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

Determine the length of the hypotenuse, A right triangular prism has volume...

A right triangular prism has volume equal to 288 cm^3. The height of the prism is 3 cm. One of the bases of the triangular face (not the hypotenuse) is equal to 12 cm, determine th

What are end-terminations, What are end-terminations? Again, we get our...

What are end-terminations? Again, we get ourselves in an area where many confusion and controversy are the order of the day. Several American institutions have tried to set sta

Rate of effusion of nitrogen gas, How can we calculate the rate of effusion...

How can we calculate the rate of effusion of nitrogen gas from a cylinder. and how much time it will take??

GRAMMAR CHECK, And then did he sit up.IS THIS A SENTENCE OR A QUESTION

And then did he sit up.IS THIS A SENTENCE OR A QUESTION

Motion in one dimension and vectors, two forces f1 500Ndue east and f2 250N...

two forces f1 500Ndue east and f2 250N due north have their common initial point f1 - f2 is

Define average and instantaneous acceleration, Average and Instantaneous Ac...

Average and Instantaneous Acceleration: Average acceleration is explained as the change in velocity   over a given time interval. As, The instantaneous acceleration of g

When the hammer strikes the two strings , In certain ranges of a piano keyb...

In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide extra loudness. For example, the note at 110 Hz has two strings at this frequency.

Michelson interferometer, How will you determine the difference in the wa...

How will you determine the difference in the wavelengths of 2D lines of sodium light buy Michelson Interferometer

Determine the inside plate temperature, A carbon steel plate (thermal condu...

A carbon steel plate (thermal conductivity = 45 W/m o C) (600 x 900 x 25) mm 2 is maintained at 310 o C. Air at 15 o C bellows over the hot plate. If convection heat transfer co-e

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