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
Least common denominator of rational expression, Perform the denoted operat...
Perform the denoted operation. (4/6x 2 )(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus
How will you use the Gantt chart for solving the sequencing, How will you u...
How will you use the Gantt chart for solving the sequencing problem?
Probability, There are 20 defective bulbs in a box of 100 bulbs.if 10bulbs ...
There are 20 defective bulbs in a box of 100 bulbs.if 10bulbs are choosen at random then what is the probability of there are just 3defective bulbs
Venm diagrams, In a class, all pupils take Mathematics (M), 18 take Chemist...
In a class, all pupils take Mathematics (M), 18 take Chemistry (C), 17 take Biology (B) and 24 take Physics (P) of those taking 3 subjects only, 5 take Physics and Chemistry, 7 ta
Solid mensuration, Find the are of the rectilinear.if it is the difference ...
Find the are of the rectilinear.if it is the difference between to isosceles trapezoid whose corrsponding sides are parallel.
The paperwork to purchase your new home, You recently started the paperwork...
You recently started the paperwork to purchase your new home, and you were just notified that you can move into the house in two weeks. You decide to hire a moving company, but are
Java program for sorting algorithms, Introduction: In this project, yo...
Introduction: In this project, you will explore a few sorting algorithms. You will also test their efficiency by both timing how long a given sorting operation takes and count
Shares and dividend, A man buys rs50 shares of a company paying 12% of divi...
A man buys rs50 shares of a company paying 12% of dividendat premium ofof rs10 find market value of 320 shares and profit%
Describe independent events in maths, Describe Independent Events in maths?...
Describe Independent Events in maths? Events are independent if the outcome of one event does not affect the outcome of the second event. If A represents one independent event
Algebra., what to do
what to do
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