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GATE Mechanical 2022 Set 1 | Question: 2

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Solution of $\triangledown ^{2} T = 0$ in a square domain ($0 < x< 1$ and $0 < y< 1$) with boundary conditions: $T \left ( x,0 \right ) = x; T \left ( 0,y \right ) = y; T\left ( x,1 \right ) = 1 + x; T\left ( 1,y \right )= 1 +y$ is

  1. $T \left ( x,y \right ) = x - xy +y$
  2. $T \left ( x,y \right ) = x + y$
  3. $T \left ( x,y \right ) = -x + y$
  4. $T \left ( x,y \right ) = x + xy + y$
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