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 unit of capacity, Unit of Capacity: The unit of capacity of a c...

Unit of Capacity: The unit of capacity of a capacitor is known as farad (f). It is given by a relation. q = cv.

Circuit theory, what is significance of kirchoff''s law?

what is significance of kirchoff''s law?

Linear acceleration, The rope shown in the figure attached hereto is wound ...

The rope shown in the figure attached hereto is wound around a cylinder of of mass 4.0 kg, radius 10cm and I=0.020kgm2 , where I is the moment of inertia about an axis along the cy

Illustrate the source of stellar energy, Illustrate the source of stellar e...

Illustrate the source of stellar energy. Describe the carbon-nitrogen cycle and proton - proton cycle occurring in stars. Write down a note on ‘Breeder reactor'.

Sketch the x-y intensity pattern, Consider the 4-f system below where an ob...

Consider the 4-f system below where an object is placed at the input plane and is illuminated by a plane wave   The object to the right is placed in the input plane where b

Natural and forced vibrations, Natural and forced vibrations When we st...

Natural and forced vibrations When we strike a tuning fork with a rubber hammer it vibrates with certain frequency. The frequency does not change even if we hit it harder.

Describe mosley''s law, Mosley studied the characteristic X-ray spectrum of...

Mosley studied the characteristic X-ray spectrum of a number of a heavy elements and concluded that the spectra of dissimilar elements are very same and with enhancing atomic value

What is meant by the term modulation, What is meant by the term 'modulation...

What is meant by the term 'modulation'? Define with the help of a block diagram, how the process of modulation is carried out in radio broadcasts.

What is an optical port, What is an optical port? In the fiber optics i...

What is an optical port? In the fiber optics industry, optical port is the component that physically produces the connection or interface in between the harness and the illumin

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