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

Computing the electric potential at a particular point, When one is computi...

When one is computing the electric potential at a particular point in space due to a continuous charge distribution what exactly is one calculating? Ans: The electric poten

Explain the maxwells equation in electromagnetism, Explain the Maxwell's eq...

Explain the Maxwell's equation in electromagnetism connecting magnetic field vector and electric displacement vector.

Fresnel and fraunhoffer approaches of diffraction, Write about the main fea...

Write about the main features in which Fresnel and Fraunhoffer approaches of diffraction differ? Mention some (at least four) applications of diffraction.

Principle of electric motor, An electric motor is a device which converts e...

An electric motor is a device which converts electrical energy into mechanical energy. Principle of electric motor : An electric motor essentially consists of a rectangular co

Mica capacitors, Mica is a mineral that can be readily sliced into thin chi...

Mica is a mineral that can be readily sliced into thin chips, makes an excellent dielectric and is used in capacitance incorporated in circuits requiring stable and accurate capaci

Define phase, Phase (Φ) : The amount which express at any instant, the disp...

Phase (Φ) : The amount which express at any instant, the displacement of the particle and it's direction of motion is known as the phase of the particle. If two elements of the

Gravity free environment vectors and projectiles, Gravity-Free Environment ...

Gravity-Free Environment Assume a zookeeper must shoot a banana from banana cannon to a monkey who hangs from the limb of a tree. This particular monkey has a habit of plummeti

Pn junction is represented as a diode, Pn junction is represented as a diod...

Pn junction is represented as a diode Pn junction is represented as a diode D in the emitter as represented in figure. If a voltage VBB is applied between bases with emitter op

Brownian motion, Brownian motion (R. Brown; 1827) It is the continuous...

Brownian motion (R. Brown; 1827) It is the continuous random motion of solid microscopic particles while suspended in a fluid medium because of the consequence of ongoing bomb

Motion in one dimension, what is the discussion of motion in one dimension ...

what is the discussion of motion in one dimension for experiment 7

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