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

Define mechanical energy, Mechanical energy E of particle, system or object...

Mechanical energy E of particle, system or object is explained as the sum of kinetic energy K and potential energy U, i.e. E = K + U. It is a scalar quantity having dimensions [ML

Define free electron theory, What is the difference among Free Electron The...

What is the difference among Free Electron Theory and Band Theory of solids? Free Electron Theory: This theory says that, metals conduct electricity due to the presence of

Evaluate the final angular speed of the carousel, As seen from above, a pl...

As seen from above, a playground carousel is rotating counterclockwise about its center on frictionless bearings. A person standing still on the ground grabs onto one of the bars o

How are appliances , How are appliances we use in the domestic circuit inte...

How are appliances we use in the domestic circuit interlinked? What are the benefits of this connection?

Can an electron be obtained from the nucleus, Can an electron be obtained (...

Can an electron be obtained (or come out) from the nucleus? Yes, electron having energy higher than the ordinary atomic electron might be come out of the nucleus because of be

Determine the doppler effect, The Doppler Effect shows that the spectrum of...

The Doppler Effect shows that the spectrum of light from a visible body moving AWAY from the Earth will experience a shift in frequency when viewed from Earth. This definite s

Length contraction (relativity of length), Length contraction (relativity o...

Length contraction (relativity of length) is the length of a body moving with a relativistic velocity v = c relative to an observer is contracted by a factor in the direction of m

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