In
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combusti ...
, Emmons problem describes the flame structure which develops inside the boundary layer, created by a flowing oxidizer stream on flat fuel (solid or liquid) surfaces. The problem was first studied by
Howard Wilson Emmons
Howard Wilson Emmons (1912–1998) was an American professor in the department of Mechanical Engineering at Harvard University. During his career he conducted original research on fluid mechanics, combustion and fire safety. Today he is most widely ...
in 1956. The flame is of
diffusion flame
In combustion, a diffusion flame is a flame in which the oxidizer and fuel are separated before burning. Contrary to its name, a diffusion flame involves both diffusion and convection processes. The name diffusion flame was first suggested by S. ...
type because it separates fuel and oxygen by a flame sheet. The corresponding problem in a quiescent oxidizer environment is known as
Clarke–Riley diffusion flame.
Burning rate[Williams, F. A. (2018). Combustion theory. CRC Press.]
Consider a semi-infinite fuel surface with leading edge located at
and let the free stream oxidizer velocity be
. Through the solution
of
Blasius equation (
is the self-similar
Howarth–Dorodnitsyn coordinate), the mass flux
(
is
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
and
is vertical velocity) in the vertical direction can be obtained
:
where
:
In deriving this, it is assumed that the density
and the viscosity
, where
is the temperature. The subscript
describes the values far away from the fuel surface. The main interest in combustion process is the fuel burning rate, which is obtained by evaluating
at
, as given below,
:
See also
*
Liñán's diffusion flame theory Liñán diffusion flame theory is a theory developed by Amable Liñán in 1974 to explain the diffusion flame structure using activation energy asymptotics and Damköhler number asymptotics.Liñán, A., Martínez-Ruiz, D., Vera, M., & Sánchez, A. ...
References
{{reflist
Fluid dynamics
Combustion