When surgery is done on the heart, it must be stopped, and a heart-lung machine takes...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
When surgery is done on the heart, it must be stopped, and a heart-lung machine takes over and pumps blood throughout the body. Additionally, the heart-lung machine cools the circulating blood to reduce the metabolic needs of the brain and other vital organs. The blood is typically cooled to a temperature of 29C. Consider a heart-lung machine that cools the blood by making it flow through a tube whose inner wall surface temperature is kept at 0C, as shown in the figure. The blood enters the tube at 37C and a velocity of 3 cm/s (v). The tube has an inner diameter of 1.0 cm. T of inner wall surface=0C (constant) Blood V =0, T = 37C Fig. 1. Cooling of blood flowing through a tube You will use a MATLAB model to determine the length of tube needed to cool the blood to 29C. As a first approximation, the properties of the blood are assumed to be that of water. Its density is 1000 kg/m, thermal conductivity is 0.530 W/(m K), and specific heat is 4200 J/(kg K). Also assume that the velocity of the blood is constant at any radius and length (vz). Question 1. Model Formulation (Only this part must be handwritten, paste to document.) a) List your assumptions for the problem. b) Starting from the most general differential equation, simplify it based on your assumptions. What would be the code for this in a MATLAB function for PDEPE? +Z c) Give the boundary conditions needed to solve this problem. What would be the code for this in a MATLAB function for PDEPE? d) Give the initial condition. What would be the code for this in a MATLAB function for PDEPE? Question 2. Length of tube needed to cool the blood For the conditions given, find the minimum length of tube (meters) to cool the blood to 29C. (Hint: This would mean that the maximum temperature in the blood is 29C.) 1. Show a plot of temperature vs. length for the r-position that ensures that this is achieved. 2. Show a plot of temperature vs. radius at half the length needed. Give a short discussion of your plots. Do they make sense based on heat transfer principles? In MATLAB, set r intervals of 0.1 mm and tube length intervals of 1 cm. (Use these also for Question 3) Question 3. Effect of velocity on length of tube needed to cool the blood Find the minimum length of tube (meters) needed to cool the blood to 29C for the following: (1) Vlow = 3 cm/s decreased by 29% So Vlow = 3 cm/s - (0.29) (3 cm/s) = 2.13 cm/s (2) Vhigh = 3 cm/s increased by 29% So Vhigh = 3 cm/s + (0.29)( 3 cm/s) = 3.87 cm/s a) For each velocity, show a plot of temperature vs. length for the r-position that ensures that the blood is cooled to 30C. b) Make a bar graph of the minimum length of tube needed for the 3 velocities you simulated (Vlow, 3 cm/s, Vhigh). Give a short discussion of your plots. Do they make sense based on heat transfer principles? When surgery is done on the heart, it must be stopped, and a heart-lung machine takes over and pumps blood throughout the body. Additionally, the heart-lung machine cools the circulating blood to reduce the metabolic needs of the brain and other vital organs. The blood is typically cooled to a temperature of 29C. Consider a heart-lung machine that cools the blood by making it flow through a tube whose inner wall surface temperature is kept at 0C, as shown in the figure. The blood enters the tube at 37C and a velocity of 3 cm/s (v). The tube has an inner diameter of 1.0 cm. T of inner wall surface=0C (constant) Blood V =0, T = 37C Fig. 1. Cooling of blood flowing through a tube You will use a MATLAB model to determine the length of tube needed to cool the blood to 29C. As a first approximation, the properties of the blood are assumed to be that of water. Its density is 1000 kg/m, thermal conductivity is 0.530 W/(m K), and specific heat is 4200 J/(kg K). Also assume that the velocity of the blood is constant at any radius and length (vz). Question 1. Model Formulation (Only this part must be handwritten, paste to document.) a) List your assumptions for the problem. b) Starting from the most general differential equation, simplify it based on your assumptions. What would be the code for this in a MATLAB function for PDEPE? +Z c) Give the boundary conditions needed to solve this problem. What would be the code for this in a MATLAB function for PDEPE? d) Give the initial condition. What would be the code for this in a MATLAB function for PDEPE? Question 2. Length of tube needed to cool the blood For the conditions given, find the minimum length of tube (meters) to cool the blood to 29C. (Hint: This would mean that the maximum temperature in the blood is 29C.) 1. Show a plot of temperature vs. length for the r-position that ensures that this is achieved. 2. Show a plot of temperature vs. radius at half the length needed. Give a short discussion of your plots. Do they make sense based on heat transfer principles? In MATLAB, set r intervals of 0.1 mm and tube length intervals of 1 cm. (Use these also for Question 3) Question 3. Effect of velocity on length of tube needed to cool the blood Find the minimum length of tube (meters) needed to cool the blood to 29C for the following: (1) Vlow = 3 cm/s decreased by 29% So Vlow = 3 cm/s - (0.29) (3 cm/s) = 2.13 cm/s (2) Vhigh = 3 cm/s increased by 29% So Vhigh = 3 cm/s + (0.29)( 3 cm/s) = 3.87 cm/s a) For each velocity, show a plot of temperature vs. length for the r-position that ensures that the blood is cooled to 30C. b) Make a bar graph of the minimum length of tube needed for the 3 velocities you simulated (Vlow, 3 cm/s, Vhigh). Give a short discussion of your plots. Do they make sense based on heat transfer principles?
Expert Answer:
Related Book For
Physics
ISBN: 978-0077339685
2nd edition
Authors: Alan Giambattista, Betty Richardson, Robert Richardson
Posted Date:
Students also viewed these databases questions
-
As shown in following figure (a), a rightcircular cylinder partially filled with fluid is rotated with a constant angular velocity Ï about a vertical y-axis through its center. The rotating...
-
a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...
-
Determine the real roots of (x) = - 1 + 5.5x 4x2 + 0.5x3: (a) Graphically and (b) Using the Newton-Raphson method to within s = 0.01%.
-
To construct a p-chart for a manufacturing process, 25 samples of size 200 were drawn from the process. The number of defectives in each sample is listed in time order in the table that follows. a....
-
An investment project provides cash inflows of $585 per year for eight years. What is the project payback period if the initial cost is $1,700? What if the initial cost is $3,300? What if it is...
-
Audience Scores on Rotten Tomatoes The variable AudienceScore in the dataset HollywoodMovies gives audience scores (on a scale from 1 to 100) from the Rotten Tomatoes website. The five number summary...
-
A radio tower rises to height h above flat horizontal ground. At the top is a magnetic dipole antenna, of radius b, with its axis vertical. FM station KRUD broadcasts from this antenna at angular...
-
Given a sorted array 2, 5, 8, 12, 16, 18, 22, 25, 29, 32 and the following interpolation search algorithm. Show the steps of the algorithm when 25 is searched. Also, when 26 is searched. array a,...
-
According to your answer in (a) = TCP, what would be the socket ID at Host A for this transmission? Further consider the settings of the transmission below: - Stop-and-wait operation is adopted, with...
-
What is the difference between qualitative and quantitative analysis. Explain with the help of examples.
-
Did the USD appreciate/depreciate relative to these currencies during the crisis 2008-2009? What could be a reason for this? What was the most recent US dollar dynamics versus these currencies?
-
0/4 points If you contribute $275 every two weeks, starting in two weeks, into a retirement plan that pays 3% compounded monthly, how much interest will you earn after 10 years? Express your answer...
-
0/4 points You owe $20,000 on your student loan that charges 5% compounded monthly. If starting next month, you pay $600/month on the loan, how many months will it take to pay it off? Express your...
-
If Edward purchases $150 worth of casualty insurance at $1.25 per $1,000 of coverage, how much coverage does he have? Explain
-
Say we have the recursive definition for the set S defined as: Basis step: 6S Recursive step:If xS,then x+3S Use the recursive definition shown above and structural induction to prove that 3 | y+12...
-
Tarick Toys Company manufactures video game consoles and accounts for product costs using process costing. The following information is available regarding its June inventories. The following...
-
Show that the coefficient of performance for a reversible heat pump is 1/(1 - TC / TH).
-
A converging lens made from dense flint glass is placed into a container of transparent glycerine. Describe what happens to the focal length.
-
Prove Eq. (7-13) Σext = M CM. Start with Σext = where Σext is the net external force acting on a system and is the total momentum of the system? Ar-0
-
Example 11.3 introduces Klein's Model I. Use the data file klein to answer the following questions. a. Estimate the consumption function in equation (11.17) by OLS. Comment on the signs and...
-
Example 11.3 introduces Klein's Model I. Use the data file klein to answer the following questions. a. Estimate the investment function in equation (11.18) by OLS. Comment on the signs and...
-
Mike's Veneer Shop owns a vacuum press that requires annual maintenance. Mike has a contract to cover the maintenance expenses for the next 5 years. The contract calls for an annual payment of \(\$...
Study smarter with the SolutionInn App