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

What is an alloy, What is an alloy? An alloy is a homogeneous hybrid of...

What is an alloy? An alloy is a homogeneous hybrid of two or more elements, at least one of which is a metal, and where the resulting material has metallic properties. The resu

what percentage should the pressure of a given mass, By what percentage sh...

By what percentage should the pressure of a given mass of gas be increased,so as to decrease its volume  by 10% at a constant temperature.

Motion, An athlete run a certain distance before taking a long jump. Why?

An athlete run a certain distance before taking a long jump. Why?

Superposition theorem, how to find output voltage using superposition theor...

how to find output voltage using superposition theorem

Electricmotor, im trying to build an electric motor and would like to know ...

im trying to build an electric motor and would like to know y they wind there copper wire in what paturn to make power and secondly what is the output per gram of copper in these t

Positive charge on n-side of the junction, Positive charge on n-side of the...

Positive charge on n-side of the junction Some  of  the  free  electrons  move  across  the junction  from  n-type  to  p-type, leaving  behind  positive  donor  ions  as  they

Its hard 4 me, what is physics and how to learn it easlly?

what is physics and how to learn it easlly?

Joules laws, Joule's laws (J.P. Joule) Joule's first law The he...

Joule's laws (J.P. Joule) Joule's first law The heat Q generated while a current I pass through a resistance R for a particular time t is given by following Q = I2 R

Explain inertia, Inertia: the resistance an object has to a alter in its s...

Inertia: the resistance an object has to a alter in its state of motion. Newton's first law of motion declares that force is NOT required to keep an object in motion. Slide

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