Derivation of the Discriminated Dimensionless Numbers that Rule the Forced Mass Convection

M. Conesa; F. Alhama; C. N. Madrid

doi:10.15866/irephy.v11i2.12591

Derivation of the Discriminated Dimensionless Numbers that Rule the Forced Mass Convection

M. Conesa^(1*), F. Alhama⁽²⁾, C. N. Madrid⁽³⁾

^(*) Corresponding author

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Abstract

Discriminated dimensional analysis (DDA, hereinafter), a fundamental extension of classical dimensional analysis (CDA, hereinafter), assumes as independent quantities or physical characteristics of vector character such as length, surface, velocity, viscosity, diffusivity… As a consequence, the dimensional equations of these quantities depend on the spatial direction they are influencing on the physical phenomenon. This causes that the resulting re-grouping of variables to form the dimensionless independent groups are different according to the use of DDA or CDA. The mass transfer problem between a horizontal plate and a forced surrounding fluid is studied assuming two type of boundary conditions, isoconcentration (Diritchlet) and prescribed mass flow at the plate (Neumann). The application of the (-theorem to the set of relevant variables provides an only dimensionless group, the Schmidt number (Sc, hereinafter). To determine the unknowns (thickness of the velocity and concentration boundary layers, as well as the mass transfer coefficient) it is enough to separately introduce these variables in the relevant list of quantities. The two dimensionless groups that emerge for the three unknowns reduce to only one for the limit cases Sc<<1 and Sc>>1, providing for these scenarios the order of magnitude of the unknowns, a result not given by CDA.
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Keywords

Dimensional Analysis; Discrimination; Forced Convection; Mass Transfer

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References

V.S. Arpaci and P.S. Larsen, Convection heat transfer. New Jersey: Prentice-Hall, 1984.

J.H. Lienhard, A heat transfer textbook, 2nd ed.: Prentice-Hall, 1987.

F. Kreith and M.S. Bohn, Principles of heat tranfer. Boston: PWS publishing Company, 1997.

O.G. Martynenko and P.P. Khramtsov, Free-Convective heat transfer. Berlin: Springer, 2005.

W.M. Kays and M.E. Crawford, Convective Heat and Mass Transfer, 3rd ed. Hightstown, New Jersey, USA: McGraw Hill, 1993.

J.P. Holman, Heat transfer, 8th ed.: McGraw-Hill, 1997.

C.N. Madrid and F. Alhama, "Discriminated Dimensional Analysis of the Energy Equation: Application to Laminar Forced Convection Along a Flat Plate," Int. J. Therm. Sci., vol. 44, no. 4, pp. 333-341, 2005.

C.N. Madrid and F Alhama, "Study of the laminar natural convection problem along a isothermal vertical plate bases on discriminated dimensional analisys," Chemical engineering communications, vol. 195 (12), pp. 1-14, 2008.

C.N. Madrid and F. Alhama, "Discrimination: A fundamental and necessary extension of classical dimensional analysis theory," International Communications in Heat and Mass Transfer, vol. 33, pp. 287-294, 2006.

W. Williams, "On the Relation of the Dimensions of Physical quantities to Directions in Space," Phil. Mag., no. 34, 1892.

H.E. Huntley, Dimensional Analysis. London: McDonald, 1952.

C. Runge, Enc. Math. Wiss., (5,1). London, 1952.

J. F. Palacios, Análisis dimensional.: Espasa-Calpe, 1955, Dimensional analysis, Mc Millan, London (1964). Edición en castellano: Espasa-Calpe, S.A., Madrid (1955).

A. T. Mills, Basic heat and mass transfer. Prentice Hall, Upper Saddle River, New Jersey, USA, 1995.

A. J. Chapman, Heat transfer. Mew York: Macmillan publishing company, 1960.

H. Gröber and S. Erk, Transmisión de calor. Madrid: Selecciones científicas, 1967.

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