1. (30 marks) The steady-state temperature T(x, y, z) of a cubic block satisfies the Laplace equa- tion Txx + Tyy + Tzz

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1 30 Marks The Steady State Temperature T X Y Z Of A Cubic Block Satisfies The Laplace Equa Tion Txx Tyy Tzz 1 (331.53 KiB) Viewed 21 times

1. (30 marks) The steady-state temperature T(x, y, z) of a cubic block satisfies the Laplace equa- tion Txx + Tyy + Tzz = 0, - 0 < x < 1, 0 < y < 1, 0 < z < 1 уу πα with the boundary conditions T(x, y, 1) sin(Tt x) sin(ny) T(1, y, z) sin(ny) sin(az) T(0,y,z) = T(x,0, z) = T(3,1, z) = T(x, y,0) = 0 Find T(x, y, z). - 9 ( = = = 2