1D transient heat conduction equation (PDE) is given by at 0 x L x pc...

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1D transient heat conduction equation (PDE) is given by a²t 0 ≤ x ≤L əx² pc where t is temperature, 0 is time. Boundary conditions are Initial condition is at дө k –ktx(0,0) = h[too – t(0, 0)] –ktx(L,0) = h[t(L,0) – to] t(x,0) = t(0)(x) (a) Define a new variable to replace original temperature variable t to make the problem homogeneous and write down the new PDE and BCs (b) Find the eigencondition and eigenfunctions for the new homogeneous problem. 1D transient heat conduction equation (PDE) is given by a²t 0 ≤ x ≤L əx² pc where t is temperature, 0 is time. Boundary conditions are Initial condition is at дө k –ktx(0,0) = h[too – t(0, 0)] –ktx(L,0) = h[t(L,0) – to] t(x,0) = t(0)(x) (a) Define a new variable to replace original temperature variable t to make the problem homogeneous and write down the new PDE and BCs (b) Find the eigencondition and eigenfunctions for the new homogeneous problem.

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ANSWER a To make the problem homogeneous we define a new variable xt as xt txt t Substituting this i... View the full answer