Question: Use Crank-Nicolson method to solve for the temperature distribution in a long, thin rod with a length of 12cm and following values: k=0.49cal/(s.cm.C) and t=0.25sec.

Use Crank-Nicolson method to solve for the temperature distribution in a long, thin rod with a length of 12cm and following values: k=0.49cal/(s.cm.C) and t=0.25sec. At t= 0sec (initial condition), the inner temperature of the entire rod is 25C. The left Boundary is initially at 90C and the right boundary condition is 41C. However, the left boundary temperature increases by an amount of 2C after every time step considered. The right boundary condition is fixed at 41C for all time steps. Note that the rod is aluminum with C=0.2174cal/(g.C) and =2.7g/cm3. Find the temperature values on the inner grid nodes for t=0.5sec. Use Thomas Algorithm to solve for the matrix form of the system of equations for the unknown inner temperatures of the rod. The rod is shown below. (Note: Show all the steps in detail. Use and show appropriate units throughout the solution. It is optional to develop a code for the Crank Nicolson problem, Q1)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

Use the Crank-Nicolson method to solve for the temperature distribution of a long, thin rod with a length of and the following values: = = At t = 0, the temperature of the rod is zero and the...

Upload PDF and/or Excel files showing all work! Use the Crank-Nicolson method to solve for the temperature distribution of a long, thin rod with a length of and the following values: = = At t = 0,...

solving for partial math as soon as possible SPECIAL PROJECT DIRECTIONS: Part 1: Set up a study about Partial Differential Equations (PDE) Discuss types and methods of solving the Differential...

Q 3 Use an appropriate numerical method to solve for the temperature distribution of a long, thin rod, shown below, with a length of 1 6 cm and following values: ) and t = 1 . 5 s e c . At t = 0 s e...

Repeat Example 30.1, but use the midpoint method 30.1 Repeat Example 30.1, but use the midpoint method to gener- ate your solution. Problem Statement. Use the explicit method to solve for the...

! Required information Use the explicit method to solve for the temperature distribution of a long, thin rod with a length of 10 cm and the following values: K'= 0.49 cal/(s - cm - C), Ax= 2 cm, and...

Use an implicit method to solve for the temperature distribution of a long thin rod with a length of 10 cm and the following values: K'= 0.49 cal/5.cm.C, Ax = 2cm and At = 0.1 sec. At t = 0, the...

Use the simple implicit method to solve for the temperature distribution of a long, thin rod with a length of 9 cm and the following values: k 0.49 cal/(s-cm-C), Az = 2 cm, and At = 0.1 s. At t = 0,...

Eg: Use the explicit method. to solve for the temperature distribution of . a long, thin, rod. With a length of 1 0 an and the following values k ' = 0 . 4 9 c a l s c m c , = 2 c m , t = 0 . 1 c m...

Please quality check my solutions for this advanced heat transfer problem. Show all work. Thank you. All original documents are located at the bottom. 3.9 COMPACT HEAT EXCHANGERS 3.9.10-1 3.9.10...

Suppose Congress changed the tax laws in a way that (1) permitted equipment to be depreciated over a shorter period, (2) lowered corporate tax rates, and (3) reinstated the investment tax credit....

Determine the value of EIS at point A of the overhanging beam ABC. 600 Nm A 1.0 m B 3 m FIG. P6.64 900 N/m C

Under IFRS all restoration costs are recognized as property, plant and equipment costs including any resulting from production related activities. Select answer from the options below True False

Managers in the Digital Age Need to Stay Human The technological advances of the digital age have allowed the global workforce to be better connected, more collaborative, and have greater personal...

2. You have to evaluate an employee who has been late frequently. A. We have guidelines around here, you know. B. I need you to try harder to be on time. C. I want you to be here at 8:55 each morning.

What kinds of slang or jargon do you regularly use? How did you become familiar with these terms? And how would you go about explaining these terms to someone who is unfamiliar with them?

B What kinds of technical words and phrases have become part of your everyday language? Have you ever Googled anyone? Would you think it odd if you had to explain the meaning of the verb Google to...