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

Orbital velocity for low earth orbit, Q. Orbital Velocity for Low Earth Orb...

Q. Orbital Velocity for Low Earth Orbit Neglecting air friction an object will sustain a low altitude orbit when the centrifugal force due to its motion in a circular orbit is

The galvanometer records a current , A galvanometer together with an unknow...

A galvanometer together with an unknown resistance in series is linked across two identical batteries each of 1.5V. whenthese batteries are connected in series the galvanometer rec

Quantum physics, in compton effect explain the presence of unmodified radia...

in compton effect explain the presence of unmodified radiation

Can two candles be taken as coherent sources, Can two candles be taken as c...

Can two candles be taken as coherent sources? Explain how.

Verify the principle of potentiometer, Verify the principle of potentiomete...

Verify the principle of potentiometer. Illustrate a circuit diagram used to compare the e.m.f. of two primary cells. Write the formula used. How can the sensitivity of a potentiome

Explain the single mode fibres in intermodal dispersion, Explain about the ...

Explain about the single mode fibres in intermodal dispersion. Into single mode fibers, the core size of the fibre is decreased to 3 to 9µm so that this supports simply axial m

Amperes law, The line integral of the magnetic flux about a closed curve is...

The line integral of the magnetic flux about a closed curve is proportional to the algebraic total of electric currents passing through that closed curve; or, in differential form,

Electronics, workind and defination and symbol of zener diode

workind and defination and symbol of zener diode

Magnetic field and electric current., the magnetic field at a dictance of 2...

the magnetic field at a dictance of 2cm from the axis of a straight conductor carrying current is 12mT.Find the currentin the conductor?

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