The Heat Transfer under Varying Conditions - Research Paper Example

LIQUID-LIQUID HEAT EXCHANGER (with steam injection) Summary Heat exchange is an important unit operation that contributes to efficiency and safety of many processes. The objective of this experiment is to study the effects of varying liquid flow rates, flow configuration (co-current and counter-current flow), and number of tubes/number of baffles on heat transfer. The results were analyzed and represented graphically based on the energy balance principle. The overall heat transfer coefficient and Logarithmic Mean Temperature Difference under the aforementioned conditions were also calculated. To achieve this, the heat transfer under varying conditions was analyzed under the assumption that; (1) energy is conserved, (2) a steady state is achieved for the heat exchanger, (3) no phase changes occur and the liquid remains in the same state during the entirety of the operation, (4) the overall coefficient of heat transfer must be independent of the temperature of the fluid and (5) the temperature of the fluid does not affect its heat capacity. The analysis and discussion is limited to single pass heat exchangers since the heat exchangers considered in this experiment contain a single pass for cold and hot liquids. The experiment showed that the configuration of heat exchanger in counter current flow has a higher effectiveness than the co-current flow. Keywords: heat exchanger, coefficient of heat transfer, steady state, co-current, counter-current, LMTD Table of Contents Summary 1 Introduction and Aims 4 Background Theory 5 Overall Heat Transfer 5 Convective Heat Transfer 6 Conductive Heat Transfer 7 Operating Procedure 7 Experimental Arrangement 7 Procedure 10 Results and Discussion 11 Data Collection and Validation 11 Co-Current Results 12 The initial Conditions 12 Analyzed Results 12 Counter-Current Results 15 The initial Conditions 15 Analyzed Results 15 Discussion 18 Conclusion 19 References 20 Appendices 21 Introduction and Aims In the 21st century, heat exchangers play a vital role in the operational and economic efficiency of equipment including refrigerators, air conditioners, and energy recovery systems. A heat exchanger can be defined as an equipment in which heat exchange takes place between two fluids that enter and exit at different temperatures. A liquid-liquid heat exchanger therefore implies that both fluids in this case are liquids. The main function of heat exchanger is to either remove heat from a hot fluid or to add heat to the cold fluid. The direction of fluid motion inside the heat exchanger can normally categorized as parallel flow, counter flow and cross flow. In this experiment, we study only the parallel flow and counter flow. For parallel flow, also known as co-current flow, both the hot and cold fluids flow in the same direction. Both the fluids enter and exit the heat exchanger on the same ends. For counter flow, both the hot and cold fluids flow in the opposite direction. Both the fluids enter and exit the heat exchanger on the opposite ends. In this experiment, we focused on the shell and tube heat exchanger. Figure 1: Double Pipe Heat exchanger with co-current flow Figure 2: Double pipe heat exchanger with counter current flow The aims of the experiment were as follows; i) To study the effects of (a) varying liquid flow rates, (b) flow configuration (co-current and counter-current flow), (c) number of tubes/number of baffles on heat transfer. ii) To practice standard procedures for validation of data collection and processing. Background Theory Overall Heat Transfer To understand the basic workings of a liquid-liquid heat exchanger, a theoretical case as shown in figure 2 below can be analyzed. It shows an energy balance in a differential flow segment of a single pass heat exchanger. Figure 3: Differential segment In the energy balance differential equation shown above, the red color represents the hot liquid passing through the heat exchanger, the gray represents the transition zone between hot and cold while the blue zone represents the cold liquid. The width of the differential segment is . The rate of heat transfer in this segment can be represented by; Whereby; is the coefficient of overall heat transfer, is the local temperature difference, is the area of contact in the segment. The overall heat transfer coefficient, is inversely proportional to the total resistance to the heat flow. Total resistance in this case refer to the sum of resistance to convective heat transfer from the hot fluid to the partition between the fluidsthe resistance to thermal conduction through the partition, and the resistance to convective heat transfer from the partition to the cold fluid,. This can be represented in the equation below as follows; Convective Heat Transfer From equation 2 above, it can be deduced that the convective heat transfer, is inversely proportional to the coefficient of convective heat transfer, This coefficient depends on the factors that include the geometry of flow, the properties of the fluid and the rate of flow. It can be represented using the Reynold’s number, Prandltl numer or the Nusselt number which are dimensionless therefore convenient. The constants represents the viscosity, density, thermal conductivity and heat capacity respectively. and on the other hand represents the velocity of flow and the characteristic length respectively. The relationship between the three dimensionless constants totally depends on the geometry of the system and the type of flow experienced in the system i.e. laminar or turbulent flow. Conductive Heat Transfer The system geometry heavily determines the resistance to heat transfer through the transition zone. For the case of this experiment, it was considered that heat was conducted radially in a cylindrical steam injection tube. The resistance to heat transfer for both the inflow and outflow pipes were considered analytically and solved using heat of diffusion equation. Overall rate of heat transfer can be given by; Where the term is the rate in the differential discharge. However since changes with the position in the exchanger, the above differential equation cannot be solved through direct integration. The value of is therefore obtained by merging the energy balances in the differential segment with equation 1. Where represents the change in temperature during the interval considered while represents the rate of heat capacity of the liquid in consideration Operating Procedure Experimental Arrangement Before commencing the operation, it was ensured that the steam injection unit was designed to work automatically in maintaining a temperature of within 500C. To allow for the operation of the heat exchangers in co-current and counter-current operations, flexible horses were used while altering the pipework for the different types of flow. The heat exchangers were also instrumented for direct readout of inlet and outlet temperatures using digital thermometers, inlet and outlet pressures, and flowrates using VA’s. Figure 4 below shows the setup. Figure 4: The arrangement of the experiment Procedure It was ensured that initial conditions are set in place through making sure that clap fittings are tightened, V4 was closed and that V1 and V2 were fully closed. The initial level T1 is checked to make sure it was 100% full and an overflow hose was directed to the bucket. V3 was then opened to allow the fluid to flow. After waiting for 5 minutes, V5 was gradually opened until it was fully open. P1 was started while simultaneously but slowly opening V2 so as to set the flowrate at 300l/hr at FI2. Another 5 minutes was allowed for this to happen. V6 was the adjusted to a set-point of 500C give or take 2 degrees and noted as TI1 V1 was then gradually opened to set the flow rate at 300l/hr at FI1. Another 5 minutes was allowed to pass so as to ensure the system was fully de-aired. The flowrates V1 and V2 were the reset since they were required to conduct the experiment. Both flowrates V1 and V2, inlet and outlet temperatures for every experimental run were recorded. For one mode of operation using one of the exchangers, at both the constant hot and the constant cold runs, the inlet and outlet pressures at the shell and tube side were recorded The systematic shutdown process was then initiated and it involved; stopping P1, fully closing V1, closing V5, connecting the hose to drain the tank, opening V4 to drain T1, fully closing V2, flushing out T1 using a bucket of water and finally closing V4 then V3. In performing the steps stated above, it was important to note that closing V5 was not necessary when changing the mode of operation or heat exchanger. V1 and P1 had to be closed and stopped respectively before altering the mode of operation or heat exchanger. Spillage was minimized when reconfiguring the rig so as to reduce the possible errors due to fluid loss. To determine the area of heat transfer, the outer diameter, for a single heat exchanger tube was taken to be and thickness of the tube wall was taken as. The number of tubes was dependent on the type of exchanger and individual lengths were measure beforehand. Results and Discussion Data Collection and Validation The accuracy of data was vital for this experiment since any small variation would give totally different results. Some sources of errors could have been systemic errors due to equipment not being set up well. However enough check were put in place to ensure this did not affect the accuracy. For instance adequate time for de-airing was allowed before the experiment commenced. Random errors could have been due to propagation of errors during calculations. For instance, since the temperature change was given by; Therefore, a source of error would be propagated all the way to the overall coefficient of heat transfer. Thus; Assuming then this systematic error would simplify to; This was then adjusted with the results accordingly. Co-Current Results The initial Conditions Discharge: 300l/hr=200l/hr Temperatures: = 15.80C, = 29.30C, = 48.30C and = 39.60C The time to reach steady state was 3mins Analyzed Results Table 1: Measuring Temp. at Fixed Hot flowrate (300l/hr) 0C 0C 0C 0C 0C 0C kW kW 0C kW/m2 200 15.8 29.3 13.5 48.3 39.5 8.8 3.0653 4.7025 19.2432 0.622 300 15.6 25.2 9.6 48.2 37.5 10.7 3.7272 3.135 20.8266* 0.408 400 15.4 23.0 7.6 48.1 37.0 11.1 3.8665 2.6473 22.099 0.366 500 15.2 21.9 6.7 48.9 36.7 12.2 4.2497 2.3334 22.968 0.254 600 15.2 20.3 5.1 48.2 35.6 12.6 4.3890 1.7765 23.27 0.199 Figure 5: Temperature Graph for fixed hot Flow Rates Table 2: Measuring Temp. at fixed cold flowrate (300l/hr) 0C 0C 0C 0C 0C 0C kW kW 0C kW/m2 200 15.1 23.5 8.4 48.9 35.5 13.4 4.6677 1.9507 21.0515 0.2361 300 15.0 25.2 10.2 48.8 38.1 10.7 3.7272 2.3687 21.6978 0.2782 400 14.9 27.0 12.1 48.7 39.5 9.2 3.2047 2.8099 21.4128 0.3344 500 14.9 28.7 13.8 49.6 41.2 8.4 2.9260 3.2047 21.7432 0.3756 600 14.9 29.2 14.3 49.2 41.7 7.5 2.6125 3.3208 21.5966 0.3919 Figure 6: Temperature Graph for fixed cold Flow Rates Counter-Current Results The initial Conditions Discharge: 300l/hr=200l/hr Temperatures: = 15.00C, = 31.20C, = 48.40C and = 38.50C The time to reach steady state was 3mins Analyzed Results Table 3: Measuring Temp at fixed hot flow rate (300l/hr) 0C 0C 0C 0C 0C 0C kW kW 0C kW/m2 200 15.0 31.2 16.1 48.4 38.5 9.9 3.9985 3.7378 20.1884 0.4718 300 14.9 26.6 11.2 48.5 37.2 11.3 3.9365 3.9361 22.3500* 0.4488 400 14.9 23.3 8.9 48.5 36.3 12.2 4.2996 4.2496 22.6000 0.4791 500 14.9 21.3 6.2 48.1 35.1 13.0 4.5283 4.5286 22.3650 0.5170 600 14.8 20.5 5.7 48.8 35.2 13.6 4.7373 4.7373 24.1300 0.5003 Figure 7: Temperature Graph for Fixed Hot Flow Rates Table 4: Measuring Temp at fixed cold flowrate (300l/hr) 0C 0C 0C 0C 0C 0C kW kW 0C kW/m2 200 15.0 23.4 8.5 48.2 34.6 13.6 4.7373 1.9739 20.2819 0.2480 300 15.3 26.2 10.9 48.8 37.5 11.3 3.9362 2.5312 20.4280 0.3158 400 14.9 27.9 13 48.6 38.7 9.9 3.4485 3.0189 20.1239 0.3823 500 14.9 29.5 14.6 49.6 40.4 9.2 3.2047 3.3904 20.5531 0.4204 600 14.9 29.2 14.3 48.5 40.3 8.2 2.8563 3.3208 20.3145 0.4166 Figure 8: Temperature Graph for Fixed Cold Flow Rates Discussion The Logarithmic Mean Temperature Difference (LMTD) was used to determine the overall coefficient of heat transfer. This was based on the experimental values of inlet and outlet temperatures and the fluid flow rates. This method was however not convenient in predicting outlet temperatures given known values of coefficient of heat transfer and inlet temperatures. For better results, a more accurate method, the number of Transfer Units method, (NTU) which is derived from LMTD but avoiding additional assumptions. NTU has an added advantage over the LMTD method since it has the ability to predict outlet temperatures without the use of iterative numerical solutions. Table one shows the general features of the two configurations of flow. The fact that the exit temperatures of the hot fluid ought to be higher than the exit temperature of the cold fluid was observed. From the analysis, it is evident that the counter current flow is more effective compared to the co-current flow due to the fact that the exit temperature of the hot liquid was lower than the exit temperature of the cold fluid. This generally agrees with Clausius Statement on heat exchangers. When the graphical results of the data obtained are compared to theoretical values, the results proved to be within acceptable limits as illustrated in the theoretical graphs below; Figure 9: the theoretical temperature profiles of (a) counter current flow and (b) co-current flow It is important to note that in the counter current flow, the outlet temperature of the cold liquid could exceed the temperature of outlet hot liquid. Conclusion It can be concluded that the heat exchanger based on steam injection follows the rules of thermodynamics. The parallel configurations indicate an exit temperature that was always hotter than the exit temperature of the cold liquid, further proving the Clausius Statement where no spontaneous heat transfer from a hot to a cold body may occurs. When flow rates are held constant, the first law of thermodynamics, energy conservation, was observed. It is therefore important to note that the counter current configuration of the heat exchanger is preferred due to its effectiveness. The experiment went as far as to prove this effectiveness as discussed above. In the counter current flow, it was capable to have exit temperature of the cold liquid being higher than the exit temperature of the hot fluid. The flow rates were however too high to achieve this scenario. References Shah, R.K. and London, A.L., 2014. Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data. Academic press. Incropera, F.P., Lavine, A.S., Bergman, T.L. and DeWitt, D.P., 2007. Fundamentals of heat and mass transfer. Wiley. Shah, R.K. and Sekulic, D.P., 2003. Fundamentals of heat exchanger design. John Wiley & Sons. Thulukkanam, K., 2013. Heat exchanger design handbook. CRC Press. Miller, C.G., 1980. Liquid/liquid heat exchanger. Hewitt, G.F., Shires, G.L. and Bott, T.R., 1994. Process heat transfer (Vol. 113). Boca Raton, FL: CRC press. Handlos, A.E. and Baron, T., 1957. Mass and heat transfer from drops in liquid‐liquid extraction. AIChE Journal, 3(1), pp.127-136. Gulawani, S.S., Joshi, J.B., Shah, M.S., RamaPrasad, C.S. and Shukla, D.S., 2006. CFD analysis of flow pattern and heat transfer in direct contact steam condensation. Chemical Engineering Science, 61(16), pp.5204-5220. Appendices 1. Sample Calculation for Table 1: Taking; T1 = , T2 = , T3 = , T4 = But for co-current flow; Where; and Therefore; Also, The overall heat transfer coefficient for the co-current flow is given by; But area of heat transfer L = 140.5cm, d = 1.27cm, number of tubes = 7; And therefore; 2. Sample Calculation for Table 3: Taking; T1 = , T2 = , T3 = , T4 = But for co-current flow; Where; and Therefore; Also, The overall heat transfer coefficient for the co-current flow is given by; But area of heat transfer L = 140.5cm, d = 1.27cm, number of tubes = 7; And therefore; Read More