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Conservation of THERMAL ENERGY in a flowing fluid involves which key terms?
A{'text': 'Just $\\rho c_p T$', 'label': 'A'}
B{'text': '$\\rho c_p DT/Dt = \\nabla \\cdot (k\\nabla T) + \\dot{q} + \\Phi$, where Φ is viscous dissipation', 'label': 'B'}
C{'text': 'Constant T', 'label': 'C'}
D{'text': '$T = 0$', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': '$\\rho c_p DT/Dt = \\nabla \\cdot (k\\nabla T) + \\dot{q} + \\Phi$, where Φ is viscous dissipation', 'label': 'B'}
Energy equation: rate of T change (left) = conduction + heat sources + viscous dissipation (right). Φ is the rate at which mechanical energy is converted to heat by viscous shear (typically negligible at low Mach, important in lubrication/high-speed flow).
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