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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005450
EISBN: 978-1-62708-196-2
... Abstract This article is a comprehensive collection of fluid dynamic equations for properties of fluids, fluid statics, fluid motion, dimensional analysis, and boundary layer flow. It presents equations for analyzing problems in fluid mechanics, continuity equation, momentum equation...
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
... Abstract Computational fluid dynamics (CFD) is a computationally intensive three-dimensional simulation of thermal fluids systems where non-linear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD...
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: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002444
EISBN: 978-1-62708-194-8
... Abstract Computational fluid dynamics (CFD) is reserved for computationally intensive three-dimensional simulations of thermal fluids systems where nonlinear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction...
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...
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.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...
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: 4F
Publisher: ASM International
Published: 01 February 2024
DOI: 10.31399/asm.hb.v4F.a0007008
EISBN: 978-1-62708-450-5
... differential equations for the fluid flow and heat-transfer phenomena during quenching. No solid-state transformations or stress-strain relationships are considered. The models consist of a set of differential equations based on the conservation of mass (continuity equation), momentum (motion 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...
Image
Published: 01 February 2024
Fig. 4 Schematic representation of a quenching system showing boundary conditions for momentum, mass, and energy equations. 1, inlet flow; 2, outlet flow; 3, nonslip wall condition; 4, free surface; 5, internal mass and momentum source More
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: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005510
EISBN: 978-1-62708-197-9
... interface. Analogous to the magnetic diffusion equation, this interface is internal to the domain because the continuity of the interface shear force at the slag-metal interface is inherent in the momentum equation. The special aspects of the boundary conditions that arise due to the presence of the slag...
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
.... From another viewpoint, the equilibrium of forces is expressed by the conservation of momentum and the definition of the stress tensor, σ, the traction vector, τ, and the body force, b , in the differential equation: (Eq 17) ∇ ⋅ σ + b = m x ¨ In welding, it is typical to assume...
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
... the momentum and continuity equation. The thermal flux from the arc is prescribed on the weld pool and arc interface. With these data, the energy equation determines the position of the liquid-solid interface. With a new temperature distribution, the momentum equation is solved. If this iteration procedure...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005238
EISBN: 978-1-62708-187-0
... to solve them, and a few examples of recent applications in shape castings and continuous casting. Governing Equations The modeling of mechanical behavior requires solution of 1) the equilibrium or momentum equations relating force and stress, 2) the constitutive equations relating stress and strain...
Series: ASM Handbook
Volume: 4C
Publisher: ASM International
Published: 09 June 2014
DOI: 10.31399/asm.hb.v04c.a0005898
EISBN: 978-1-62708-167-2
... Abstract This article focuses on the basic turbulent flow, and the thermal, mass-transfer, and hydrodynamic phenomena for use in modeling physical processes during induction melting. It provides a discussion on transport phenomena equations that includes the approximation of convective terms...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003302
EISBN: 978-1-62708-176-4
... properties of materials. Several inelastic properties such as hardness, yield strength, and fracture toughness appear in a majority of these equations. However, the exponent of the velocity term in these models has been observed to range between 2 and 5. Based on the momentum considerations, these authors...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005503
EISBN: 978-1-62708-197-9
..., the Reynolds number (a dimensionless number characterizing a ratio of inertia force to viscous force) is low, and the flow is modeled as a creeping flow with lubrication, as treated with the Hele-Shaw formulation. With the Hele-Shaw model, the continuity and momentum equations for the melt flow...