.t311111ij11111113.._1_a_b_o_,-,_a_t_o_r.::_y_ _______ ) 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<Gr Pr<l<f. analysis since the diffusion of water through the bulk of the 141 towel fibers does not need to be considered. Churchill and Chu (also found in Welty, Wicks, and Wilson15 l) give the following modification of this correla­ The drying rate is determined by a balance between heat tion, which is valid for Gr Pr<l09 transfer and mass transfer. The rate of water removal from the towel, mv, can be written in terms of the heat transfer h L 0.670 (GrPr)" 4 coefficient as (6) = o.68 + [ ( ) 9116 ]419 T l + 0.492 Pr (1) A slightly older version of this correlation is given by or, in terms of the mass transfer coefficient as Gryzagoridis161 (also found in Kreith and Bohn171) as 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<GrPr<la8. where In all of these correlations, the effect of ambient condi­ rate of evaporation tions on the rate of drying, namely the temperature and the drying area humidity of the room, are incorporated through the Grashof heat transfer coefficient mass transfer coefficient number. The temperature at the surface of the drying towel molecular weight of vapor species is assumed to be the wet-bulb temperature for the given temperature of vapor conditions. Therefore, under relatively dry conditions, the temperature of interface wet-bulb temperature will be low compared to the ambient mole fraction of vapor in the gas air temperature. This will increase the Grashof number and mole fraction of vapor at interface consequently increase the predicted rate of drying. latent heat at temperature Ti 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.