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AN EASY HEAT AND MASS TRANSFER EXPERIMENT FOR TRANSPORT PHENOMENA
M ATTHIAS U. NOLLERT University of Oklahoma • Norman, OK 73019
major challenge in any transport phenomena class, five students each. The groups were randomly assigned to either undergraduate or graduate, is to relate the solve the problem either experimentally or analytically. Teams A mathematical analysis to the physical phenomena were given four weeks to complete the assignment and were being studied. In the undergraduate curriculum, this problem asked to turn in a five-page written report on their results. is addressed by including a one- or two-semester unit-opera Using the same groups, each team was then assigned the part tions-laboratory sequence into the curriculum that, in prin of the problem they had not already completed. For example, ciple, gives students the opportunity to make the important teams that had used the analytical approach were asked to use connections between theory and practice. Most graduate the experimental approach. The teams were given the addi chemical engineering programs offer no laboratory class on tional requirement that their analytical solution should be com transport phenomena. pared to their own experimental data. These results were also Graduate students whose research field is related to trans to be turned in as a five-page written report. port phenomena are expected to learn the connection be ANALYTICAL SOLUTION tween theory and practice through their research. Students specializing in other areas probably have too many demands The drying of a solid is a problem that has a long history on their time to take such a course. Therefore, a need exists and there are a number of excellent review articles and for simple laboratory exercises that can be incorporated into books about the subject, although typically the topic is not a traditional lecture-type graduate class for little or no cost directly addressed in the undergraduate curriculum. Good and without imposing an undue burden on the students. sources for information on this problem, which are easily We have developed a combined experimental and analyti accessible for both graduate and undergraduate students, are cal problem that involves the drying of a solid. This is a Perry 's Chemical Engineer's Handbook[IJ and Unit Opera 2 problem that involves coupled heat and mass transfer. The tions of Chemical Engineering.[ J problem statement given to the student was as follows: One needs to determine the mass of water in the solid (in Using either an experimental approach or a combina
tion of analytical and numerical methods, determine Dr. Matthias U. Nollert is Associate Professor the drying time for a typical bath towel under two of Chemical Engineering at the University of ambient conditions: warm and humid or cool and dry. Oklahoma. He obtained his BS degree in chemi cal engineering from the University of Virginia While you are free to choose your own precise defini and his PhD from Cornell University. He has tions for these two conditions, they should be close to taught graduate transport phenomena for seven years. His research interests include the fluid 80°F and eighty percent relative humidity (rh)for the mechanics of the cardiovascular system. warm state and 60°F and forty percent relative humid ity for the cool state. The class was divided into self-selected teams of three to
© Copyright ChE Division of ASEE 2002
56 Chemical Engineering Education ... a need exists for simple laboratory exercises that can be incorporated into a traditional lecture-type graduate class for little or no cost and without imposing an undue burden on the students . ... We have developed a combined experimental and analytical problem[involving] the drying of a solid. .. that involves coupled heat and mass transfer. this case, the towel) as a function of time. As long as the where towel is wet enough for the water to form a continuous layer on the surface of the towel fibers, the drying rate will be (4) constant. Once this surface water has been removed, the drying rate decreases substantially and is limited by the and diffusion of water from the interior space of the solid to its surface. For practical purposes, the towel is dry to the touch C µ when the surface water has been removed, so it is not neces Pr=+ (5) sary to consider the slower, second phase of drying (also which is valid for free convection near vertical plates with known as the falling-rate period). This greatly simplifies the 104
M k (y - y)A hmL = 0.68 Prl /2 Grl /4 ffi = V y I 114 (7) (2) k (0.952 + Pr) v (1- y)L which is valid for lO
The problem then becomes one of estimating the appropri EXPERIMENTAL SOLUTION ate heat or mass transfer coefficients. There are a substantial The drying rate can be easily determined with equipment number of correlations for heat transfer coefficients on verti that can be found in most research laboratories. All that is cal plates which are readily available to students in most needed is an accurate balance to determine the weight change standard textbooks. Appropriate correlations for mass trans of the towel. Controlling the ambient temperature and hu fer coefficients are much more difficult to find. Consequent! y, midity is the part of the problem that lends itself to a variety all student groups used the more easily obtainable heat trans of creative solutions. 13 fer coefficients. For example, Bird, Stewart, and Lightfoot l The students came up with two basic approaches for the give the following correlation in terms of the Grashof (Gr) experimental requirements. One was to place the towel in a and the Prandlt (Pr) numbers sealed chamber where the temperature and humidity could be maintained using some chemical means. The second ap h L 114 T =0.59( Gr Pr) (3 ) proach was to use an open system, but to measure continu-
Winter 2002 57 ously the temperature and humidity to make sure that condi tions were constant, or nearly so.
Both approaches appeared to work equally well with the 350 ------~ limited sampling available in this class. The groups using a I 300 cJI •• • warm and moist 0 • I sealed system placed within the chamber an open container ci [0 cool and dry :::- 250 00 e •• holding either concentrated acid or salt solutions to maintain Cl> 0 • ] 200 the humidity. This works, but some groups had difficulties 0 (5Sb ... 0 150 Oo maintaining a low humidity. The rate of evaporation from ., ., 100 • • the towel was enough to increase the humidity in the cham i 50 ber. This was not a problem for the groups that used an open 0 +---~-- -~--~---~----< system. Here, the problem was to accurately measure the 0 5 10 15 20 25 humidity. Some groups had access to a digital humidity Time (hours) meter. Others simply used a wet-bulb and a dry-bulb thermometer. 9 We gave limited guidance to the groups regarding the () 8 1 details of their individual experimental techniques. This ap ., • warm and moist § 7 proach seemed to work extremely well. All groups devel 0 I o cool and dry ... 6 •• oped reasonable and inexpensive experimental equipment. ~ 0 3: 5 Each group also came up with a unique solution. We there "C 0 Cl> 4 •• fore suggest that anyone planning to use this problem should -e •• .,0 3 0 not overly constrain the groups by giving them too many .Q <( 2 suggestions or tips. 0 •• 0 • The data obtained by the groups was the moisture content 0 00 of the towel as a function of time. As previously indicated, 0 10 20 30 40 50 60 this plot should be linear. All of the groups obtained highly Time (hours) linear plots for the constant rate region regardless of the details of how the experiment was done. Representative Figure 1: Parts A and B. Representative experimental plots of the data are shown in Figure 1. The slope (i.e., the data from two of the six groups in the class showing the drying rate) was different for each group, even with approxi mass of water in the towel- as a function of time for the two conditions, warm and moist and cool and dry. The size of mately the same ambient conditions. This probably reflects the towel and its initial moisture content were different for measurement errors or subtle differences in the material A and B, so the drying rates cannot be directly compared. used and the actual conditions. The nominal conditions for each group were: A-80°F and eighty percent rh, or 60 °F and sixty percent rh; B-70°F THE MOMENT OF TRUTH and 81 % rh , or 70 °F and 29% rh. At this point, all of the groups had experimental data that followed a straight line as well as a theoretical prediction for equations used to predict how an experimental system be the slope of that line. The difficulty was that the experi haves. The source of these equations does not seem to matter mental data did not fit the prediction. The differences in terms of developing a prediction. Are the equations de ranged from a low of about thirty percent to a high of rived from a fundamental law that is always expected to be about a factor of two between the predicted heat transfer true (conservation of energy, for example), or are they de coefficient and the value obtained from the correlation. rived by fitting a range of experimental data (correlations for While these results should not be too surprising, most of the heat transfer coefficient)? the groups had a difficult time explaining why correla At the undergraduate level, most students do not appreci tions performed so poorly. ate the importance of the answer to this question. We de These results led to a lively class discussion on the mean mand more of graduate students. Graduate students should ing of a heat transfer coefficient and on how these numbers be learning to interpret data and they should be developing are determined. The importance of matching experimental their critical thinking skills. They should be able to distin conditions and definitions to those used in developing the guish between faulty data and a faulty theory. This problem correlations was stressed. provides an opportunity for them to address these issues. This experiment highlights a potentially confusing part of All of the groups correctly identified problems with the any transport course, namely the difference between a theo experimental techniques as leading to some of the differ retical prediction and a correlation. What students see are ences between the prediction and the experimental data.
58 Chemical Engineering Education None of the groups, however, critically examined the weak est link in their predictions, namely the correlation for the 19 53 letter to the editor ) heat transfer coefficient. None of the groups went to the primary literature to examine the limitations and potential Dear Sir: errors of the heat transfer coefficient correlations they used. Safety in the chemical industry has moved to center stage To address this, the problem statement could be improved since the Bhopal tragedy of 1984. It is usually achieved by by explicitly requiring each group to estimate potential add-on equipment such as controls, alarms, and trips after sources of error in their analysis. the plant has been designed. A concept, called Inherently Safer The students' responses to this problem were generally Design (ISD) by Professor Trevor Kletz, has captured global quite favorable. Several students commented that they en attention and is gaining support from industry as well as re joyed the challenge of designing and conducting an experi searchers. It parallels "Pollution Prevention" and "Waste ment. This problem also provided a change of pace from the Minimization" concepts in pollution control and is in tune standard lecture format and problems that require solving a with similar other concepts such as "Green Chemistry," "Sus partial differential equation-typically the mainstay of gradu tainable Plant Design," and "Life-Time Cost Analysis," etc. ate transport classes. The open-ended and nonspecific nature Basically, it builds safety into the process development and of the problem statement was of some concern in developing early design stages so that the add-on safety measures are not this problem, but a survey given to the students at the end of needed or are minimized. Further, the remaining risks are the semester indicated that the problem statement was not more easily controlled. The leading professional bodies, such too vague and that the level of difficulty was appropriate. as the Institution of Chemical Engineers (U.K.) and the Ameri Also, all students indicated they found that working in groups can Institute of Chemical Engineers (U.S.A.) are actively was helpful for this problem. supporting it, as are the regulators, such as the Health & Safety Executive (U.K.). SUMMARY Realizing the significant potential oflSD to provide a quan We have presented a simple experimental and analytical tum leap in process safety, the U.K. Engineering and Physi problem concerning the drying rate of the typical bath towel. cal Sciences Research Council has funded a project on mak This problem can be incorporated into a graduate-level trans ing its use more widespread and user friendly. As a step in port phenomena class with no cost and relatively little effort that direction, we wish to determine the current status of ISD on the part of the students. The problem uses common items use by way of a brief questionnaire. It can be obtained from to demonstrate an important concept in coupled mass and our web site as follows: heat transfer. Students must reconcile differences between For responders from industry and consulting organizations experiments and the heat transfer or mass transfer coeffi cient obtained from correlations found in standard textbooks. http://www.lboro.ac.uk/departments/cg/isd/isd_ind/htm The problem also provides an excellent opportunity for while those from academia, research and development orga critical thinking. We will modify the problem statement to nizations, and regulatory bodies should download from include an explicit statement requiring students to critically http://www.lboro.ac.uk/departments/cg/isd/isd_acd/htm examine both their experimental design and their analytical solution. The questionnaire takes less than ten minutes to complete. We would be grateful if your readers will spare the time to do REFERENCES so at the earliest time possible and return it by e-mail, fax, or 1. Perry, R.H., and D.W. Green, Perry's Chemical Engineer's post. After all, all chemical engineers have a stake in making Handbook, 7th ed., McGraw Hill, New York, NY (1997) our industry safer so its public image, as well as its profit 2. McCabe, W.L., J .C. Smith, and P. Harriott, Unit Operations ability, improves. of Chemical Engineering, 5th ed., McGraw Hill, New York, NY (1993) The responders to our questionnaire will be kept posted on 3. Bird, R.B ., W.E. Stewart, and E.N. Lightfoot, Transport future developments in this project if they indicate on the Phenomena, John Wiley & Sons, New York, NY (1960) questionnaire that they want updates. 4. Churchill, S.W., and H.H.S. Chu, Int. Journal Heat and Mass Transfer, 18, 1,323 (1975) Thank you, 5. Welty, J.R., C.E. Wicks, and R.E. Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 3rd ed., John Wiley Professor J.P. Gupta, Visiting Fellow & Sons, New York, NY (1984) ( [email protected]. uk) 6. Gryzagoridis, J., "Natural Convection from a Vertical Flat Dr. David Edwards, Senior Lecturer Plate in the Low Grashof Number Range," Int. Journal ([email protected] Heat and Mass Transfer, 14, 162 (1971) 7. Kreith, F., and M.S. Bohn, Principles of Heat Transfer, 5th Department of Chemical Engineering Ed. International Thomson Publishing Co. , New York, NY Loughborough University (1997) 0 Loughborough, Leices., England LEll 3TU
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