the conservation & non conservation form of navier stoke equations are mathematically equal, but physically how we differntiate it?. can anyone expalin this..

Conservative is usually thought of as

rate of change of momentum = sum of forces,

working on a fixed frame and looking at boundary fluxes and forces.

Non-conservative is usually thought of as

sum of forces = mass * acceleration,

following a fixed collection of 'fluid particles' as it moves through time and space.

Your thinking in deriving the two should be following the two concepts. It's an exercise in differing philosophies (at least for me).

In Unsteady Fluid flow problems, the any flow quantities (mass, mom and ener)inside the domain will change based on contribution of time, space and convection.

If its Eulerian approach then our CV is fixed so we get a time effect and combined effect of (Space + Convection = flux)... so its called as conservation form

If its Lagrangian approach then our CV is moving so we cant separate the effect of time and space... so now we get the convection and combined effect of (time + space = material derivative).. So its called as Non-Conservation form

I understood in this way.. but i am not sure abt it..