Develop a MATLAB code to solve the FTCS 2D heat diffusion equation -AV f in a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Develop a MATLAB code to solve the FTCS 2D heat diffusion equation -AV² f in a domain (x,y)= (0,1)x(0,1) with initial condition: f(x,y,0)= x(1-x)y(1-y)= f(x,y) and boundary conditions: f(x,0,t)= f(x,l,t) = f(0, y,t)=f(1,y,t)=0. at Use the following parameters: x=0.1; Ay= Ax=0.05; At=(Ax² /x)/4;1=20At Generate a solution and compare to the series analytical solution 120-n'r [-1]+12nn-1] +24+24 [1])(-2+2[-]"). N (x,y)= Σ Σ series n'x¹m² n-1m-1 series (a) Show a surface plot of fari. (x,y,0)-f(x,y) (this quantity should be (10) Question: Why do this test? (b) In a second surfate plot shown fres(X,Y,tat) (c) In a third surface plot show Frics (X,Ust float)-Series (X,Y,t final) FICS (d) Report L_ norm for the error. This number should be (10) CIN =100]: Lxsin(nxx)sin(mzy)e series Develop a MATLAB code to solve the FTCS 2D heat diffusion equation -AV² f in a domain (x,y)= (0,1)x(0,1) with initial condition: f(x,y,0)= x(1-x)y(1-y)= f(x,y) and boundary conditions: f(x,0,t)= f(x,l,t) = f(0, y,t)=f(1,y,t)=0. at Use the following parameters: x=0.1; Ay= Ax=0.05; At=(Ax² /x)/4;1=20At Generate a solution and compare to the series analytical solution 120-n'r [-1]+12nn-1] +24+24 [1])(-2+2[-]"). N (x,y)= Σ Σ series n'x¹m² n-1m-1 series (a) Show a surface plot of fari. (x,y,0)-f(x,y) (this quantity should be (10) Question: Why do this test? (b) In a second surfate plot shown fres(X,Y,tat) (c) In a third surface plot show Frics (X,Ust float)-Series (X,Y,t final) FICS (d) Report L_ norm for the error. This number should be (10) CIN =100]: Lxsin(nxx)sin(mzy)e series
Expert Answer:
Answer rating: 100% (QA)
To solve the 2D heat diffusion equation using the Forward Time Centered Space FTCS method in MATLAB ... View the full answer
Related Book For
Numerical Methods With Chemical Engineering Applications
ISBN: 9781107135116
1st Edition
Authors: Kevin D. Dorfman, Prodromos Daoutidis
Posted Date:
Students also viewed these programming questions
-
Blue Ridge Builders is a general contractor with revenues over $125 million dollars per year is frequently awarded the contracts for building large public facilities like court houses, hospitals,...
-
What criteria to consider when selecting an app for partnership to cross promote each other's app on the Google Play Store? Include source.
-
Supply and Demand. Given the following data for individuals, draw the market demand curve and market supply curve for CDs. Assume that these are the only individuals in the entire market. Price is...
-
Let a function f be the line graph connecting the data points (1, 2), (4,9), and (6,3). (a) Write the formula for a piecewise-linear function f that passes through these data points whose domain is 1...
-
Find the z-score corresponding to a score of X = 60 for each of the following distributions. a. = 50 and = 20 b. = 50 and = 10 c. = 50 and = 5 d. = 50 and = 2
-
On January 1, 2019, Otano Ltd. had cash and share capital of 60,000,000. At that date, the company had no other asset, liability, or equity balances. On January 2, 2019, it purchased for cash...
-
The following residuals and predicted values were obtained from an experiment that related yield of a chemical process \((y)\) to the initial concentration \((x)\) of a component (the time order of...
-
The Lifestyle Clothes Company produced 24,000 units during April of the current year. The Cutting Department used 4,000 direct labor hours at an actual rate of $11.20 per hour. The Sewing Department...
-
A program has created an Object called "friend." This object includes the following fields: firstName, bDay, favColour and phoneNumber. An ArrayList of the object friend is declared with the...
-
Spencer Duck (SSN 000-22-1111) is single and his eight-year-old son, Mitch, lives with him nine months of the year in a rented condominium at 321 Hickory Drive in Ames, Iowa. Mitch lives with his...
-
Read the case study Personality Tests in Employment: Legal and Ethical Issues Answer the questions (at least a couple of good "solid" paragraphs per question), 1. Discuss the legal issues involved in...
-
Submit your favorite top 3 tips you have learned about writing a resume and cover letter from the video and article in this folder. 1. Tip 1: 2. Tip 2: 3. Tip 3: Video :...
-
Should marketers proceed (or not) with inserting their voice into social justice conversations? If so, how should they choose which conversations to join and how should they expect their customers...
-
Alisha Incorporated manufactures medical stents for use in heart bypass surgery. Based on past experience, Alisha has found that its total maintenance costs can be represented by the following...
-
Ken is 63 years old and unmarried. He retired at age 55 when he sold his business, Understock.com. Though Ken is retired, he is still very active. Ken reported the following financial Information...
-
y' (1) - If 2x + 3x + xy=1 and y(1)=-4, find y' (1) by implicit differentiation. -3 Thus an equation of the tangent line to the graph at the point (1,-4) is
-
Enter a balanced equation for the dissolution of CaCO3. Expressyour answer as a chemical equation. Identify all of the phases inyour answer. I tried to put CaCO3(s)?Ca+2(aq)+CO3?2 (but it doesnt...
-
The following selected information was taken from Sun Valley Citys general fund statement of revenues, expenditures, and changes in fund balance for the year ended December 31, 2019: Revenues:...
-
Solve Eq. (1.2.70) subject to an initial condition c(x, 0) = 1 and homogeneous boundary conditions at x = 0 and x = L. at a2c = D 32 (1.2.70)
-
What ODE is solved by the following MATLAB code and what method is used? Include the initial condition in your answer. 1 function problem4_23 2 3 4 nsteps = 100; y = 1; t = 0; h = 0.01; 5 6 g=figure;...
-
Lets assume we have a computer that can solve a 100 100 system in 1 second using Gauss elimination. Estimate the time required to solve the following problems on the same computer. You must indicate...
-
A fertilizer producing company purchases nitrates, phosphates, potash, and an inert chalk base and produces four different fertilizers A, B,C, and D. The cost of these nitrates, phosphates, potash,...
-
Heavy fuel oil, initially semisolid at $15^{\circ} \mathrm{C}$ is to be heated and pumped through a $15 \mathrm{~cm}$ diameter (inside) pipe at the rate of $20000 \mathrm{~kg} / \mathrm{h}$. The pipe...
-
The topological optimization is discussed in chapter 1. Here, we will consider a topological optimization problem for a chemical process plant. The layout of the chemical process plant has been shown...
Study smarter with the SolutionInn App