Superimpose the three curves on the one axis, Mathematics

Submit solutions for all of the following questions. Remember to set out your answers showing all steps completely and explicitly justify your steps.

1. Provide, in no more than two pages, a sample of your working and attempted solutions of various exercise problems that have been set in MAB521/MAN521.

2. Consider an advection diffusion equation describing the evolution of a concentration profile of a dissolved solute in a one-dimensional domain. The advection diffusion model is given by:


with boundary conditions270_limit_123.pngC(x, t) = 0 and initial condition C(x, 0) = f (x).

Here D is the diffusivity and v is the advection velocity.

(a) Show that the advection diffusion equation, including the initial condition and boundary conditions, can be transformed into a linear diffusion equation by introducing new variables x¯ = x - vt and = t.

(b) Using the transformation from part (a) and the fundamental solution developed in class, find and write down the solution for C(x, t) where C(x, 0) _ 0 everywhere except that some mass Q is placed at position x = 0 at t = 0.

(c) For Q = 1 and D = 1, use a computer package to plot

i. C(x, t) at t = 1 for v = 0, v = 0.1 and v = 1.0. Superimpose the three curves on the one axis.

ii. C(x, t) at t = 10 for v = 0, v = 0.1 and v = 1.0. Superimpose the three curves on the one axis.

(d) The method of moments can be used help analyze physical problems that are governed by advection diffusion processes. The first moment of the solution is defined as M1 = ∫x2x1 xC(x, t) dx. Use your solution from part (b) to evaluate the first moment when v = 0 and v 6= 0.

(e) Give a physical explanation for the results you observe in part (d). Describe a practical use for the first moment of the solution?

(f) Without using your solution from part (b), directly evaluate the first moment of the advection diffusion equation for this problem using the governing equation.

State any assumptions that you have made to arrive at your solution.

Posted Date: 4/2/2013 5:11:04 AM | Location : United States

Related Discussions:- Superimpose the three curves on the one axis, Assignment Help, Ask Question on Superimpose the three curves on the one axis, Get Answer, Expert's Help, Superimpose the three curves on the one axis Discussions

Write discussion on Superimpose the three curves on the one axis
Your posts are moderated
Related Questions
Find the sum of first 40 positive integers divisible by 6 also find the sum of first 20 positive integers divisible by 5 or 6. Ans:          No's which are divisible by 6 are

Kelli calls her grandmother every month Kelli also calls her cousin.If Kelli calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by t

School run known to possess normal distribution with mean 440 sec & SD 60 sec. What is probability that randomly chosen boy can run this race in 302 sec.

Explain Combining Negative Signs in integers? You've learned about positive and negative integers. BASICS :   When you place a negative sign in front of an integer, you get

Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sinx-4sin 3 x

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

Jackie invested money in two different accounts, one of that earned 12% interest per year and another that earned 15% interest per year. The amount invested at 15% was 100 more tha

Each of the series 3+5+7+..... and 4+7+10.......... is continued to 100 terms find how many terms are identical. Ans) 48 terms would be common to both the series... first take co

Ipswich has two ambulances. Ambulance 1 is based at the local college and ambulance 2 is based downtown. If a request for an ambulance comes from the local college, the college-bas

Evaluate following limits. Solution Here the first two parts are actually just the basic limits including inverse tangents and can easily be found by verifying the fol