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For 2-D, steady-state, no-generation conduction, the governing PDE is:
A{'text': '$\\nabla^2 T = \\rho c_p \\partial T/\\partial t$', 'label': 'A'}
B{'text': "$\\partial^2 T/\\partial x^2 + \\partial^2 T/\\partial y^2 = 0$ — Laplace's equation", 'label': 'B'}
C{'text': '$\\partial T/\\partial t = \\partial T/\\partial x$', 'label': 'C'}
D{'text': '$T = const$', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': "$\\partial^2 T/\\partial x^2 + \\partial^2 T/\\partial y^2 = 0$ — Laplace's equation", 'label': 'B'}
Steady ⇒ time term vanishes. No generation ⇒ source term vanishes. The heat equation collapses to Laplace: $\partial^2 T/\partial x^2 + \partial^2 T/\partial y^2 = 0$. Requires 2 boundary conditions per direction.
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