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

Show the conditions for total internal reflection, Show the conditions for ...

Show the conditions for total internal reflection to happen. Arrive at the relation between refractive index and critical angle. What do you mean by optical fibre? on what rules do

Fleming''s left-hand rule, Stretch the fore-finger, central finger and thum...

Stretch the fore-finger, central finger and thumb left hand mutually perpendicular. Then if the fore-finger shows in the direction of field   and the central in the direction of cu

Calculate the sunrise local horizon points, This problem examines the seaso...

This problem examines the seasonal solar radiation budget at three geographical locations: the Equator, 40º North, and 80º North. NOTES: At a given geographical location, N

Resistances of resistance boxes, Are made up of alloys (manganin, constanta...

Are made up of alloys (manganin, constantan or nichrome) these materials have moderate Resistivity which is practically independent of temperature so that the specified value of re

gamma rays and x-rays, Can radiations like gamma rays and x-rays be made p...

Can radiations like gamma rays and x-rays be made prevented to enter a place by a magnetic field? Ans) Rutherford noted that gamma rays were not deflected (or at least, not easi

Optics, how does a magnifying glass work to produce a large or smaller imag...

how does a magnifying glass work to produce a large or smaller image?

Why x-rays are not used in microscopes, Q. Why X-rays are not used in micro...

Q. Why X-rays are not used in microscopes? 1) The wavelength of X-rays is slighter than that of the visible light. 2) X-rays can't be focussed as visible radiations are foc

Layer of transparent optical coating on a transparent medium, In terms of t...

In terms of the wavelength of the pertinent light how thick must the layer of transparent optical coating on a transparent medium be in order to create maximum destructive interfer

What is physical quantity, A quantity that can be calculated by instrument,...

A quantity that can be calculated by instrument, clearly defined and has proper units is known as physical value. Physical quantities are described as fundamental and derived quant

Complete spectrum of all forms of electromagnetic radiation, Q. Illustrate ...

Q. Illustrate that does the solar radiation contain a complete spectrum of all forms of electromagnetic radiation? Answer:- It is true that it does. It holds all the forms

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