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

Cro, explain the function of various type of screen in cro ?

explain the function of various type of screen in cro ?

Motion of a swing, Motion of a swing Periodic Motion :  Motion that re...

Motion of a swing Periodic Motion :  Motion that repeats itself in equal intervals of time is known as periodic motion.

Ampere, Ampere; A (after A.M. Ampere, 1775-1836) The basic SI unit of e...

Ampere; A (after A.M. Ampere, 1775-1836) The basic SI unit of electric current, described as the current that, while going through two infinitely-long parallel conductors of ne

Determine expression for the bound ray, A symmetric, multimode slab wavegui...

A symmetric, multimode slab waveguide has a core width 2ρ, a uniform cladding index n cl and a linear, graded-index profile n(x) in the core that is continuous and symmetric about

High frequency alternating current by a loud speaker, Give reason that ultr...

Give reason that ultrasonics not be produced by passing high frequency alternating current by a loud speaker At these high frequencies, inductive reactance is so high where is

Calormetry, in water equivalent how the temperature or water and solid equa...

in water equivalent how the temperature or water and solid equal?

Eotvos law of capillarity, Eotvos law of capillarity (Baron L. von Eotvos; ...

Eotvos law of capillarity (Baron L. von Eotvos; c. 1870): The surface tension gamma of liquid is associated to its temperature T, the liquid's critical temperature, T*, & its

Define heat engine, Define Heat engine Heat engine is a device by which...

Define Heat engine Heat engine is a device by which a system is made to undergo a cyclic process that results in conversion of heat into work. It is explained as the ratio o

Mathematical expression for dispersive power, Arrive at the mathematical ex...

Arrive at the mathematical expression for dispersive power of the material of a prism in terms of angle of deviation. Determine the critical angle for the material of refractiv

Which of the two objects will start to slide first, Two objects are placed ...

Two objects are placed on a flat turntable at 10.0 cm and 20.0 cm from the center, respectively. The coefficient of static friction with the turntable is 0.50. The turntable's

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