If the linear law of heattransfer applies, then the heat equation takes on the forma²ukəx²диһи —at'0 < x < L,t > 0where h is a constant. Find the temperature u(x,t) if the initial temperature isf (x) throughout and the ends x = 0 and x = L are insulated. See figure below.insulated0°insulatedL0°heat transfer fromlateral surface ofthe rod We can expand f (x) into its Fourier series (sine only)E Bu sin ( ) - bn sin (x)Ex) = f(x) - IB, Sin%3Dn=1with2(-)bnf (x) sinx ) dxCompare coefficients and find B, = bn and find the same answer as before:Σ-n?n?atL22y(x, t) :L(x)ef(x) sin-x) dx ) sinLn=1

Name: I have attached some notes to the question please show steps Problem 1
Uploaded: 2024-03-20T07:07:37.000Z
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Description: I have attached some notes to the question please show steps Problem 13.3.5: Suppose heat is lost from the lateral surface of a thin rod oflength L into a surrounding medium at temperature zero. If the linear law of heattransfer applies, then the hea