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
How do you solve a table to get the function rule?

The next topic that we desire to discuss here is powers of i. Let's just take a look at what occurring while we start looking at many powers of i . i 1 = i

john walked to school at an average speed of 3 miles/hr and jogged back along the same route at 5miles/hr. if his total time was 1 hour, what was the total number of miles in the

1. The lifetime T (in days) of an electrical component has reliability function given by: R(t) = e -0.01t for time t > 0. An electrical system consists of four such components. Th

Marty used the subsequent mathematical statement to show he could change an expression and still get the similar answer on both sides: 10 × (6 × 5) = (10 × 6) × 5 Which mathematica

Certain model of new home distributed with a mean of $150,000. Find percentage of buyers who paid between $150,000-155,000 if standard deviation is $1800.

Continuity : In the last few sections we've been using the term "nice enough" to describe those functions which we could evaluate limits by just evaluating the function at the po

In the previous section we looked at the method of undetermined coefficients for getting a particular solution to p (t) y′′ + q (t) y′ + r (t) y = g (t)    .....................