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In steady state analysis, you assume anything that changes with time is 0. ie: d*rho/dt = 0. In transient, you keep all your d/dt terms. Steady state simplification is a handy tool to make many differential equations solvable, by reducing their "dimension", as x-direction, y-direction, z-direction, and time are each dimensions.

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Q: Difference between steady state and transient analysis?
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