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. Combust ...
, a Burke–Schumann flame is a type 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. ...
, established at the mouth of the two concentric ducts, by issuing fuel and oxidizer from the two region respectively. It is named after S.P. Burke and T.E.W. Schumann, who were able to predict the flame height and flame shape using their simple analysis of infinitely fast chemistry (which is now called as
Burke–Schumann limit) in 1928 at the
First symposium on combustion.
Mathematical description
Consider a cylindrical duct with axis along
direction with radius
through which fuel is fed from the bottom and the tube mouth is located at
. Oxidizer is fed along the same axis, but in the concentric tube of radius
outside the fuel tube. Let the
mass fraction in the fuel tube be
and the
mass fraction of the oxygen in the outside duct be
. Fuel and oxygen mixing occurs in the region
. The following assumptions were made in the analysis:
* The average velocity is parallel to axis (
direction) of the ducts,
*The mass flux in the axial direction is constant,
*Axial diffusion is negligible compared to the transverse/radial diffusion
* The flame occurs infinitely fast (
Burke–Schumann limit), therefore flame appears as a reaction sheet across which properties of flow changes
* Effects of gravity has been neglected
Consider a one-step irreversible
Arrhenius law,
, where
is the mass of oxygen required to burn unit mass of fuel and
is the amount of heat released per unit mass of fuel burned. If
is the mass of fuel burned per unit volume per unit time and introducing the non-dimensional fuel and mass fraction and the Stoichiometry parameter,
:
the governing equations for fuel and oxidizer mass fraction reduce to
:
where
Lewis number The Lewis number (Le) is a dimensionless number defined as the ratio of thermal diffusivity to mass diffusivity. It is used to characterize fluid flows where there is simultaneous heat and mass transfer. The Lewis number puts the thickness of the ...
of both species is assumed to be unity and
is assumed to be constant, where
is the
thermal diffusivity
In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure. It measures the rate of transfer of heat of a material from the hot end to the cold end. It has the SI ...
. The boundary conditions for the problem are
: