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

Valve & digital electronics: thermionic emission, (i) The procedure of ejec...

(i) The procedure of ejection of electrons from a metal surface by the application of heat is known as thermionic emission and emitted electrons are known as thermions and current

Motion in one dimension, a freely falling object near the Earth''s surface ...

a freely falling object near the Earth''s surface has constant?

What are non-mechanical waves , The waves which do not needs medium for the...

The waves which do not needs medium for their propagation are known as non- mechanical or electromagnetic waves. Examples : Light, heat (Infrared), radio waves, gamma- rays, X-r

What is nuclear fusion, In nuclear fusion two or more than two lighter nucl...

In nuclear fusion two or more than two lighter nuclei join to form a single heavy nucleus. The volume of one molecule so formed is less than the sum of the masses of parent nuclei.

Which device has a czechoslovakian word meaning, What mechanical and electr...

What mechanical and electronic device has a name derived from a Czechoslovakian word meaning "work; compulsory service"? Ans: From a Czechoslovakian word meaning "work; com

Elementary Mechanics, A bird flies in the east direction with a speed of 5 ...

A bird flies in the east direction with a speed of 5 ms-1. The wind is blowing towards north at a speed of 3 ms-1. Determine the relative velocity of the bird with respect to the w

Determine the diameter of ring in newtons rings experiment, In a Newton's r...

In a Newton's rings arrangement the diameter of a bright ring is 0.5cm. Determine the diameter of ring if the lens placed on the plane glass plate is replaced by another one having

Force, what is deforming force

what is deforming force

Cart and the brick momentum and collisions, Cart and The Brick Collisio...

Cart and The Brick Collisions among objects are governed through laws of momentum and energy. While a collision occurs in an isolated system, a total momentum of the system of

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