Write a MATLAB code to implement the solution

Assignment Help MATLAB Programming

Reference no: EM133160780

Question 1: Solve the nondimensional transient heat conduction equation in two dimensions, which represents the transient temperature distribution in an insulated plate. The governing equation is

∂²u/dx² + ∂²u/dy² = ∂u/dt

where u = temperature, x and y are spatial coordinates, and t = time. The boundary and initial conditions are:

Solve using the alternating direction-implicit (ADO technique. Write a MATLAB code to implement the solution. Plot the results using a three-dimensional plotting routine where the horizontal plan contains the x and y axes and the z axis is the dependent variable u. Construct several plots at various times, including the following:

(a) the initial conditions;
(b) one intermediate time, approximately halfway to steady state;
(c) the steady-state condition.

Question 2: In many engineering applications, advection (or convection) and diffusion are the dominant physical transport mechanisms over much of the domain of interest. Consider the case of a plume of contaminant being transported in flowing river. The well-known governing equation for such transport is the advection-diffusion equation below;

∂c/dt = ∇.(D∇c) - ∇.(vc)

where c is the concentration of the plume, D is the diffusivity (or diffusion coefficient), v is the velocity the concentration is moving.

Address the following problems below by writing your own MATLAB code utilising numerical methods of your own choice (ideally two methods or more). You need to justify or explain the theory behind the methods you are using. A good report will consider the comparison of the performances of the methods chosen.

a. Consider a one-dimensional problem where diffusion effects are omitted. The equation above reduces to

∂c/dt = v∂c/dx

The initial distribution (t = 0) of concentration co is a Gaussian i.e

C_o(X) = 0.7Se-(x-0.5/0.1)² On the domain 0 < x < 2, with constant velocity v = 1, solve and plot the initial profile of c, as well as c at t = 1.

b. Now consider the case where the migration of the plume is subject only to diffusion process with D = 1. Still with the same initial condition, plot the concentration profile at t = 0.5

c. Finally, consider the case where the migration of the plume is subject to both advection, and diffusion. With all the parameters above plot the concentration profile at t = 1.

Reference no: EM133160780

Questions Cloud

Communicate the message electronically : Reflect on a time when you had to communicate important and urgent information electronically in the workplace or classroom.

What should the criteria for effectiveness be : What information should be collected and from whom should it be collected?

Part of developmentally appropriate curriculum : Explain why play is an important part of a developmentally appropriate curriculum. Describe how play can help to support a child's physical, cognitive,

Informal performance management system : The study by Lee et al. (2020) found that frontline managers use both formal and informal performance management systems in order to manage the demands of their

Write a MATLAB code to implement the solution : Write a MATLAB code to implement the solution. Plot the results using a three-dimensional plotting routine where the horizontal plan contains the x and y axes

Analyze a specific instance of organizational change : Critically analyze a specific instance of organizational change that you have led an/or experienced Using appropriate academic sources to support your work, giv

Hr competencies-organizational performance : The role of change agent as mediator in the relationship between HR competencies and organizational performance. By: Long, Choi Sang, Wan Ismail

Buddhism-religion or philosophy : Why is vesak the mostimportant Buddhist holiday? Why are so few festivals celebrated by all Buddhists?

Make selection decisions based on all available information : Organizations should make selection decisions based on all available information except:

User Account

All Pages