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
railway tunnel of radius 3.5 m and angle aob =90 find height of the tunnel

Application Interpolation and extrapolation are widely used by businessmen, administrators, sociologists, economists and financial analysts. While interpolation hel


What are some equations for 36?

We're here going to take a brief detour and notice solutions to non-constant coefficient, second order differential equations of the form. p (t) y′′ + q (t ) y′ + r (t ) y = 0

Determine dy & Δy  if y = cos ( x 2 + 1) - x as x changes from x = 2 to x = 2.03 .  Solution Firstly let's deetrmine actual the change in y, Δy . Δy = cos (( 2.03) 2

If a^n+1 + b^n+1/a^n + b^n is the arithmetic mean of a and b then find n. Answer:Arithmatic mean of a,b is =(a+b)/2  from the problem (a+b)/2=(a^n+1 +b ^n+1)/(a^n+b^n)  then (a+

Solve 6 sin ( x/2)= 1 on [-20,30] Solution Let's first work out calculator of the way since that isn't where the difference comes into play. sin( x/2)= 1/6   ⇒x/2= sin

Optimization is required in situations that frequently arise in finance and other areas. Organizations would like to maximize their profits or minimize thei