Heat Transfer from Steam to Water - Lab Report Example

Paper Outline 1. Introduction 2. Background 3. Aim and Objective 4. Equipment and apparatus 5. Method 6. Theoretical Concept 7. Procedure 8. Results 9. Discussion 10. Thermal Analysis 10.1. Possible errors 10.2. Statistical Summary 11. Conclusion 1. Introduction This experiment mainly focuses on the aspect of heat transfer. It is designed to test the ultimate coefficient of heat transfer for the two techniques identified. One method uses the shell heat exchanger while the other uses the tube heat exchanger. The data collected during the experiment is expected to reflect the variation in the flow rates of heat from the two sources, as well as the comparison of the trends. It is hypothesized that there is a direct proportionality between the heat flow rates and the overall coefficient of heat transfer, since the rate of flow increases in the same trend as the coefficient of transfer in the data. 2. Background This research is derived from the basic knowledge of heat energy. The heat content of an object is reflected in the temperature behavior in the object. In the process of evaporation, it is clear that steam gives up the latent heat of vaporization to an object subjected to it, leading to condensation on the surface (Incropera and Dewitt 49). The object of condensation carries a sensible heat at the same temperature as that of the original steam. The experiment tests the pattern and rate of heat flow from steam to the object on which condensation takes place. In the steam, the latent heat of vaporization is generated instantly while condensation of the steam to water takes place. From the background of evaporation, the quantity of latent heat is between 2 to5 times more than the quantity of the sensible heat in the water after it cools (Fan 77). The data collected will be used to conduct analysis and test the hypothesis be plotting the relationship between the transfer rate and the rate of flow of the heat. 3. Aim and Objective The principle purpose of this project is to test on the heat transfer as the steam changes to liquid water. This requires an important process of determining the quantity of heat energy consumed during the entire procedure of condensing the steam. It also aims to estimate the quantity of the latent heat used in other processes. Like in the case of boiling, heat is used to transform water into steam. This experiment compares the heat spent in heating water to its boiling point to that released during condensation of the steam. Finally, this experiment evaluates the manner of heat transfer in condensation to find out if the temperature changes in the process. 4. Equipment and apparatus The equipment in this project includes a tank, pumps, heat exchanger, steam jet vacuum, surface condenser. This experiment is to compute the coefficient of heat transfer. The equipment and apparatus include the following: 4.1. Steam jet vacuum It exists in the design of a thermo-compressor. The vacuum is less costly to use, as its maintenance is easy. It usually requires additional steam for adequate condensation. 4.2. Mixing condenser This apparatus has a number of plates and nozzles to use in mixing of the condenser. The liquid water and the steam, which has condensed are passed out through the lower parts of the mixing condenser. 4.3. Pumps The experiment uses two types of pumps. These include vacuum pump and steam jet vacuum. They cause and maintain a vacuum inside the evaporation unit. The vacuum comes about due to the changes of temperature in the condenser as water vapor forms water. 4.4. Vacuum pump The most popular pump used in this procedure is the ring pump. It has two sections, on for a rapid start-up while the other is used in the production unit. 4.5. Surface Condenser The surface condenser literally does the cooling as the steam condenses. All this time, the condensing water and the steam do not mix at all. The surface condenser is built in a similar design as the normal straight-tube exchanger. 5. Methodology 5.1. The Heating Process in Tank Equipment Fig 1: Heating Process in the Tank 5.2. Corning The Heat Exchanger Equipment The figure 2 below demonstrates the apparatus of corning the heat exchanger from the inlet side. The steam inlet pipe appears on its right hand side, which is in the background of this figure. Fig 2:Corning heat exchanger 6. Theoretical Concept The rate at which heat transfer takes place is found by condensing the vapor. This is a very important process used in manufacturing plants inside the steam vessels, in which the condensation causes the steam to produce the latent heat. This also applies in the distillation as well as the evaporation. Steam generated therefore condensed to produce latent heat of vaporization. The latent heat is generated at a constant temperature, that boiling point of water. 6.1. Models Produced 6.1.1. Model 1- Condensation in the Plane Surfaces The equations are as shown below: Ln (Ts – T1) / (Ts - T) = (W / p)((k - 1) / K)t - ----- Model 1 Where: ρ is the water density V is the Volume of water t is the time in seconds T is the tank temperature as a time function W is the rate of flow of water in lbm / min Ts is the temperature of water vapour T1 is the initial temperature of the tank K = exp (U0A0)/Wcp ----- Model 2 Where: Uo is the overall coefficient of heat transfer Ao is the area of heat transfer cP is the water heat capacity Plot for model 1 generates a gradient calculated as  Slope = (W / p)((k - 1) / K) – Model 3  Converting the time into minutes, we generate the new model as follows  1 / U0 = D0 / Dihifi + D0 / Dihi + (D0Ln (Do / Di) / 2kw) + 1 / h0 + 1 / hf0 ------Model 4 Where: Do is the tube external Diameter Di ­is the tube internal Diameter hfi is the coefficient of heat transfer because of fouling in the inner surface of the tube­ hi­ is the coefficient of transfer between water and metal in the inner tube surface kw­ is is the thermal conductivity of copper tube ho is the coefficient of heat transfer between steam and metal in the inner surface of the tube hfo = heat transfer coefficient due to fouling on the outside tube surface Model 4 is used in a case where the fouling is significant. In an insignificant fouling case, model five below is applicable. 1 / U0 = D0 / Dihi + (D0Ln (D0 / Di)) / 2kw + 1 / ho ------ Model 5 The rate used for ho was 2000 Btu / hr - ft2 – o F, from which model 6 was generated  Nu = 0.023Re^0.8 * Pr ^ 0.4  ---- Model 6 Therefore, Nu = hiDi / k ---------- Model 7 Where Nu represents the Nusselt k represents the water thermal conductivity  Nu = hiDi / k- ---------- Model 8 Where: Re represents the Reynolds number 𝜇 = water viscosity 𝜈= average liner velocity for the water Pr = Cpu / k –Model 9 Where Pr = Prandtl number Model 1 and 2 were used in computing the over-all coefficient of heat transfer for the experimental data. Model 3 and 9 on the other hand were used for the predicted coefficient. 6.1.2. Model 2 – Condensation vapor in horizontal tube Film wise condensation takes place when the steam strikes the surface of steam with low temperature. The vapor condenses to form a film on the surface. If the condensate flows due to gravity and the condition of streamline flow is found in the entire film thickness, then the heat movement is by conduction. The thickness of the film undergoing condensation is directly proportional to the amount of heat transferred. This is because the heat transfer is by conduction. In this regard, the film thickness relies on the removal of the condensate from the surface. In the drop wise condensation, the cooling takes place on the surfaces and the substances are mixed to prevent the condensing vapor from making the surface wet. The steam is thus condensed in drops instead of a film. 7. Procedure The procedure of this experiment is outlined as shown below: 7.1. Heating the Liquid in the Tank The procedure involved draining of the tank storage by opening its valve and filling the tank with cold water. This is done using the filling valve. The stirrer set on by use of a long extension cord. It used a power source in the room to avoid interference with the equipment. Stirrer was set to maximum speed to make the temperature uniform before turning on the computer. The next process was to record the data, using computer. The control valve of the water was turned on as the water control valve was regulated to flow rate of approximately 40 lb. per minute. The flow begins with a very high speed then stabilizes after a few minutes. After reducing the rate of flow to 40 lb per minute, the capture of data was terminated. The next step was to open the steam inlet valve using the rare valve in the right side of the tank. A new record of data with flow rates was begun, showing a consistent rates of water flow, preceding the heating of the tank. The pressure of the steam was regulated, increasing it to 5 psi. This was with the help of the steam regulator on the right side of the steam inward valve. Increasing the pressure implies rotating the valve clockwise. On the other hand, reducing it means we turn the valve counterclockwise. It was necessary to readjust the water valve in order to maintain a steady water flow rate at 40 lb per minutes. The recording of data proceeded until the water tank attains a temperature of 135 oF. To stop the logging of data required a simple action, clicking on the stop sign. This completely shut down the steam. The next process is to turn off the pump and the stirrer and to drain the water from the tank. This procedure was done repeatedly to reach a flow rate of 70 lb per minutes of water. After completing the data record, the final step is to turn off the equipment and keeping the extension cord. 7.2. Corning of the Heat Exchanger The initial step of this experiment was to put on the computer, opening the data capturing program and starting the heated tank with the Corning Heat Exchanger. The next step was to click on the arrow marked start to begin capturing the data of temperature. This is followed by draining the water by closing the drain valve. It sets the flow rate of water at 2 gallons per minute. The next step was to open the steam valves and recording the pressure of the steam. The next process was to check the rate of water flow to ensure it is consistent and does not drift. This runs continuously until the temperature is stable. As the temperature stabilizes, the final temperature was written down because data logging capacity is lacking in the program. The next step was to examine the tubes and the existing transitions between the boiling and the non-boiling transfer of heat. The process was done repeatedly for different flow rates of water such as 4, 8, 10 and 14 gallons per minute. 8. Results The data captured in the program generated graphs given with the functions temperature such as the density of water, water viscosity, heat conductivity in relation to the temperature and the water heat capacity. These were instrumental in the determination of the constants with remaining elements of temperatures in the experiment. The graphs were provided in the data including the transfer of heat from the water vapor to liquid water. The graphs were accompanied by equations for the necessary calculations of the experiment as provided in the tables below: Tank 40 Values   slope K ln K Uo Uo(Btu/ft^2-hr-F) Weel 1 0.0262 1.196123 0.179085 5.601531 336.0918354 week 2 0.0317 1.247482 0.221127 6.916554 414.9932467 week 3 0.0297 1.228304 0.205634 6.431943 385.916572 Table 1: Calculation of over-all coefficient of transfer for 40 lb per min Tank 70 Values   slope K ln K Uo Uo(Btu/ft^2-hr-F) Weel 1 0.0333 1.135183 0.126794 6.940394 416.4236267 week 2 0.0356 1.145882 0.136175 7.453878 447.2326724 week 3 0.0344 1.140275 0.13127 7.185372 431.1223342 Table 2: Calculation of over-all coefficient of transfer for 70 lb per min Week 1 flow of Cooling water (gpm) Water in Temp (F) Water out Temp (F) Steam in Temp (F) Steam out Temp (F) Water flow rate in (lbm/hr) q (Btu/hr) Deltatlm U 2 58.6 204.3 212.8 176.7 1000 145700 41.64979458 282.7979445 4 58 147.8 198.6 103.4 2000 179600 48.04943773 302.1673827 6 58.3 130.8 198.1 90 3000 217500 47.28738093 371.829259 8 58 133.8 197.8 85.4 4000 303200 43.14307587 568.1299085 10 57.9 121.5 197.4 85.2 5000 318000 47.52916868 540.8744447 Table 3: Week 1 Data Week 2 flow of Cooling water (gpm) Water in Temp (F) Water out Temp (F) Steam in Temp (F) Steam out Temp (F) Water flow rate in (lbm/hr) q (Btu/hr) Deltatlm U 2 60.2 193 210.5 203 1000 132800 59.6881496 179.8620421 4 62 175 200 161 2000 226000 53.76953407 339.7830626 6 61 160.3 198 128.5 3000 297900 51.1616525 470.7122495 8 59.5 138.5 197.5 100 4000 316000 49.17133414 519.522847 10 62 125 197 91.5 5000 315000 47.63100977 534.6263079 Table 3: Week 2 Data Week 3 flow of Cooling water (gpm) Water in Temp (F) Water out Temp (F) Steam in Temp (F) Steam out Temp (F) Water flow rate in (lbm/hr) q (Btu/hr) Deltatlm U 2 60 196 210 202 1000 136000 55.24934069 198.9946356 4 59 178 204 172 2000 238000 59.21222098 324.9340071 6 59 161 197 121 3000 306000 47.82792719 517.2129944 8 59 137 196.5 98 4000 312000 48.53051191 519.7198233 10 59.5 123.5 196 91 5000 320000 49.18431909 525.9601922 Table 4: Week 3 Data gpm U1 U2 U3 Avg of (U1,U2,U3) standard Deviation 2 282.7979 179.9 198.99 220.55 44.7 4 302.1674 339.8 324.93 322.29 15.47 6 371.8293 470.7 517.21 453.25 60.62 8 568.1299 519.5 519.72 535.79 22.87 10 540.8744 534.6 525.96 533.82 6.115 Table 5: Calculation of Statistical Summary In tables 1 and table 2, we used equations labeled model 2 and model 3 to compute the over-all coefficient of heat transfer from the results of experiment in the data collected. Fig 3: Week 1- 40 lb / Min Fig 4: Week 2- 70 lb / Min Fig 5: Week 3- 40 lb / Min Fig 6: Week 1- 70 lb / Min Fig 7: Week 1 40 lb/min vs 70 lb/min Fig 8: Week 2- Tank 70 lb / Min Fig 9: Week 2 40 lb/min VS 70 lb/min Fog 10: Week 3- 70 lb / Min Fig 11: Week 3 40 lb/min VS 70 lb/ min 9. Discussion The calculation of temperatures for the heating water in the tanks used model 1, after which graphs were plotted against time. The calculation of the gradients from excel spread sheet generated the statistical summary including the standard deviation and the average for the over-all heat coefficients of heat transfer. Tank 40 Values   slope K ln K Uo Uo(Btu/ft^2-hr-F) Weel 1 0.0262 1.196123 0.179085 5.601531 336.0918354 week 2 0.0317 1.247482 0.221127 6.916554 414.9932467 week 3 0.0297 1.228304 0.205634 6.431943 385.916572 Table 6: Calculation of Slopes – Tank 40 Tank 70 Values   slope K ln K Uo Uo(Btu/ft^2-hr-F) Weel 1 0.0333 1.135183 0.126794 6.940394 416.4236267 week 2 0.0356 1.145882 0.136175 7.453878 447.2326724 week 3 0.0344 1.140275 0.13127 7.185372 431.1223342 Table 7: Calculation of Slopes – Tank 70 10. Thermal Analysis 10.1. Possible Errors Table 8 below shows the calculation of the percentage error in the calculation of the difference between the experimental and the expected or predicted value of the over-all coefficient of heat transfer for the 40lb per minute flow rate. Table 9 shows similar results but for the 70 lb per minutes flow rate. For W =40   Uo Exp Uo Pre week 1 5.60153059 5.99377984 week 2 6.916554111 5.99377984 week 3 6.431942866 5.985644243 Ave 6.316675856 5.991067975 std 0.665046297 0.004697089 % error 5.15% Table 8: Calculation of Statistical Summary – Tank 40 For W=70   Uo Exp Uo Pre week 1 6.940393779 8.495554 week 2 7.453877874 8.495554 week 3 7.185372237 8.485107 Ave 7.19321463 8.492072 std 0.256831864 0.006032 % error -18.06% Table 9: Calculation of Statistical Summary – Tank 70 The computations were done to produce the correlation between the experimental values and the expected or the predicted results of the over-all coefficients of heat transfer for the flowing water. The calculation of the errors was done to assist in the determination of the possible causes of the errors. There error of prediction in the calculation of the coefficients was 5.15 % for the 40lb per minute tank and -18.06 % for the 70 lb per minute tank of water. It demonstrates that indeed, the flow rate of the heat increased, the error increased in the 40lb / minute tank and reduced in the 70lb per minute tank. To reduce the possible errors, there is need to increase the range of data and thus to increase the data observation points. There is further need to calibrate the measurement equipment to ensure that they are precise to eliminate the zero error. It is also important to be careful in the measurements to avoid human errors and to apply the right models of calculation to minimize errors of commission and omission. The summary of the calculations are shown below: gpm U1 U2 U3 Avg of (U1,U2,U3) standard Deviation 2 282.7979 179.9 198.99 220.5515408 44.7 4 302.1674 339.8 324.93 322.2948175 15.47 6 371.8293 470.7 517.21 453.2515009 60.62 8 568.1299 519.5 519.72 535.7908596 22.87 10 540.8744 534.6 525.96 533.8203149 6.115 Table 10: Calculations of the over-all coefficient of heat transfer Fig 12: Over-all coefficient of Heat Transfer against flow rate of water - Week 1 Fig 13: Over-all coefficient of Heat Transfer against flow rate of water - Week 2 Fig 14: Over-all coefficient of Heat Transfer against flow rate of water - Week 3 Fig 15: Over-all coefficient of Heat Transfer against flow rate of water – All weeks Fig 14: Over-all coefficient of Heat Transfer against flow rate of water - Average 11. Conclusion The data confirms that the over-all coefficient of heat transfer for the 40 lb per minutes flow rate was 6.32 while that of the 70 lb per min was 7.19. This qualifies the hypothesis and proves that it is true. Indeed, the experiment shows that the flow rate of water increases in positive linear proportionality with the over-all coefficient of heat transfer. Works Cited Incropera F. and Dewitt D., Fundamentals of heat and mass transfer 5th edition, McGraw-Hill, 2005. Fan, Maohong. Heat Transfer from Steam to Water; Laramie, WY, 2012. Name of the Student Category Criteria Points earned Technical Writing (40 Points) Title (1 Point)   Presented in corporate memo format – 1 pt. 1 Summary   Briefly describes what was done and why it was done – 2 pts. 2 (6 Points)   Summarizes results – 3 pts. 3     Doesn't refer to other sections of the report – 1 pt. 1 Background and Methods (11 Points)   Shows a figure, either a line drawing or a well-labeled photo, of the apparatus used in the experiment, and includes descriptions – 2 pts. 2   Shows the theoretical equations used – 2 pts. 2   Procedures are clear and provide enough detail that the experiment could be repeated by peers – 2 pts. 2   Section is written in correct tense and in paragraph form – 2 pts. 2   Extraneous information minimized – 3 pts. 3 Results and Discussion   Shows results and analysis in both paragraph and graphical formats where appropriate – 3 pts 3 (9 Points)   Figures, tables, and equations are referred to in the text using figure numbers – 2 pts. 2     Results are discussed, with significant findings included – 3 pts. 3     Reasons for possible errors and/or recommendations (if necessary) – 1 pt. 1 References   Correct in-body citations used – 3 pt. 3 (7 Points)   Lab manual and any other references are included – 2 pts. 1     All citations are written in ACS format – 2 pts. 2 Grammar   Paper is clear and easy to read, with complete sentences and few spelling, punctuation, or grammar mistakes – 5 pts. 5 (6 Points)   Tone of the paper is formal with no slang, and any abbreviations are appropriate and defined – 1 pt. 1 Data Analysis   Appropriate equations are used – 4 pts. 4 (20 Points)   Calculations are performed correctly – 5 pts. 5     Statistical analyses complete – 5 pts. 5     Statistical analyses correct – 4 pts. 4     Comparison with typical values is presented – 2 pt. 2 Other technical content   Submitted via email – 5 pts. 5 (20 Points)   Appendix mentions supporting file(s) attached to email – 1 pt. 1     All figures and tables are clear and easy to follow with appropriate number of digits – 3 pts. 3     Tables / figures include number, figure legend, appropriate units, and labeled axes or columns – 3 pts. 2.5     Captions are in the correct location and properly formatted – 3 pts. 2.5     Equations are in the proper format and are numbered – 2 pts. 2     Paper is understandable without supporting material – 3 pts. 3 Late Penalty   10% per day     Points Earned % worth Score Total Technical Writing (40 Points) 39 60% 58.5 96.75 Data Analysis (20 Points) 20 5% 5 Other technical content (20 Points) 19 35% 33.25 Read More