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

Voltage signal:digital voltage signal, The signal which has only two values...

The signal which has only two values. I.e. either a constant high value of voltage or zero value is known as digital voltage signal

Microwave Radiative Transfer in the Atmosphere, I''m transmitting microwave...

I''m transmitting microwave radiation from antenna to satellite..so when radiation(photons) is transmitted,how they interact with the molecules in the atmosphere layer by layer..I

Determine magnetic circuit of uniform cross-sectional area, A section throu...

A section through a magnetic circuit of uniform cross-sectional area 2cm 2 is shown in Figure. The cast steel core has a mean length of 25cm. The air gap is 1mm wide and the

Water drain counter clockwise in the northern hemisphere, Q. Illustrate tha...

Q. Illustrate that water drain counter clockwise in the northern hemisphere and clockwise in the southern hemisphere? Answer:- This isn't a myth. It drains counter clockwi

What are the objectives of annealing, What are the objectives of annealing?...

What are the objectives of annealing? Slow cooling rate from the eutectoid temperature yields course pearlite - a mixture of relatively coarse crystals of ferrite and cementite

Calculate the temperature distribution in the channel, Water at 10 Celsius ...

Water at 10 Celsius flows at uniform velocity of 0.1 m/sec into a parallel plate channel, which is wide in the third direction. The parallel plates are at 20 Celsius and are 1.0 cm

Determine the dispersive power of the prism, What are the demerits of Huyge...

What are the demerits of Huygens' eyepiece? The angles of deviations for violet and red colors of a crown prism are 5.23 o and 5.15 o respectively. Determine the dispersive po

Explain galvanometer increase voltage sensitivity, Q. In a galvanometer, in...

Q. In a galvanometer, increasing the current sensitivity does not necessarily increase voltage sensitivity. Explain An interesting point to note is that raising the current sen

What is reluctance?, It is the opposition offered by the material of the fl...

It is the opposition offered by the material of the flux. Reluctance α mean length of flux path and reluctance α 1/cross section A Reluctance=1/μ 0 μ r A Here μ 0 a

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