Transient state or unsteady state?
Hi everybody.
I have a doubt. It´s the next: On the conductive heat transfer topic what is the difference between transient state and unsteady state? could I use them indiscriminately? Thanks. Conde de la Fère. 
Dear Conde de la Fère,
In conductive HT (as well as in other fields) the term "transient" indicates the problem is timedependent (in your case, for example, the temperature depends on time in addition to space location), while "steady" means the problem does not depend on time. The term "unsteady" is therefore equivalent to "transient". 
Hi, in general terms I'd consider the terms "transient" and "unsteady" to be equivalent. Both indicate that the problem is dependent on time, as Rami just said.
However, I think that there's a subtle difference between both terms: On the one hand, the term "transient" is usually employed to indicate the evolution over time of the solution from an initial state until it reaches the steady state (the solution does not change any more). On the other hand, the term "unsteady" could indicate that the solution does not reach such steadystate solution, it varies over time always. Such situation may arise for example when you have a source term within the solid, or boundary conditions that vary over time. Cheers, Michujo. 
Thanks
Thank everybody for helping me in this question.
Best regarts, Conde de la Fère. 
Suppose one has a problem with spatial boundary conditions that are periodic in time. There may be a solution that is periodic in time, invariant from cycle to cycle, but varying within a cycle. This would seem to be a sort of steady state. If one starts with (nonperiodic) initial conditions which evolve over time to the periodic state, then one might, without question, call the evolving system transient. But what would you call the timeperiodic state? The "state" would seem to be steady as it is not evolving, though it varies within a cycle. Would you call it "periodsteady", "quasisteady", or what?
What I have in mind is peristaltic flow in a channel or a leaky piston in a cylinder, serving as a damper. 
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however, such flows are unsteady, the forcing frequency is fixed in your example but the cycles are only statistically equivalent each other. Actually, this is the classical framework for UnsteadyRANS. 
F. M. Denaro posted:
however, such flows are unsteady, the forcing frequency is fixed in your example but the cycles are only statistically equivalent each other. Actually, this is the classical framework for UnsteadyRANS. Consider this problem of 2D incompressible peristaltic flow with moving upper boundary given by Yu=Y0(1+a*cos(2*pi*(xv0*t))) and bottom boundary the negative of this, or simulating half of the domain with full slip, nopenetration BC on lower boundary. We treat the time using a finite element method, so we construct a 3D mesh with 2 space dimensions and time. We truncate the domain in the time dimension to, say, one period and apply periodic boundary conditions in time. Now we have a simple (nonlinear) boundary value problem with the fluid flow being driven by the "moving" boundary. We solve this using "stationary" methods. At any fixed time the mesh boundary is moving with velocity v0 as it progresses. If a stationary solution exists (and I am confident that it does at small Re), I contend the cycles on the full domain will necessarily periodic, and obviously without statistical fluctuations. This brings me back to the question of how do we name this flow? 
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Assuming a laminar condition this flow repeats the solution in a deterministic sense. But it is unrealistic that such flow is really laminar as, in generla, the Reynolds number is usually high. Therefore you can realize a URANS simulation, you still truncate the time integration to a single period but the solution has a statistically meaning. However, laminar o turbulent, both problem are timedependent in the characteristic period. This is only my opinion ;) 
But the Reynolds number can be quite small for peristaltic flows which describe the motion of fluids in organisms, the movement of food through the intestines for example.

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