Problem 2: In steady-state heat transfer (or in electrostatics), Laplace equation, V?u= 0, is valid when the medium is h

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Problem 2 In Steady State Heat Transfer Or In Electrostatics Laplace Equation V U 0 Is Valid When The Medium Is H 1 (65.25 KiB) Viewed 18 times

Problem 2: In steady-state heat transfer (or in electrostatics), Laplace equation, V?u= 0, is valid when the medium is homogeneous (i.e., the medium is independent on spatial variables). For a nonhomogeneous medium, Laplace equation generalizes to Vu vu+ Vu=0, U where v(I, y, z) is a function describing the medium properties. For a homogeneous medium, v = c, where c is a constant. Consider a rectangle filled with a medium described by v(x) = et and excited from one side = by the source f(x). Then, the problem can be described by Un + ur + Uyy = 0, 0<<<a, 0<< <b, u(0, 3) = 0, u(a,y) = 0 u(x,0) = f(-), = u(a,b) = 0 Solve it.