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Question: You need to do analytical solution of following Navier-Stokes equation
Navier-Stokes Equation
Applying the mass, momentum and energy conservation, we can derive the continuity equation, momentum equation and energy equation as follows.
Continuity Equation:
Dρ/Dt + ρ∂Ui/∂xi = 0
Momentum Equation
ρ∂Uj/∂t + ρUi∂Uj/∂xi = -∂P/∂xj - ∂τij/∂xi + ρgj
I II III IV V
I: Local change with timeII: Momentum convectionIII: Surface forceIV: Molecular-dependent momentum exchange (diffusion)V: Mass force
Energy Equation
ρcμ∂T/∂t + ρcμUi∂T/∂xi = -P∂Ui/∂xi + λ∂2T/∂xi2 - τij∂Uj/∂xi
I : Local energy change with timeII: Convective termIII: Pressure workIV: Heat flux (diffusion)
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