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

Electric field in the evacuated region of space, The electric potential at ...

The electric potential at a point in a consistent electric field in an evacuated region of space is 4 . 0 volts. The electric potential at a end 25 cm to the east of the first poin

How many types of fibers end are there, How many types of fibers end are th...

How many types of fibers end are there? Basically there are two types of fibers end are: adhesive encapsulated and state of the art fused, though some manufactures dispense alo

Kinematics, the difference and examples of kinematic in one dimension from ...

the difference and examples of kinematic in one dimension from two dimension?

PULLEY, In a pulley system the eqn for length of inextensible string is y p...

In a pulley system the eqn for length of inextensible string is y plus sq. root of x^2+h^2=constant ? how to differentiate y plus sq. root of x^2+h^2=constant to get vel & accn rel

What are the characteristics of dead stars, What are the characteristics of...

What are the characteristics of dead stars? Dead stars are generally cold balls of material in empty space. A teaspoonful of white dwarf matter would weigh as more as an Ele

Truck and the ball- vectors and projectiles, Truck and The Ball Suppose...

Truck and The Ball Suppose a pickup truck moving along with a constant speed along a city street. Within the course of its motion, a ball is projected straight upwards through

State free expansion process, Free Expansion process: In free expansion of ...

Free Expansion process: In free expansion of gas, the gases enlarge in vacuum. Thus, work done Δw=0 In free expansion if state changes from 1 → 2 only the initial and final s

What are the three particles that make up an atom, What are the three parti...

What are the three particles that make up an atom? Atoms are made up of electrons, protons, and neutrons. The protons and neutrons are found together in the core of the atom, k

Ideal transformer, In an ideal transformer , the no. of turns in primary & ...

In an ideal transformer , the no. of turns in primary & secondary are 200 & 1000 respectively .If power input to primary is 10kW at 200V.Calculate i)output voltage ii)current in

Get an expression for work done, Get an expression for work done during rev...

Get an expression for work done during reversible isothermal expansion. Get the terms open, isolated and closed system. Give examples.

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