Numerical methods final project, programming homework help

All of the assignment
Final Project/Exam MAE384
due: Tuesday, December 6th 2016, noon, Room ERC311
Read the following carefully. No exceptions.
Treat this final project as a take home final exam, i.e., no collaboration whatsoever with
anybody is allowed. You have to solve the project entirely on your own. You can freely
reference the class slides and the book, as well as the posted homework solutions on
blackboard.
For each problem, document all steps you took to solve the problem. This can be
handwritten, but must be legible for credit.
For all code results, use format long; and format compact;
In all coding, use only functions covered in class. It will be considered a violation of the
Academic Integrity Policy if you use any build-in functions of Matlab that calculate the
inverse of a matrix, interpolations, spline, diff, integration, ode, fft, etc.
You must submit hardcopies of all your work. An online only submission will result in no
credit.
You must upload all your coded functions combined into a single text file to the Final
Project link on Blackboard (for example copy/paste all functions into a single Word or text
file and upload that file). Do not upload the .m files. Uploading the .m files directly will
give no credit. Scanned versions of your functions are not acceptable and will result in
no credit.
You must staple your work. Failure to adequately stable/bind your work together will result
in a grading penalty, e.g., papers not attached to your cover sheet containing your name will
not be graded.
.
You must include your name in a legible manner together with your ASU ID. Your name
must be written in the following manner: LastName (as it appears in myASU), FirstName (as
it appears in myASU). Failure will occur either a grade of zero if your homework submission
cannot be identified, or a grading penalty.
.
The Core Course Outcomes points will be the indicated points multiplied by 3.
1
where ß = 0.01 and q(t) is the heat flow from the rod into the fluid, given by
An organization wants to develop a new solar oven that can be used to heat light-sensitive
liquids. A cylinder (A) that contains the light-sensitive liquid is placed inside an insulated box
(B). A curved mirror (C) is used to reflect the sun’s light onto a black cylindrical rod (D) of
length L = 1 that absorbs the light and transports heat to the liquid inside the cylinder (A).
q(t) =
ƏT
(x = 0,t)
ar
with initial condition
O(t = 0) = 300
С
Tasks:
x=L
D
(1) 15 points, CCO 5) By hand, write all the discrete equations necessary to solve for the
temperatures T and 0, including all boundary conditions, initial conditions, and stability step
size restrictions. State your choice of numerical methods to solve the problem and their order
of accuracy. The equations and methods must match the ones used in your code. Equations
that appear solely in code will not receive any credit.
Required submission:
– Handwritten (or typeset) all discrete equations needed to solve the problem, incl. stable
time step, boundary conditions and initial conditions.
– Name of numerical methods used
– Order of accuracy of the numerical methods used
x=0
B
A
The temperature inside the rod (D) can be modeled by the following non-dimensional PDE,
ӘГ
a2T
α
ar2
= Q(x,t)
at
where T is the temperature, t is time, x is the spatial coordinate along the length of the rod, a =
0.1 is the thermal diffusivity, and Q(x,t) is a source term due to the sun’s light, given by
0
if 0 < x < 0.3 Q(e,t) = { (2) ( 30 points, CCO 2 & 5) Solve for the temperature distribution in the rod. Calculate and report the maximum temperature in the rod at t = 1.2 with an accuracy of +/- 0.005. Do not attempt to find the analytical solution to the problem to determine the true solution. Justify that your solution has the required accuracy. Report the number of subintervals necessary and the time step size At used. Use the parameters used to obtain this solution in the following sub-problems (3) through (5). Required submission: - Maximum temperature at t=1.2 with an accuracy of +/- 0.005. - Table with all results justifying this answer. - Number of subintervals and time step size used to obtain the answer within the requested range. - Upload of all functions and scripts used to solve tasks (2)-(10) to Blackboard - Hardcopy printout of all functions and scripts used to solve tasks (2)-(10) (3) (~ 5 points, CCO 6) Plot T vs x every 1 time unit starting at t= 0 and ending at t= 5 together in one single plot. Clearly annotate the plot with legends. Required submission: - Hardcopy printout of a single clearly annotated plot of T vs x containing solutions at t=0,1,2,3,4, and 5 time units 200 sin(T*0.73) sin(t) sin(321) if 0.3 5x51 Note the absolute signs in the formula for Q. The boundary and initial conditions of the above PDE for the rod (D) are 0 T(x = 0,t) T(x = 1,t) T(x,t=0) = 300 = 300 where 0 is the temperature of the fluid inside the cylinder (A). O develops according to the following ODE: dᎾ +B(0 – 300)2 = 9(t) dt 2 3 (8) E 15 points, CCO 4 & 6) Sample the source term Q at x=0.75 every 0.1 time units in the time interval 0