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The Euler equations can be formulated in a "convective form" (also called the "Lagrangian form") or a "conservation form" (also called the "Eulerian form"). The convective form emphasizes changes to the state in a frame of reference moving with the fluid.
An example of a set of equations written in conservation form are the Euler equations of fluid flow: + = + (+) = + ((+)) = Each of these represents the conservation of mass , momentum and energy , respectively.
Convection cooling is sometimes said to be governed by "Newton's law of cooling." When the heat transfer coefficient is independent, or relatively independent, of the temperature difference between object and environment, Newton's law is followed. The law holds well for forced air and pumped liquid cooling, where the fluid velocity does not ...
The Lagrangian and Eulerian specifications of the kinematics and dynamics of the flow field are related by the material derivative (also called the Lagrangian derivative, convective derivative, substantial derivative, or particle derivative). [1] Suppose we have a flow field u, and we are also given a generic field with Eulerian specification F ...
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 ...
Confusingly, sometimes the name "convective derivative" is used for the whole material derivative D/Dt, instead for only the spatial term u·∇. [2] The effect of the time-independent terms in the definitions are for the scalar and tensor case respectively known as advection and convection.
It describes the rate of change of vorticity of the moving fluid particle. This change can be attributed to unsteadiness in the flow ( ∂ω / ∂t , the unsteady term) or due to the motion of the fluid particle as it moves from one point to another ((u ∙ ∇)ω, the convection term).
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments ) acting on the rigid body.