O A heated fluid at temperature T (degrees above ambient temperature) flows in a pipe with fixed length and circular cross section with radius r. A layer of insulation, with thickness w
O A heated fluid at temperature T (degrees above ambient temperature) flows in a pipe with fixed length and circular cross section with radius r. A layer of insulation, with thickness w
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![2. Problem 4.30 in [Boyd-Vandenberghe]. Solve the problem on CVX for the
following parameters:
α₁ = .5, α₂ = .7, α3 = .9, α₁4 = .1;
03:
Cmax = 100;
Tmin= 5, Tmax = 20;
Tmin= 10, Tmax 30;
Wmin = 1, wmax = 5.
(Note: You must use CVX in geometric programming mode.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde27b5cb-cd0c-4d35-bbc9-1c5df406bf15%2F496f4786-2b22-4717-82b6-235883e2bdb0%2F33f3z7x_processed.png&w=3840&q=75)
Transcribed Image Text:2. Problem 4.30 in [Boyd-Vandenberghe]. Solve the problem on CVX for the
following parameters:
α₁ = .5, α₂ = .7, α3 = .9, α₁4 = .1;
03:
Cmax = 100;
Tmin= 5, Tmax = 20;
Tmin= 10, Tmax 30;
Wmin = 1, wmax = 5.
(Note: You must use CVX in geometric programming mode.)
Transcribed Image Text:4.30 A heated fluid at temperature T (degrees above ambient temperature) flows in a pipe
with fixed length and circular cross section with radius r. A layer of insulation, with
thickness w<r, surrounds the pipe to reduce heat loss through the pipe walls. The
design variables in this problem are T, r, and w.
The heat loss is (approximately) proportional to Tr/w, so over a fixed lifetime, the energy
cost due to heat loss is given by a₁Tr/w. The cost of the pipe, which has a fixed wall
thickness, is approximately proportional to the total material, i.e., it is given by a2r. The
cost of the insulation is also approximately proportional to the total insulation material,
i.e., a3rw (using w < r). The total cost is the sum of these three costs.
The heat flow down the pipe is entirely due to the flow of the fluid, which has a fixed
velocity, i.e., it is given by a Tr². The constants ai are all positive, as are the variables
T, r, and w.
Now the problem: maximize the total heat flow down the pipe, subject to an upper limit
Cmax on total cost, and the constraints
Tmin ≤ T ≤ Tmax,
1min ≤r≤rmax,
Express this problem as a geometric program.
Wmin w Wmax,
w ≤ 0.1r.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 4 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
