alleryStart learning →For 2-D, steady-state, no-generation conduction, the governing PDE is:
A$\nabla^2 T = \rho c_p \partial T/\partial t$
B$\partial^2 T/\partial x^2 + \partial^2 T/\partial y^2 = 0$ — Laplace's equation
C$\partial T/\partial t = \partial T/\partial x$
D$T = const$
Answer & Solution
Correct answer: B. $\partial^2 T/\partial x^2 + \partial^2 T/\partial y^2 = 0$ — Laplace's equation
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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