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

Interferometer, working and construction of interferometer

working and construction of interferometer

Roller Coaster Physics, A 30-g car rolls from a hill 12 cm high and is trav...

A 30-g car rolls from a hill 12 cm high and is traveling at 154 cm/s as it travels along a 275 cm horizontal track. What is the momentum of the car?

Drag, The parachute on a race car that weighs 8750 N opens at the end of a ...

The parachute on a race car that weighs 8750 N opens at the end of a quarter-mile run when the car is traveling 38 m/s. What net retarding force (magnitude) must be supplied by the

Chemical action in lead acid battery, Chemical action in lead acid battery:...

Chemical action in lead acid battery: When the lead acid battery is delivering current, the sulphuric acid breaks up into Hydrogen ions (H 2 ) carrying a positive charge and Su

Condesed matter, sodium metal with a body centred cubic structure has two a...

sodium metal with a body centred cubic structure has two atoms per unit cell. the radius of sodium atom is 1.85 å. calculate its electrical resistivity at 0 oc, if the classical va

Sound, experiments on how sound waves travel faster in iron

experiments on how sound waves travel faster in iron

Galilean relativity, Galilean Relativity Galilean invariance or Galilea...

Galilean Relativity Galilean invariance or Galilean associatively states which the laws of motion are the similar within all inertial frames. Galileo Galilei first define this

How many arsenic atoms should there be for each silicon atom, Silicon has 1...

Silicon has 1.45 x 10 10 free electrons/cm 3 at room temperature. If you wanted to have 3x10 6 as many electrons from arsenic doping as thermal free electrons from silicon at ro

Explain the initial and the final locations of the charge, A charge of 2.00...

A charge of 2.00x 10 -6 C is moved against a constant electric field. If 4.50 x 10 -4 J of work is done on the charge. what is the potential difference between the initial an

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