2006-1488: LABORATORY DEMONSTRATIONS/EXPERIMENTS IN FREE AND FORCED CONVECTION HEAT TRANSFER
Edgar Clausen, University of Arkansas EDGAR C. CLAUSEN Dr. Clausen currently serves as Adam Professor of Chemical Engineering at the University of Arkansas. His research interests include bioprocess engineering (fermentations, kinetics, reactor design, bioseparations, process scale-up and design), gas phase fermentations, and the production of energy and chemicals from biomass and waste. Dr. Clausen is a registered professional engineer in the state of Arkansas.
William Penney, University of Arkansas W. ROY PENNEY Dr. Penney currently serves as Professor of Chemical Engineering at the University of Arkansas. His research interests include fluid mixing and process design. Professor Penney is a registered professional engineer in the state of Arkansas. Page 11.857.1
© American Society for Engineering Education, 2006 Laboratory Demonstrations/Experiments in Free and Forced Convection Heat Transfer Introduction A number of papers have been written recently on methods for improving or supplementing the teaching of heat transfer including the use of spreadsheets to solve two dimensional heat transfer problems 1, a new transport approach to teaching turbulent thermal convection 2, the use of computers to evaluate view factors in thermal radiation 3, and a new computational method for teaching free convection 4. Supplemental experiments for use in the laboratory or classroom have also been presented including rather novel experiments such as the drying of a towel 5 and the cooking of French fry shaped potatoes 6. Hunkeler and Sharp 7 found that 42% of students in senior laboratory over a four year period were Type 3 learners, that is, action oriented “hands on” common sense learners. Thus, an excellent method for reinforcing course content is to actively involve students in laboratory exercises or demonstrations which are designed to compare their experimental data with data or correlations from the literature. As part of the combined requirements for CHEG 3143, Heat Transport, and CHEG 3232, Laboratory II, junior level chemical engineering students at the University of Arkansas were required to perform simple heat transfer experiments or demonstrations using inexpensive materials that are readily available in most engineering departments. During the first offering in the Fall semester of 2004, the students were required to design, implement and analyze the results from basic experiments. During the second offering in the Fall semester of 2005, the students were asked to suggest and implement improvements in the basic experimental design which could lead to better agreement between their experimental results and results from literature correlations. This exercise has several benefits: • It provides an opportunity for students to have additional “hands on” experience; • It demonstrates a physical application of correlations found in the textbook; and, • It helps students develop an appreciation for the limitations of literature correlations. Results from three of these experiments (free convection cooling of an upward facing plate, forced convection cooling by flowing air over an upward facing horizontal plate, and forced convection heating of a rod by flowing air through an annulus) are described below. In addition, survey and test results are presented which help to demonstrate whether the experiments/demonstrations improved or enhanced the students’ understanding of the appropriateness and limitations of heat transfer correlations found in the literature. Free Convection Heat Transfer from an Upward Facing Horizontal Plate
Free convection heat transfer is encountered in many practical applications, including heat transfer from pipes, transmission lines, baseboard heaters and steam radiators. Correlations are available for predicting free convection heat transfer coefficients for many different geometries. One of the important geometries is the upward facing horizontal heated surface or plate, the subject of this investigation. The overall objectives of this experiment were to: 1. Determine the experimental free convection heat transfer coefficient for the top surface of Page 11.857.2 a horizontal hot plate exposed to air, and 2. Compare these results with results generated from the appropriate correlation of Churchill and Chu 8: 1 Nu = 0.54Ra 4 104 < Ra < 107 (1) 1 Nu= .0 15Ra 4 107 < Ra <1011 (2) Figures 1 and 2 show schematics of the experimental apparatus, and Figures 3 5 show photographs of the actual equipment used in the experiment. A list of equipment and detailed safe experimental procedures was presented by Clausen et al. 9, and may also be obtained from the corresponding author. Briefly, an aluminum plate was heated to ~65°C by setting it on a wooden platform in an insulated box, closing the lid and heating the surrounding air in the box with an ordinary hair dryer inserted in the top of the box. After heating the plate, it was set on an insulated surface in a still room and wrapped with insulation so that only the black painted surface was exposed (see Figures 2 and 4). A photograph of the second year modification of the experiment is shown in Figure 5, where a drop cloth curtain was used to better isolate the apparatus from air disturbances. A thermocouple was inserted into the plate, and temperature was measured as a function of time while observing the slow cooling of the plate due to free convection.
Figure 1. Insulated Wooden Box for Heating the Aluminum Plate Page 11.857.3 Figure 2. Experimental Setup for Cooling the Horizontal Insulated Plate
Figure 3. Photograph of Wooden Box Figure 4. Photograph of Apparatus for Used to Heat the Aluminum Plate Cooling the Insulated Horizontal Plate Page 11.857.4 Figure 5. Photograph of Drop Cloth used to Isolate the Environment Surrounding the Aluminum Plate It was desired to compare an experimentally determined heat transfer coefficient with correlations found in the literature. A heat balance on the plate, with no heat generation, yields: dT − (hA (T − T ) + εσA (T 4 − T 4 )) = ρV ()C (3) S SURFACE ∞ S SURFACE ∞ P dt Although small, the heat balance was also corrected for the heat flow by conduction from the aluminum plate through the insulation to the table. Experimental data of temperature vs. time were thus used to determine the “best fit” experimental heat transfer coefficient by integrating Equation 3 numerically using a TK Solver 4 th order Runga Kutta integration. The heat transfer coefficient from the literature was determined using Equations 1 and 2, where the Rayleigh number is calculated as: gβ (T − T )L3 Ra = SURFACE ∞ Pr (4) ν 2 In Equation 4, the length of the plate is the characteristic length in free convection and, for a horizontal flat plate, L = A S/P. Assuming that the surrounding air is an ideal gas, the volumetric expansion coefficient may be calculated as: 1 β = (5) T Finally, the heat transfer coefficient, hCORR , may be calculated from the Nusselt number as:
kNu h = (6) CORR L
Page 11.857.5 Figure 6 shows a plot of the experimental temperature with no drop cloth as a function of time, as well as a curve showing a numerical integration of Equation 3 using the “best fit” experimental heat transfer coefficient. The emissivity (ε) of the black painted surface was assumed to be 0.98. The experimental heat transfer coefficient was 8 W/m 2K at a surface temperature of 352 K, while the coefficient based on the Churchill/Chu relationship was 5.6 2 W/m K. Thus, a correction factor (h EXP /h CORR ) of 1.4 was needed in order to match the experimental data with the correlation. When the drop cloth was added, the correction factor fell to 1.2, indicating that the addition of the drop cloth was significant in eliminating air currents.
360 + + + 355 + + + + + 350 + + + + + 345 + + + + + 340 + + +
Temperature (K) Temperature + + 335 + + + + + 330
325 0 500 1000 1500 2000 2500 3000 3500 4000 Time (s) Figure 6. Temperature vs. Time Experimental Data (+) and Predicted by Equation 4 2 Multiplied by a Factor of 1.4 (h EXP = 8 W/m K at T SURFACE = 352 K) Forced Convection Heat Transfer from an Upward Facing Horizontal Plate
Forced convection heat transfer occurs when the fluid surrounding a surface is set in motion by an external means such as a fan, pump or atmospheric disturbances. This study was concerned with forced convection heat transfer from a fluid (air) flowing parallel to a flat plate at varying velocities. The objectives of this experiment were to: 1. Determine the experimental forced convection heat transfer coefficient for parallel flow
over a flat plate. Page 11.857.6 2. Compare the experiment heat transfer coefficient with the coefficient calculated from the correlations presented by Cengel 8, who gives the following correlations for local heat transfer coefficients for forced convection flow over a horizontal plate: 5.0 3/1 Nu x = hx x / k = .0 332 Re x Pr for laminar conditions, i.e., Re < 500,000 (7) 8.0 3/1 5 7 Nux = hx x / k = .0 0296Re Pr for turbulent conditions, i.e., 5x10 < Re < 10 (8) The integrated average coefficients are given by 5.0 3/1 Nu = hx / k = .0 332 Re x Pr for laminar conditions, i.e., Re < 500,000 (9) Nu = hx / k = .0( 037Re 8.0 −871)Pr 3/1 turbulent conditions, 5x10 5 < Re < 10 7 (10) The experimental set up and procedures were essentially the same as shown in Figures 1 4, except that multiple plates were used along with a three speed fan. Thus, forced convection heat transfer was measured for horizontal plates at two selected distances from the fan and at three different air speeds. An anemometer was used to measure the air velocity over the plate at five different lateral positions to determine the average air velocity. A schematic of the experimental set up is shown in Figure 7 and photographs of the apparatus are shown in Figures 8 and 9. As is shown in Figure 9, a series of cardboard honey comb diffusers was used during year 2 in an attempt to minimize air turbulence. The diffusers were located just after the fan (connected to the fan outlet by a plastic “garbage bag” channel) and immediately in front of the aluminum plates. Once again, a list of equipment and detailed safe experimental procedures was presented by Clausen et al. 10 , and may also be obtained from the corresponding author.
Figure 7. Location of Fan and Plates for the Horizontal Plate Heat Transfer Experiment Page 11.857.7 Figure 8. Photograph of Experimental Horizontal Plate Heat Transfer Experiment
Figure 9. Photograph of Diffuser and Connection between Fan and Diffuser
Page 11.857.8 Figure 10 shows a plot of the experimental temperature for the first plate, without the air diffuser, as a function of time at an air velocity of 4.82 m/s. The procedure for obtaining the experimental heat transfer coefficient was essentially the same as in the previous experiment. The ratio of the experimental heat transfer coefficient to the correlation heat transfer coefficient ranged from 2.7 3.3 (average of 3.0) for the first plate at three different fan velocities, and ranged from 1.7 2.4 (average of 2.1) for the fourth plate. When the air diffuser was added, the ratio was 1.8 1.9 for the first plate and ranged from 2.8 5.0 (average of 3.9) for the fourth plate. Thus, the diffuser only marginally affected the effects of air turbulence on temperature measurement. Perhaps the addition of a drop cloth in combination with the diffuser would have improved the ratio.
69.5 + 69 + 68.5 + 68 +
67.5 + 67
66.5 +
66 + 65.5 + Plate Temperature (C) Temperature Plate 65 +
64.5 + 64 0 50 100 150 200 250 300 Time (s) Figure 10. Temperature vs. Time Experimental Data from the First Plate at an Air Velocity of 4.82 m/s Forced Convection Heat Transfer from Hot Air in an Annulus to the Inner Cylinder
Another important geometry for forced convection heat transfer is the heating or cooling of a fluid flowing through an annulus between an outer pipe and an inner cylinder. The objectives of this experiment were to: 1. Determine the experimental forced convection heat transfer coefficient for the heating of a brass rod, contained in an annulus, as air flows through the annulus, and Page 11.857.9 2. Compare these results with the heat transfer coefficient from the Dittus Boelter equation 8: Nu = 0.023 Re 0.8 Pr 0.4 (11)
where the hydraulic diameter of the annulus (D H = D PIPE – D ROD ) is used as the characteristic length in both the Reynolds and Prandtl numbers. Figure 11 shows a schematic of the experimental apparatus, and Figures 12 and 13 show photographs of the equipment used in the experiment. A list of equipment and detailed safe experimental procedures was presented by Clausen et al. 10, and may also be obtained from the corresponding author. Ice was used to cool a brass rod to a temperature of 10 12°C. The wood and brass rods were then inserted into the PVC tube as shown in Figure 11, and a thermocouple was inserted into the brass rod. The wood rod was used to provide an inside cylinder which is much longer than the brass rod, so that fully established turbulent flow existed prior to the hot air reaching the brass rod. The hair dryer was then inserted into the bottom of the PVC tube, and temperature inside the brass rod was monitored with time. After the air flow had reached steady state, the velocity and ambient air temperature of the air exiting the annulus were recorded. The procedure was repeated for different hair dryer speeds. The cylinder is shown in the center of Figure 12. A photograph of the air diffuser, used during the second year modification of the experiment, is shown in Figure 13. The diffuser was connected to the bottom of the PVC tube in an attempt to minimize air turbulence, much like the diffuser in the horizontal plate experiments.
Figure 11. Schematic of Annulus Heating Apparatus Page 11.857.10 Figure 12. Schematic of Annulus Heating Apparatus
Figure 13. Two Views of Diffuser Used in Annulus Heating Apparatus Figure 14 shows a plot of the experimental temperature for the rod, without the air diffuser, as a function of time at an air velocity of 4.22 m/s. The procedure for obtaining the experimental heat transfer coefficient was much the same as in the previous experiment. The ratio of the experimental heat transfer coefficient to the correlation heat transfer coefficient ranged from 1.6 2.2 for the range of air velocities, with an average of 1.8. When the air diffuser was added, the ratio held at 1.0 (h EXP = h CORR ) for all air velocities, showing that this air diffuser was effective in minimizing turbulence in this system that was unaffected by outside air currents. Page 11.857.11
28
26 + + 24 + + 22 + + 20 + + 18 + + 16 +
Rod Temperature (C) Temperature Rod + 14 + + 12 +
10 -25 0 25 50 75 100 125 150 175 200 225 Time (s)
Figure 14. Temperature vs. Time for Experiment # 1 with the 1 in Diameter x 8.1 in Long Brass Rod Heated by a 62°C, 4.22 m/s Air Stream in a 3 in Pipe Assessment of Educational Value
After the second offering of this experimental program during the Fall, 2005, semester, the participating students were asked to evaluate the effectiveness of the program as an educational tool, and were also given a short competency quiz to also evaluate effectiveness. Results from the survey of the18 participating students are shown in Table 1. Perhaps most importantly, the students felt that the experiments/demonstrations helped to increase their understanding of heat transfer (Statement 1), and gave them a better understanding of the applicability and limitations heat transfer correlations and data (Statement 2). The students also felt that experiments/demonstrations should be developed in conjunction with other courses besides heat transfer (Statement 3), and preferred the use of group reports (as used in this exercise) in place of individual reports (as used in most of the other assignments) (Statement 7). The students were less enthusiastic about including the experiments/demonstrations as a regular part of Lab 2 (Statement 4), using the experiments/demonstrations in place of more traditional laboratory experiments (Statement 5), and in working in the smaller groups of 2 3 people (used in this exercise), as compared to the groups of 3 5 people used in other experiments (Statement 6). Most of the experiments in this exercise actually required a longer time commitment than traditional laboratory experiments, and the students were not particularly fond of TKSolver as a computational tool. Finally, as expected, the students disliked the method of grading used on the experiments/demonstrations (a maximum of two submissions to get it correct; receive an ‘A’ or ‘F’) (Statement 7), and instead preferred the usual method of grading a single laboratory report Page 11.857.12 submission. Table 1. Results from the Heat Transfer Experiments/Demonstrations Survey Fall, 2005 Survey Statement % of Students Surveyed 5 4 3 2 1 1. The heat transfer experiments/demonstrations helped to 11 67 17 0 5 increase my understanding of heat transfer 2. The heat transfer experiments/demonstrations gave me a 5 78 11 5 0 better understanding of heat transfer correlations and data, their applicability and limitations 3. Experiments/demonstrations should be developed in 5 72 17 5 0 conjunction with other courses besides heat transfer 4. Heat transfer experiments/demonstrations should be 0 44 44 5 5 included as a regular part of Lab 2 5. I prefer the experiments/demonstrations to more 5 44 33 17 0 traditional laboratory experiments 6. I prefer working in groups of 2 3 people, instead of 3 5 11 22 50 11 5 people 7. I prefer group reports in place of individual reports 33 39 11 17 0 8. I prefer the method of grading used on the heat transfer 0 5 28 44 22 experiments/demonstrations to traditional grading in Lab 2 5—strongly agree 4—agree 3—no opinion 2—disagree 1—strongly disagree The students were also given competency quizzes to demonstrate whether the experiments accomplished the stated objectives of the exercise. Each student was given a different competency quiz, depending upon which experiment the student ran. The questions which pertain to this paper are: 1. In layman’s terms, what is the difference between free and forced convection? 2. What was the diffuser (or curtain) supposed to do to improve your results? Did it help? Why or why not? 3. What correlation was used in predicting the forced (or free) convection heat transfer coefficient for your experiment? A name or description is sufficient. What are its limitations? Each student was given three questions pertaining to his or her experiment, and was expected to give a short answer to each of the questions. The quiz was not announced, and notes and textbooks could not be used during the quiz. The quizzes were graded on a 0 6 point basis (2 points per question). Four of the 15 students taking the quiz scored 6/6, 8 of the students scored 5/6, and 4 of the students scored 4/6. These results demonstrate competency, and show that the
objectives of the exercise had indeed been met. Page 11.857.13 Nomenclature 2 AS heat transfer area, m Cp specific heat, J/kg K DH hydraulic diameter of the annulus, m DPIPE diameter of outer pipe, m DROD diameter of rod (inner cylinder), m g gravitational constant, m/s 2 h area average convection heat transfer coefficient, W/m 2 K 2 hCORR heat transfer coefficient from literature correlations, W/m K 2 hEXP heat transfer coefficient from experimental data, W/m K 2 hx local heat transfer coefficient at length x along a flat plate, W/m K k fluid thermal conductivity, W/Mk L characteristic length in free convection, As/P, m Nu area average Nusselt number, hx/k or hD/k Nu x local Nusselt number at location x along flat plate, hx/k P perimeter, m Pr Prandtl number of the fluid Ra Rayleigh number Re Reynolds number, = VDρ/ for cylinder or Vxρ/ for a flat plate Re x local Reynolds number at location x along flat plate, Vxρ/ t time, s T temperature, K Tω ambient temperature of surroundings, K TSURFACE surface temperature, K v fluid velocity, m/s V volume of plate or cylinder, m 3 x length along flat plate in flow direction, m β volumetric expansion coefficient, = 1/T, K 1 ε surface emissivity ρ fluid density, kg/m 3 σ Stefan Boltzmann constant, W/m2K4 Bibliography
1. Besser, R.S., 2002, “Spreadsheet Solutions to Two Dimensional Heat Transfer Problems.” Chemical Engineering Education , Vol. 36, No. 2, pp. 160 165. 2. Churchill, S.W., 2002, “A New Approach to Teaching Turbulent Thermal Convection,” Chemical Engineering Education , Vol. 36, No. 4, pp. 264 270. 3. Henda, R., 2004, “Computer Evaluation of Exchange Factors in Thermal Radiation,” Chemical Engineering Education , Vol. 38, No. 2, pp. 126 131. 4. Goldstein, A.S., 2004, “A Computational Model for Teaching Free Convection,” Chemical Engineering Education , Vol. 38, No. 4, pp. 272 278. 5. Nollert, M.U., 2002, “An Easy Heat and Mass Transfer Experiment for Transport Phenomena,” Chemical Engineering Education , Vol. 36, No. 1, pp. 56 59. 6. Smart, J.L., 2003, “Optimum Cooking of French Fry Shaped Potatoes: A Classroom Study of Heat and Mass Transfer,” Chemical Engineering Education , Vol. 37, No. 2, pp. 142 147, 153. 7. Hunkeler, D., Sharp, J.E., 1997, “Assigning Functional Groups: The Influence of Group Size, Academic Page 11.857.14 Record, Practical Experience, and Learning Style,” Journal of Engineering Education , Vol. 86, No. 4, pp. 321 332. 8. Cengel, Y.A., 2003, Heat Transfer: A Practical Approach, McGraw Hill Book Company, New York. 9. Clausen, E.C., Penney, W.R., Colville, C.E., Dunn, A.N., El Qatto, N.M., Hall, C.D., Schulte, W.B., von der Mehden, C.A., 2005, “Laboratory/Demonstration Experiments in Heat Transfer: Free Convection,” Proceedings of the 2005 American Society of Engineering Education-Midwest Section Annual Conference . 10. Clausen, E.C., Penney, W.R., Dunn, A.N., Gray, J.M., Hollingsworth, J.C., Hsu, P.T., McLelland, B.K., Sweeney, P.M., Tran, T.D., von der Mehden C.A., Wang, J.Y., 2005, “Laboratory/Demonstration Experiments in Heat Transfer: Forced Convection,” Proceedings of the 2005 American Society of Engineering Education-Midwest Section Annual Conference . Page 11.857.15