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A significant feature of the Cauchy equation and consequently all other continuum equations (including Euler and Navier–Stokes) is the presence of convective acceleration: the effect of acceleration of a flow with respect to space.
Defining equation SI units Dimension ... Convective acceleration = ... Defining equation (physical chemistry) List of electromagnetism equations;
The Keulegan–Carpenter number can be directly related to the Navier–Stokes equations, by looking at characteristic scales for the acceleration terms: convective acceleration: ( u ⋅ ∇ ) u ∼ V 2 L , {\displaystyle (\mathbf {u} \cdot \nabla )\mathbf {u} \sim {\frac {V^{2}}{L}},}
A significant feature of the Navier–Stokes equations is the presence of convective acceleration: the effect of time-independent acceleration of a flow with respect to space. While individual continuum particles indeed experience time dependent acceleration, the convective acceleration of the flow field is a spatial effect, one example being ...
The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...
The derivation of the Navier–Stokes equations as well as their application and formulation for different families of fluids, is an important exercise in fluid dynamics with applications in mechanical engineering, physics, chemistry, heat transfer, and electrical engineering.
Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat transfer by bulk fluid flow ).
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