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species conservation equation

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Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005636
EISBN: 978-1-62708-174-0
... welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005234
EISBN: 978-1-62708-187-0
... MODEL of the solidification of a metal alloy involves coupling of energy, species, mass, and momentum conservation equations ( Ref 1 , 2 , 3 , 4 , 5 , 6 , 7 ). This article examines critical features of four key areas of modeling transport phenomena associated with casting processes: Heat...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005525
EISBN: 978-1-62708-197-9
.... A reversal of antimony microsegregation at low solid fraction and the tin-controlled flow cause the unusual antimony macrosegregation in (b). Source: Ref 68 Abstract This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005434
EISBN: 978-1-62708-196-2
... ). Equation 12 can easily be generalized to gas mixtures. The molecular mean free path for species i is: (Eq 13) λ i = 1 ∑ j n j σ T i , j c i , j ¯ c i ′ ¯ and the mean free path for the mixture becomes: (Eq 14) λ = ∑ i...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005237
EISBN: 978-1-62708-187-0
... 31 , 2000 , p 1283 – 1292 21. Poirier D.R. , Nandapurkar P.J. , and Ganesan S. , The Energy and Solute Conservation Equations for Dendritic Solidification , Metall. Trans. B , Vol 22 , 1991 , p 889 – 900 22. McBride E. , Heinrich J.C. , and Poirier...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003589
EISBN: 978-1-62708-182-5
... and their equilibria in solids. Such reactions can be written according to Krö ger-Vink notation and must obey the usual rules of electrochemical equations (mass and charge conservancy). The key difference is an additional conservation law, the “rule of the lattice conservancy,” which states that only a stoichiometric...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005521
EISBN: 978-1-62708-197-9
... 〉 / 〈 w l 〉 , mathematical developments of the average conservation equations lead to: (Eq 6) ∂ 〈 w 〉 ∂ t − div   [ D ˜   g r a d 〈 w 〉 ]   − d i v [ D ˜   ( 1 − k ) 〈 w 〉 k g s + ( 1 − g s )   g r a d   g...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005520
EISBN: 978-1-62708-197-9
... 30 46. Poirier D.R. , Nandapurkar P.J. , and Ganesan S. , The Energy and Solute Conservation Equations for Dendritic Solidification , Metall. Mater. Trans. B , Vol 22 ( No. 6 ), 1991 , p 889 – 900 47. Lee P.D. and Hunt J.D. , Hydrogen Porosity...
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.9781627081870
EISBN: 978-1-62708-187-0
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005429
EISBN: 978-1-62708-196-2
... N.W. and Mermin N.D. , Solid State Physics , Saunders College , Philadelphia, PA , 1976 16. Hohenberg J. and Kohn L.J. , Phys. Rev. B , Vol 136 , 1962 , p 864 17. Kohn W. and Sham L.J. , Self-Consistent Equations Including Exchange and Correlation...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003580
EISBN: 978-1-62708-182-5
... for Binary Systems Temperature Effects on <italic>E</italic>-pH Diagrams for Ternary Systems Principle of <italic>E</italic>-pH Diagrams for Adsorbed Species <italic>E</italic>-pH Equations for Oxygen and Sulfur Adsorbed on Iron Potential-pH Diagrams for Oxygen and Sulfur Adsorbed on Iron...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005501
EISBN: 978-1-62708-197-9
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006823
EISBN: 978-1-62708-329-4
..., which is based on the ASME Boiler and Pressure Vessel Code, uses the same equations to calculate minimum thicknesses for vessel components as those given in the FFS code (2007) for the shell, heads, and nozzles. The drum was conservatively assumed to be completely filled with fluid with a specific...
Series: ASM Handbook
Volume: 2B
Publisher: ASM International
Published: 15 June 2019
DOI: 10.31399/asm.hb.v02b.9781627082105
EISBN: 978-1-62708-210-5
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005437
EISBN: 978-1-62708-196-2
... Abstract This article presents the governing equations for moving a solidification front, based on the balance of mass, momentum, energy, and solute. It reviews how material properties and geometry can be analyzed in the context of the governing equations. The article provides several example...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005208
EISBN: 978-1-62708-187-0
... Abstract This article begins with balance equations for mass, momentum, energy, and solute and the necessary boundary conditions for solving problems of interest in casting and solidification. The transport phenomena cover a vast range of length and time scales, from atomic dimensions up...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.9781627081962
EISBN: 978-1-62708-196-2
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005415
EISBN: 978-1-62708-196-2
..., modeling microstructure evolution typically proceeds along the route of nucleation, growth, and coarsening, either focusing on one stage or treating them as concurrent processes ( Ref 51 ). The phase-field governing equations treat both conserved ( Eq 6 ) and nonconserved ( Eq 12 ) fields, corresponding...
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001731
EISBN: 978-1-62708-178-8
... as a qualitative tool to identify and characterize molecular species (including solvated molecular ions) and as a quantitative tool to assess the quantities of inorganic, organic, and biochemical species present in various samples. Of the many applications of this technique, this article will emphasize...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006679
EISBN: 978-1-62708-213-6
... of the oxidized and reduced species at equilibrium, that is, when the current is zero in the electrolysis. Table 1 Types of reactions in controlled-potential electrolysis and applicable Nernst equations Type of reaction (a) Nernst equation (b) I. Oxidized and reduced species soluble...