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If a CFD code can compute heat conduction but is missing CONVECTION terms, what equation is being solved?
A{'text': 'Navier-Stokes', 'label': 'A'}
B{'text': 'Heat diffusion equation (pure conduction): $\\rho c_p \\partial T/\\partial t = k\\nabla^2 T + \\dot{q}$', 'label': 'B'}
C{'text': 'Stefan-Boltzmann', 'label': 'C'}
D{'text': 'Laplace equation only', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': 'Heat diffusion equation (pure conduction): $\\rho c_p \\partial T/\\partial t = k\\nabla^2 T + \\dot{q}$', 'label': 'B'}
Without bulk fluid motion, only diffusion contributes. The heat-diffusion equation governs T(x,y,z,t) in a solid (or a stagnant fluid). For steady-state ($\partial/\partial t = 0$) and no generation ($\dot{q} = 0$), it reduces to Laplace's equation $\nabla^2 T = 0$.
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