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

Tardon, Tardon A particle that has a positive real mass & travels at a ...

Tardon A particle that has a positive real mass & travels at a speed less than c within all inertial frames.

Equation of continuity, An equation that states a fluid passing through a p...

An equation that states a fluid passing through a pipe flows at a rate that is inversely proportional to the cross-sectional area of the pipe. i.e., if the pipe constricts, the flu

Similarities in construction of MOSFET and JFET, Similarities in Constructi...

Similarities in Construction of MOSFET and JFET (i)  JFET is a three terminal semiconductor device (source, drain and gate) in which current conduction is by majority carriers

Determine the initial rate of voltage rise, A circuit having of a 10μF capa...

A circuit having of a 10μF capacitor connected in series with a 25 k resistor with a switchable 100V d.c. supply. When the supply is connected, calculate (a) The time constant,

Direction of the current if any induced to flow in the loop, Question: ...

Question: A wire loop as well as a bar magnet lie in one and the same horizontal plane. The bar magnet is exterior of the loop. The bar magnet is rotating at a constant rate co

What is the illuminance, An overhead light fixture holds three light bulbs....

An overhead light fixture holds three light bulbs. Every light bulb has a luminous flux of 1892 lm. The light fixture is 1.8 m above the floor. What is the illuminance o

Kinematics, an aeroplane is moving horizontally with a velocity of u . it d...

an aeroplane is moving horizontally with a velocity of u . it drops a packet from a height h. the time taken the packet in reaching the ground is?

Astrophysics question, consider a star orbitining in the sperically graviat...

consider a star orbitining in the sperically graviational potential Y=(Vc)2 ln(r/r0). a)use conservation of energy and angular momentum to obtain equation for dr/dt and d(teta)/dt

Explain insulators, Insulators: Insulators are those substances which d...

Insulators: Insulators are those substances which do not permit to pass electric current by them. e.g. Wood, Plastic, rubber, glass etc

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