Derive the conservation law, Physics

Assignment Help:

Suppose a fluid (say, water) occupies a domain D ⊂ R3 and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid as well as diffused within it; let u= u(x,t) be the concentration of the substance( mass per unit volume). Let 677_Derive the conservation law1.pngbe the concentration flux (mass per unit area per unit time, analogous to heat flux). Let B(x) be a ball of radius r > 0 contained in D. Derive the conservation law.

1003_Derive the conservation law.png

Fick's law for diffusion states  that the concentration flux due to diffusion is proportional to the gradient of the concentration flux due to diffusion is proportional to the gradient of the concentration. Deduce that Φ = - kΔ + uV.

Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:

1290_Derive the conservation law2.png

in the absence of diffusion(k=0), this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.


Related Discussions:- Derive the conservation law

Explain change in kinetic energy, Two blocks are tied together by a horizon...

Two blocks are tied together by a horizontal string and pulled a distance of 2.7 m across an air hockey table with a constant force of 35 N. The force is directed at an upward angl

State polarization of the incident light, The light passing through a quart...

The light passing through a quarter wave plate is analysed by a rotating Nicol prism. It is get that the intensity of the emergent light beam from the rotating Nicol prism becomes

Explain average velocity, AVERAGE VELOCITY: The ratio of the total disp...

AVERAGE VELOCITY: The ratio of the total displacement to the total time taken by the body is known as average velocity and represented by V ?av.

Determine expression for the bound ray, A symmetric, multimode slab wavegui...

A symmetric, multimode slab waveguide has a core width 2ρ, a uniform cladding index n cl and a linear, graded-index profile n(x) in the core that is continuous and symmetric about

How can light be classify in simplest form, How can light be classify in si...

How can light be classify in simplest form? Answer:- The common description of light (visible) is electromagnetic radiation visible to the human eye. It is only a little p

Heat therapy - microwave diathermy, Microwave diathermy The microwave ...

Microwave diathermy The microwave diathermy can be produced in special tube which can be placed several inches from the region to be treated . Microwave can penetrate deep int

Special resistor materials: tin, Tin: Atomic number ...

Tin: Atomic number 50 Symbol Sn Atomic weight 118.69 Discovery Known since ancient

Explain destructive interference, Does destructive interference violate the...

Does destructive interference violate the principle of conservation of energy? Briefly explain.

What is unavoidably wrong with the ray tracing diagram, A person is making ...

A person is making a ray tracing diagram to determine the characteristics of an image formed by a converging lens. Consequently far the person has gotten as far as drawing one of t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd