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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
... A COMPLETE 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...
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
... Abstract This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during solidification processing. It presents transport equations and several examples of their applications to illustrate the physics present in alloy solidification...
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
... conservation equation must be considered for each of the N species that may be involved in NR gas-phase reactions. For species i : (Eq 40) ∂ ∂ t ( ρ ω i ) = − ∇ · ( ρ v ω i ) − ∇ · j i + M i ∑ k = 1 N R v i k R k g...
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
... equations: continuity, momentum, energy, and solute conservation. The mushy zone is treated as a porous medium. More details pertaining to the transport equations, as well as modifications for numerical implementation, can be found in Ref 12 , 13 , 14 , 15 , 16 , 17 . Continuity Equation...
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 temperature aqueous solutions and adsorbed species and in prediction of corrosion of nickel and copper. acid-base reaction copper corrosion E-pH diagram electrochemical reaction electron transfer equilibrium potential Nernst equation nickel solvated proton transfer temperature aqueous solution...
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
... the surface: must be speci ed. When all of these data are that the heat transfer from the surface of the gathered, one can, in principle, evolve the appro- priate equations in time and nd a solution to the rod to the bath can be characterized by a con- problem at hand. This is usually done numeri- ðð ð cally...
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
... properties also temperature stays at T1, unaffected by the and conducted through the surface: must be speci ed. When all of these data are quench, and that the heat transfer from the sur- gathered, one can, in principle, evolve the appro- priate equations in time and nd a solution to the face of the rod...
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
...-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 number of the cationic and anionic lattice elements can be formed...
Book

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.a0005415
EISBN: 978-1-62708-196-2
... and nonconserved order parameters. Typical examples of the conserved order parameters include concentration of a chemical species, density, and molar volume in a multicomponent and multiphase system. Examples of the nonconserved order parameters include long-range order parameters for atomic ordering, inelastic...
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: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005520
EISBN: 978-1-62708-197-9
..., pressure, and other solute concentrations ( Ref 38 , 39 ). Although the total number of moles of gaseous species in the system is conserved to a first approximation, the concentration of gas-forming elements steadily increases due to partitioning from the solid, where its solubility an order...
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
... encountered in controlled-potential electrolysis, together with the relevant Nernst equations. Equation A in Table 1 (for a type I reaction) shows the logarithmic relationship between the working-electrode potential and the ratios of the concentrations of the oxidized and reduced species at equilibrium...
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
... of conservation equations averaged over a REV made of a mixture of solid and liquid phases. The general approximation of static phases and a binary system is made. Additionally, the densities of the solid and liquid phases are assumed constant and equal. The system is only made of a binary mixture of constituents...
Series: ASM Handbook
Volume: 2B
Publisher: ASM International
Published: 15 June 2019
DOI: 10.31399/asm.hb.v02b.a0006486
EISBN: 978-1-62708-210-5
... is important not only in the elastic range, as characterized by the modulus of elasticity, E , but also in the inelastic range, where the stress exceeds the yield stress. The shape of the stress-strain curve can be characterized by the Ramberg-Osgood equation, which relates stress, F , to strain, ε, over...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005426
EISBN: 978-1-62708-196-2
... equations were derived by conserving properties such as computed mass, momentum, and energy. To be more precise, consider the approximation to the aforementioned mass equation. A conservative approximation has the property that if ν and μ are two cells that share face α, then when one sums the finite-volume...
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
... extensions KS Kohn and Sham LAPW Linearized augmented plane wave LCAO Linear combination of atomic orbitals LDA Local density approximation LSDA Local spin density approximation MES Murnaghan's equation of state MTO Muffin tin orbital OPW Orthogonalized plane wave PAW...
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
... Determination When there are only two species in the sample, it is possible to determine the concentrations of both by solving two simultaneous equations (in principle, three species can be simultaneously analyzed for by solving three simultaneous equations, and so on). For example, the simultaneous...
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
... through G 4 are influence coefficients that depend on t c / r i , a /c, a / t c , ϕ, and Q and are conservatively calculated using equations given in paragraphs 9B.5.10 and 9B.14.3 and Table 9B.13 of the FFS code; A 0 = 90.93, A 2 = 502.3968, A 4 = 7.206574, A 1 = 0.107416, A 3 = 7.206574...