The Eckert number (Ec) is a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
used in
continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such ...
. It expresses the relationship between a flow's
kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its a ...
and the boundary layer
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
difference, and is used to characterize heat transfer
dissipation
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy (internal, bulk flow kinetic, or system potential) transforms from an initial form ...
.
It is named after
Ernst R. G. Eckert
Ernst Rudolph Georg Eckert (September 13, 1904 – July 8, 2004) was an Austrian American engineer and scientist who advanced the film cooling technique for aeronautical engines. He earned his Diplom Ingenieur and doctorate in 1927 and 1931, respe ...
.
It is defined as
:
where
* ''u'' is the local
flow velocity
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the ...
of the continuum,
* ''c
p'' is the constant-pressure local
specific heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of he ...
of the continuum,
*
is the difference between wall temperature and local temperature.
References
Dimensionless numbers of fluid mechanics
Dimensionless numbers of thermodynamics
Continuum mechanics
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