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

Determine the rate of change of flux - magnetic field, An e.m.f. of 25V is ...

An e.m.f. of 25V is induced in a coil of 300 turns when the flux linking with it alters by 12mWb. Find the time, in milliseconds, in which the flux makes the change. An ignitio

How does f'' evaluate with f, Que: Consider two identical tiny metal ba...

Que: Consider two identical tiny metal balls one having a charge of +1 micro-coulombs and the other having a charge of +3 micro-coulombs. The balls are separated from each one

Two-dimensional physics problem, An object is thrown at 25 m/s at 39 degree...

An object is thrown at 25 m/s at 39 degrees above the horizontal from a 40m tall cliff. How long is it in the air?

Classes of magnetic materials: paramagnetism, In the case of materials so...

In the case of materials some of the atoms or ions in the material have a net magnetic due to unpaired electrons in partially filled orbits. However, the individual magnetic mome

Electrostatic shielding, Electrostatic shielding/screening is the phenomeno...

Electrostatic shielding/screening is the phenomenon of protecting a particular region of space from external electric field. Sensitive instruments and appliances are affected serio

Working and construction of moving coil galvanometer, Get a mathematical ex...

Get a mathematical expression for the torque on a loop placed in a uniform magnetic filed. Define the working and construction of moving coil galvanometer?

Determine the voltage across the capacitor, In the circuit shown in Figure,...

In the circuit shown in Figure, with the switch in position 1, the capacitor is uncharged. If he switch is moved to position 2 at time t =0s, measure (i) The initial curren

Explain how to calculate constant voltage source, Power is to be supplied f...

Power is to be supplied from a source whose resistance is 20 K ? to a load of 100 ?. Would you consider it as a constant voltage source or current source? Explain. Ans. G

Find the resistance r in the circuit, The current is an RL circuit drops fr...

The current is an RL circuit drops from 1.1 A to 13 mA in the first second following removal of the battery from the circuit. If L is 12H, find the resistance R in the circuit.

Characteristics of resistance in parallel, Characteristics of Resistance in...

Characteristics of Resistance in parallel: Different amount of current passing by each resistance. i.e. I = I1 + I2 + I3 + I4 ........ The potential difference across every

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