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Lecture

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In course

MATH-212: Analyse numérique et optimisation

L'étudiant apprendra à résoudre numériquement divers problèmes mathématiques. Les propriétés théoriques de ces méthodes seront discutées. ...

Instructor

Marco Picasso

Official source

https://mediaspace.epfl.ch/media/0_823xgbua

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Related concepts (32)

Diffusion

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.

Convection

Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow. Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see Convection cell).

Convection–diffusion equation

The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.

Molecular diffusion

Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules.

Forced convection

Forced convection is a mechanism, or type of transport, in which fluid motion is generated by an external source (like a pump, fan, suction device, etc.). Alongside natural convection, thermal radiation, and thermal conduction it is one of the methods of heat transfer and allows significant amounts of heat energy to be transported very efficiently. This mechanism is found very commonly in everyday life, including central heating, air conditioning, steam turbines, and in many other machines.

Related lectures (50)

Convection-Diffusion: Boundary Layer Analysis

Discusses boundary layer analysis in convection-diffusion problems, focusing on numerical schemes and stability.

Diffusion and Convection Transport

Explores the microscopic description of diffusion and convection transport, emphasizing similarities between chemical diffusion and heat conduction.

Heat transport: Conduction, Convection, Radiation

Explores heat transport through conduction, convection, and radiation in micro and nanosystems.

Chemical Equilibria and Reactivity

Explores the kinetic model of gases, Maxwell's law, diffusion, effusion, Graham's law, and gas pressure.

Thermal Transport & Steady-state