In combustion, 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 in 1956.[1][2][3] The flame is of diffusion flame 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

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Source:[4]

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 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

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References

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  1. ^ Emmons, H. W. (1956). The film combustion of liquid fuel. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 36(1‐2), 60-71.
  2. ^ Clarke, J. F. (1969). Emmons' problem according to the Oseen approximation. The Physics of Fluids, 12(1), 241-243.
  3. ^ Baum, H. R., & Atreya, A. (2015). The Elliptic Emmons Problem. In ICHMT DIGITAL LIBRARY ONLINE. Begel House Inc.
  4. ^ Williams, F. A. (2018). Combustion theory. CRC Press.