Login

Create Account
+14156709189
info@expertsmind.com
Submit Homework/Assignment
Get quote & make Payment
Get Solution
differential equation, Mathematics
Suppose a fluid (say, water) occupies a domain D? R^(3 ) 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 Ø= Ø(x,t) be 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.
?_(B (x))¦u_(t ) dV= ?_(? B(x))¦?Ø.n_0 dS.?
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 Ø= k?+uV.
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion transport equation:
u_t= ?.(k?u)+ ?.(uV).
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.
Suppose a fluid (say, water) occupies a domain D? R^(3 ) 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 Ø= Ø(x,t) be 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.
?_(B (x))¦u_(t ) dV= ?_(? B(x))¦?Ø.n_0 dS.?
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 Ø= k?+uV.
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion transport equation:
u_t= ?.(k?u)+ ?.(uV).
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.
Posted Date: 3/23/2013 7:10:39 PM  Location : United States
Ask an Expert
Related Discussions:
differential equation, Assignment Help, Ask Question on differential equation, Get Answer, Expert's Help, differential equation Discussions
Write discussion on differential equation
Your posts are moderated
Write your message here..
Related Questions
What are 20 math integer equations that equal 36?.., .what are 20 math inte...
.what are 20 math integer equations that equal 36?..
Class 10, chapter permutation & combination ex :4.6
chapter permutation & combination ex :4.6
Rectilinear figure, what is a redtilinear figure? like what are for the req...
what is a redtilinear figure? like what are for the requirments for a shape to be called that? example a regular polygon has all sides and angles equal. i cant find that kind of dr
How to add mixed numbers, Q. How to Add Mixed Numbers? Ans. If you...
Q. How to Add Mixed Numbers? Ans. If you have to add mixed numbers, you might try this method first: First rewrite the mixed number as a whole number plus a fracti
Calculus, I need help with my calculus work
I need help with my calculus work
Matrices, how solve the inverse matrices using the matlab?
how solve the inverse matrices using the matlab?
Factorization, #question.x2y24x2y+3.
#question.x2y24x2y+3.
Use the definition of the right and lefthanded limits, Use the definition...
Use the definition of the limit to prove the given limit. Solution Let ε> 0 is any number then we have to find a number δ > 0 so that the following will be true. 
Power series  sequences and series, Power Series We have spent quite...
Power Series We have spent quite a bit of time talking about series now and along with just only a couple of exceptions we've spent most of that time talking about how to fin
Zeroday attack, What is ZeroDay Attack? Explain ZeroDay Attack
What is ZeroDay Attack? Explain ZeroDay Attack
Assignment Help
Accounting Assignment Help
Economics Assignment Help
Finance Assignment Help
Statistics Assignment Help
Physics Assignment Help
Chemistry Assignment Help
Math Assignment Help
Biology Assignment Help
English Assignment Help
Management Assignment Help
Engineering Assignment Help
Programming Assignment Help
Computer Science Assignment Help
IT Courses and Help
ExpertsMind Services
Online Tutoring
Projects Assistance
Exam Preparation
Coursework Help
Programming Courses
Engineering Courses
Why Us ?
~Experienced Tutors
~24x7 hrs Support
~Plagiarism Free
~Quality of Work
~Time on Delivery
~Privacy of Work