Question

Solution of ∇2𝑇 = 0 in a square domain (0 < x < 1 and 0 < y < 1) with boundary conditions: T(x, 0) = x; T(0, y) = y; T(x, 1) = 1 + x; T(1,y) = 1 + y is

Options :

  1. T(x, y) = x – xy + y

  2. T(x, y) = x + y

  3. T(x, y) = –x + y

  4. T(x, y) = x + xy + y

Show Answer

Answer :

T(x, y) = x + y

Solution :

T(x, 0) = x ⇒ option (c) is not correct.
T(0, y) = y ⇒ all options satisfied.
T(x, 1) = 1 + x ⇒ only option (b) is satisfied.
T(1, y) = 1 + y ⇒ only option (b) is satisfied.

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