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conservation equations

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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
... electromagnetic fields. Conservation equations that represent important physical phenomena during casting processes are presented. The article provides a discussion on how the physical phenomena can be solved. It provides information on a well-established array of general and specific computational tools that can...
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: 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...
Image
Published: 01 December 2008
. Magnification in (b) reveals the dendritic microstructure of the alloy, with an interdendritic black region corresponding to a eutectic microstructure that is not resolved at this scale. The size of the highlighted square would be typical of the representative elementary volume used to solve conservation More
Image
Published: 01 December 2009
. Magnification in (b) reveals the dendritic microstructure of the alloy, with an interdendritic black region corresponding to a eutectic microstructure that is not resolved at this scale. The size of the highlighted square would be typical of the representative elementary volume (REV) used to solve conservation More
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: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003402
EISBN: 978-1-62708-195-5
... respectively. V barrel = π DN , where D is the diameter of the screw and N is the speed in revolutions per second. Physical Laws Once the system is identified, one would express conservation of mass, momentum, and energy within the system boundaries ( Ref 21 , 22 ). The conservation equations...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005510
EISBN: 978-1-62708-197-9
... Navier-Stokes equations, and the temperature field using energy conservation equations were first developed ( Ref 24 , Ref 25 , Ref 26 , Ref 27 , Ref 28 , Ref 29 , Ref 30 , Ref 31 , Ref 32 , Ref 33 , Ref 34 , Ref 35 , Ref 36 ) for the ESR process. Early versions of these models focused...
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
.... Macroscopic Conservation Equations in Pure Gases Moles are usually used instead of molecules at the macroscopic scale. Molar quantities are related to their molecular counterparts by the Avogadro's number N ( ≅ 6.022 × 10 23 ) , including the universal ideal gas constant, R...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005233
EISBN: 978-1-62708-187-0
... that total energy, in all its forms, must be conserved These three principles lead to the basic three equations of motion: the mass, or continuity, equation; the momentum equation; and the total energy equation. Each of the articles that follow in this Section develops these fundamental balance...
Series: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006409
EISBN: 978-1-62708-192-4
... on solving a set of partial differential equations that express the conservation of mass, momentum, and energy, and can be solved either by mesh-based (e.g., finite-element modeling [FEM]) or mesh-free (e.g., smoothed particle hydrodynamics) methods ( Ref 26 ). The strength of macroscopic descriptions lies...
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.a0001480
EISBN: 978-1-62708-173-3
... efficient. Energy Equation and Heat Transfer The conservation of energy is the fundamental principle that underlies all thermal analysis, including that of welds. In the simplest terms, it states that while energy can be added or extracted, no energy can be created or destroyed in the domain being...
Series: ASM Handbook
Volume: 6A
Publisher: ASM International
Published: 31 October 2011
DOI: 10.31399/asm.hb.v06a.a0005587
EISBN: 978-1-62708-174-0
... more accurate and more efficient. Energy Equation and Heat Transfer The conservation of energy is the fundamental principle that underlies all thermal analysis, including that of welds. In the simplest terms, it states that while energy can be added or extracted, no energy can be created...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005236
EISBN: 978-1-62708-187-0
... grains). This article concentrates on these intermediate length scales, where transport phenomena govern the spatial and temporal evolution of the structure. To calculate this evolution, conservation equations are written for each individual phase (liquid or solid), with the most challenging aspect being...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005406
EISBN: 978-1-62708-196-2
... evolution of the structure. To calculate this evolution, conservation equations are written for each individual phase (liquid or solid), with the most challenging aspect being the treatment of the interfaces between phases and the nonequilibrium condition of the liquid metal during the solidification state...
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: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003291
EISBN: 978-1-62708-176-4
... Often, the design of pressurized components is based on simple and desirably conservative design rules, and, in many cases, a simple mean diameter hoop (MDH) stress equation is used only because experience has proved it to be conservative in most cases: (Eq 28) MDH = p ( d o − t...
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.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...