ME462
Thermal Design

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Catalog Description: (Prerequisities - ES202 and ME302) Applications of the thermodynamic, heat transfer, and fluid flow principles to the modeling and design of thermal systems. These systems include pumps, fans, and heat and mass exchangers. A project which includes designing, constructing and testing a heat exchanger provides the focus for the course.


 
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  Assignments   Hints  


Homework 1

Problem Hint Answer
1 Start with the most basic form of the Mechanical Energy Equation. Pick the correct system, and all goes well. a) 409 HP
2 This is just a Reynolds number review, and from that standpoint not very challenging. What is a pain, though, is all the mundane stuff that real world engineering is full of. What is the pipe diameter? Where do you find it? What is the density of methyl alcohol? Where do I go to find it? And I best be sure that my Reynolds number is dimensionless and unitless! Turbulent flow
3 What are you going to do about that elbow? There are many choices for how to handle K here. As a designer, you have to choose something and be willing to justify it. (As such, my "answers" on the right are not answers, but rather, the numbers I got by making my own choices.) 22.3 HP
4   ?? HP (Should be smaller.)
5 If you've got an EES program working for the in class example, this will be a cinch. You are welcome, of course, to do an interative solution by hand. (I hope you don't have to do it by hand, but remember, your clients aren't going to like receiving bogus results from you - or no results - and they won't accept "the software didn't work" as an excuse!) An intermediate answer: f=0.03497

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Homework 2

Problem Hint Answer
1 Pay attention to those pipe symbols. That first doohickey is a basket strainer.
For this problem, p1 is not atmospheric, but a variable.		 For Vdot = 0.03 m3/s, ΔP/ρg = 5.41 m
2 Another problem that would involve an iterative solution if your did it by hand. My advice: don't do it by hand!

The one pipe solution is pretty easy. No iteration required for that one. Get that running in EES, update your guess values, and use that as a template for the two pipe solution. Repeat for the three pipe solution.

How do the losses compare from the exit of the pump to the exit of the pipes in the multiple pipe situtation?		 One pipe solution: Wdot,in=44.5 kW
3

Ahhh, at last a problem that I don't need to iterate on! This should be straight forward, keeping in mind that Qdot = UA×LMTD.

Many thermal designers categorize heat exchanger problems as either design problems or analysis problems. This is a design problem. That is, you are given a certain Qdot and you have to find out how large a HXR you need to achieve it. And so, even though you don't need an EES code to do this, it might be a good idea to get one running anyway so that you can modify it and fiddle with the parameters to help in your design project.

 25.6 m2

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Homework 3

Problem Hint Answer
1 Just as easy as the original HW 2, Problem 3. Or is it? What the heck... A=?!
2 How do your answers for (a) and (b) compare? Why? Some possible intermediate answers:

LMTD method: LMTD=191 F

ξ-NTU method: ξ=0.0891
LMTD-F problems Note that I have made life easy for you by giving you the UAs. A more practical problem would involve your finding these based on finding the hs first. (But you have a design project for this, yes?)

You can not use mdotcp(T1 - T2) to find Qdot for the condensing fluid. Why not? What is the effective cp for a phase-changing fluid anyway? So what do you do? Here's a little hint: Remember there are two ways to think about Qdot, the heat trasnfer way and the thermo way.
  1. 15 m2
  2. 18.3 m2
  3. 5.40 x 106 Btu/hr, 1.44 lbm/s, 115.3 lbm/s
  4. 103 kW
7 Not a design problem. Rather, an analysis problem. Should you use the F-LMTD method or the ξ-NTU method? An intermediate answer: ξ=0.355
8 This one is light on the calculations, heavy on the concepts. If you understand what ξ means, and what happens when HXRs get really long, you'll knock this out in a few minutes. 

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Homework 4

Problem Hint Answer
1 This should be pretty straight forward. (Do remember that in cylindrical systems, however, (Like maybe your HXR?) Rcond is not L/kA. What is it?)

No I didn't goof, those are mixed units! It happens a lot in engineering practice. A good example is the EER and SEER numbers you see listed on refrigerators. They are really COPs, but with units! And mixed English/SI units at that!		 b) Tinter=992°F (Your answer may vary depending on the values of k you use.)
Concept Questions There are many resources available to you here. One is your textbook. Another is other textbooks, like your undergraduate heat transfer text. Yet another is the clickable concept map in the Other Stuff section.

The reason these questions are so important is that if you can't answer them (or figure out what the answers to them are) then there's a good chance you will use an incorrect Nusselt correlation in your HXR design - and that ain't good at all!		  
3 Do not underesitmate the importance of this problem! And get started on it right away! You gotta' do this in your HXR design, or at least something a lot like it.

One thing to keep in mind is that 1/UA=Rtotal can be used to find U by itself even without knowing A. Once you've got U then you can find the required A and thus L. Sound like a design problem? It is!

Do you need an LMTD correction factor (F) here? Why or why not? 		An intermediate answer: hinside≈1200-1500 B/hr-ft2-°F
U=4.98 B/hr-ft2-°F
L=1195 ft!
4 We're looking for something qualitative here, but that doesn't mean you can't (or shouldn't) write an equation to which to refer. Be specific.  

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Homework 5

Problem Hint Answer
1 & 2

Problem 1 aims to make the distinction between the incremental SPB and the average SPB. Remember the incremental one is more useful, as the average SPB says nothing about diminishing returns. Anyway, how are you going to estimate the incremental SPB?

In problem 2 don't freak out that your ROI is negative for the Basic model. This means that you lose money in the first four years.
  1. Go with the less expensive Supersoft Plus for an SPB of 3 years or less.
  2. The Supersoft Plus also maximizes ROI.
HXR testing exercise
  1. How does mdot,hcp(Th,in-Th,out) compare to mdot,ccp,c(Tc,out-Tc,in)?
  2. Just use the data reduction equation (bad memories from ME311!) you derived and plug and chug. What is F for this HXR? Why?
  3. We are looking for a first estimate for wUA here. If it bugs you that you are making your data reduction equation look like something it really isn't remember that we can only estimate uncertainty anyway.
  1. ?
  2. UAA=487 B/(hr-ft-°F)
  3. wUA/(UA)≈16%

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Homework 6

Problem Hint Answer
1 & 2 Plug and chug free points!  
3 a. Since you are probably going to use EES to generate the system curve anyway, why not come up with a curvefit for the HXR head loss? Be sure to treat the major losses before and after the HXR separately. Why? Another hint, treat the hydraulic fluid as oil, as that's what it probably is anyway.

b. Your answer will vary based on how you treated the losses and the assumptions you make. (And yes, it's a crappy figure, but this happens in practice too!)

 (d)Vdot=95-105 gpm

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Homework 7

Problem Hint Answer
1 Very much like the in class example on cavitation.  
2 This problem is neither long nor difficult. It is thought provoking, however, at least to me. It shows you the power of dimensional analysis. See how far the pump affinity laws can get you to a (semi-)realistic answer with such little effort? And if you didn't have the performance curves at the altered conditions, the pump affinity laws are all you got!  

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