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

Causality principle for the klein- gordon equation, Suppose Fluid (say, wat...

Suppose Fluid (say, water) occupies a domain D 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

Reflection and refraction, Reflection and Refraction Describing reflec...

Reflection and Refraction Describing reflection and refraction, involving total internal reflection. You might drag the control at the top to modify the angle of incidence and

Plane transmission grating, Discuss the diffraction of light through n slit...

Discuss the diffraction of light through n slits using plane transmission grating.

Are certification important in the fiber optics industry, Are certification...

Are certification important in the fiber optics industry? It will depend upon the type of certificate, what is certified and through who is granted. Several certifications refe

Calculate the reaction gibbs energy, Under standard state conditions at 37 ...

Under standard state conditions at 37 o C, a biochemical reaction :             A ↔ B + C has an equilibrium constant K = 0.0422  mol/dm 3 . (i) Calculate the standard

Applications of neodymium-yttrium-aluminium-garnet laser, What are the appl...

What are the applications of Neodymium-Yttrium-Aluminium-Garnet Laser? Applications of Neodymium-Yttrium-Aluminium-Garnet Laser: a. Used into materials processing as like we

Scattering, derive an expression for the total cross section for the scatte...

derive an expression for the total cross section for the scattering of light by a polorisable molecule in term of the incedent wave length.

One would expect proton to have very large, One would expect proton to have...

One would expect proton to have very large: (1) Ionization potential (2) Radius (3) Charge (4) Hydration energy Ans:(4) Hydration energy

Person travels faster than light in a space shuttle, What happens if a pers...

What happens if a person travels faster than light in a space shuttle?  Ans) Interstellar space travel is manned or unmanned travel among stars. The concept of interstellar trav

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