Introduction to Heat and Mass Transfer

Transcription

1 Introduction to Heat and Mass Transfer Week 16 Merry X mas! Happy New Year 2019!

2 Final Exam When? Thursday, January 10th What time? 3:10-5 pm Where? What? Lecture materials from Week 1 to 16 (before Radiation) Calculator is allowed(with extra batteries if required; no programming) Open book, open notes and homework solutions, no communication devices

3 Next Topic Heat Exchangers» Types of Heat Exchangers» Overall Heat Transfer Coefficient» Heat Exchanger Analysis» Log Mean Temperature Difference

4 Types of Heat Exchangers Heat exchangers designed to heat between two streams of fluid for a given application Choice of a particular type depends on several practical considerations» Parallel Flow» Counter Flow» Cross Flow» Shell and Tube» Compact Baffles and fins used to improve heat transfer rates

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10 LMTD Method Good for design problems when the following data is known:» Inlet and outlet temperatures for hot and cold streams» Mass flow rates for hot and cold streams» All relevant properties for hot and cold streams Compute log mean temperature difference depending on whether parallel flow, counter flow, cross flow or other Determine overall heat transfer coefficient depending on type of flow, geometry and fouling factor Evaluate the necessary heat transfer area

11 e-ntu Method Good for performance check when the following is known:» Inlet temperatures for hot and cold streams» Mass flow rates for hot and cold streams» All relevant properties for hot and cold streams» Overall heat transfer coefficient and area Compute NTU using given data Calculate ratio of heat capacity rates Determine maximum possible heat transfer rate from given temperatures and minimum heat capacity rate Look up e using charts Get the actual heat transfer rate and compute outlet temperatures for hot and cold streams

12 Overall Heat Transfer Coefficient Heat transfer characterized as: q UAT m Overall heat transfer coefficient depends on:» Convective heat transfer coefficient on inside and outside surfaces of tube» Wall thickness of tube» Fouling resistance (factor) affected by fluid velocity, temperature and service time

13 Fouling Factor

14 Heat Exchanger Analysis Hot fluid stream loses heat» Heat transfer:» Heat capacity rate: Cold fluid stream gains heat» Heat transfer:.,,, q m C T T. h p h h i h o C,,, q m C T T. m C h h p, h c p c c o c i» Heat capacity rate: C. m C c c p, c Local temperature difference: T T T The above expressions are valid for any heat exchanger h c

15 Parallel Flow Heat Exchanger Hot Stream Cold Stream Th T dt h h T T dt c c c Both fluids flow along the same direction T hi, Can T c be greater than T h at any point? Can T h,o be less than T c,i? Can T c,o be greater than T h,i? T ho, T T 2 1 T co, T ci,

16 Parallel Flow Heat Exchanger (contd.) Log mean temperature difference T LMTD Parallel Flow T ln T T 2 T T T T 1 h, i c, i Parallel Flow T T T 2 h, o c, o

17 Counter Flow Heat Exchanger Hot Stream Cold Stream T c Th T dt h h dt c T c Two fluids flow in the opposite direction Can T c be greater than T h at any point? Can T h,o be less than T c,o? Can T h,o be greater than T c,i? T 1 T hi, T co, T ho, T 2 T ci,

18 Counter Flow Heat Exchanger (contd.) Log mean temperature difference T LMTD Counter Flow T ln T T 2 T T T T 1 h, i c, o Counter Flow T T T 2 h, o c, i

19 Special Cases T T hi, ho, C h C c T co, Hot fluid temperature does not change Vapor stream in condensation T ci, T hi, Cold fluid temperature does not change Liquid stream in evaporation C h C c T ho, T T ci, co,

20 Special Cases (contd.) T hi, C h C c T ho, T co, T hi, T ci, Both fluids change temperature at the same rate T ci, C h C c T ho, T co,

21 Special Cases (contd.) For multiple-pass heat exchangers, we can write: q UAT LMTD Multiple Pass T F T LMTD Multiple Pass LMTD Counter Flow Correction factor (F) is empirical available from charts for various common configurations

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26 LMTD Method Good for design problems when the following data is known:» Inlet and outlet temperatures for hot and cold streams» Mass flow rates for hot and cold streams» All relevant properties for hot and cold streams Compute log mean temperature difference depending on whether parallel flow, counter flow, cross flow or other Determine overall heat transfer coefficient depending on type of flow, geometry and fouling factor Evaluate the necessary heat transfer area

27 Example 1 A single-pass, cross flow heat exchanger uses hot exhaust gases (mixed) to heat water (unmixed) from 30C to 80C at a rate of 3 kg/s. Properties of exhaust gases are considered to be similar to air and the gases enter and exit at 225C and 100C, respectively. The overall heat transfer coefficient is 200 W/m 2 -K.» Estimate the surface area (m 2 ) of the heat exchanger

28 HW # 8 prob. 3 A parallel flow, concentric tube heat exchanger is designed to heat a fluorocarbon liquid using hot water. The fluorocarbon is supplied through the inner tube at temperature Tc,i and the water is supplied through the annulus at Th,i. The inner tube is thin-walled and has a diameter D and length L. Assume all fluid properties are known.

29 HW # 8 prob. 3 (contd.) (a) The mass flow rates of the two fluids are set such that the temperature difference between the two fluids at the heat exchanger outlet is 40% of the temperature difference at the inlet. Assuming the overall heat transfer coefficient U is known, derive an expression for the total heat transfer rate, q, of the heat exchanger using the LMTD method. Express your answer in terms of the symbols given.

30 HW # 8 prob. 3 (contd.) (b) The mass flow rates of the two fluids are increased such that the heat transfer coefficient for each fluid is four times what it was in part (a). the temperature difference between the two fluids at the heat exchanger outlet is now 50% of the temperature difference at the inlet. Using the LMTD method, determine q*/q, the ratio of the new total heat transfer rate to that obtained in part (a).

31 Closure Coverage thus far..» discussed various types of heat exchangers» presented analysis related to parallel flow and counter flow arrangements

32 Closure (contd.) Different types of heat exchangers Use of log mean temperature difference to describe parallel flow and counter flow heat exchangers» Parallel Flow:» Counter Flow: T T T 1 2 T 1 ln T 2 Corrections for other types of heat exchangers LMTD Parallel Flow Parallel Flow T T T T T T 1 h, i c, i 2 h, o c, o Counter Flow Counter Flow T T T T T T 1 h, i c, o 2 h, o c, i

33 Next Topic Heat Exchangers» Heat Exchanger Analysis Effectiveness and NTU

34 e-ntu Method Good for performance check when the following is known:» Inlet temperatures for hot and cold streams» Mass flow rates for hot and cold streams» All relevant properties for hot and cold streams» Overall heat transfer coefficient and area Compute NTU using given data Calculate ratio of heat capacity rates Determine maximum possible heat transfer rate from given temperatures and minimum heat capacity rate Look up e using charts Get the actual heat transfer rate and compute outlet temperatures for hot and cold streams

35 Effectiveness For heat exchangers, we define effectiveness as:» where,» q = Actual heat transfer (W)» q max = Maximum possible heat transfer (W) The maximum temperature difference leads to maximum possible heat transfer e q q» C min is the smallest of C c and C h max max min h i c i q C T T,,

36 Effectiveness (contd.) Effectiveness: e C T T C T T C T T C T T h h, i h, o c c, o c, i min h, i c, i min h, i c, i Effectiveness varies between 0 and 1 We can show that: e f NTU C, r NTU UA C min C r C C min max

37 Effectiveness (contd.) NTU and C r are dimensionless parameters Relationships for e as function of NTU listed in Table 11.3; while the inverse relationships listed in Table 11.4 The same available in graphical format in Figs through e-ntu extremely useful for design of heat exchangers under certain conditions

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44 Example Cold water leading to a shower enters a thin-walled doublepipe counter-flow heat exchanger at 15C at 0.25 kg/s and is heated to 45C by hot water entering at 100C at 3 kg/s. The overall heat transfer coefficient is 950 W/m 2 -K.» Determine the rate of heat transfer (kw)» Compute the heat transfer surface area (m 2 ) Use e-ntu method for analysis!

45 HW # 8 prob. 4 Cold water leading to a shower enters a thin-walled doublepipe counter-flow heat exchanger at 15C at 0.25 kg/s and is heated to 45C by hot water entering at 100C at 3 kg/s. The overall heat transfer coefficient is 950 W/m 2 -K.» Compute the heat transfer surface area (m 2 ) Use the LMTD method for analysis!

46 Previous Example A single-pass, cross flow heat exchanger uses hot exhaust gases (mixed) to heat water (unmixed) from 30C to 80C at a rate of 3 kg/s. Properties of exhaust gases are considered to be similar to air and the gases enter and exit at 225C and 100C, respectively. transfer coefficient is 200 W/m 2 -K. The overall heat» Estimate the surface area (m 2 ) of the heat exchanger (Use e-ntu method for analysis)

47 Questions What is effectiveness of heat exchanger? When is e-ntu method preferred in analysis of the heat exchangers? Consider two double-pipe counter-flow heat exchangers that are identical except one is twice as long as the other. Which one has the higher effectiveness?

48 HW # 8 prob. 5 Water (C p =4180 J/kg C) enters the 2-cm-internal diameter tube of a double-pipe counter-flow heat exchanger at 20C at 2 kg/s. Water is heated by steam condensing at 120C(h fg =2203 kj/kg) in the shell. If the overall heat transfer coefficient is 800 W/m 2 C.» Determine the length of the tube required in order to heat the water to 80 C using (a) the LMTD method and (b) the e-ntu method for analysis

49 HW # 8 will due on 1/10 (Thursday), right before the class! Late HW will not be accepted!!

50 Closure Coverage thus far..» discussed effectiveness of heat exchangers» presented comparison of LMTD and e-ntu methods for heat exchanger calculations

51 Closure (contd.) Use of effectiveness and NTU concepts to evaluate performance of heat exchangers» Effectiveness characterizes performance: e q q max e» NTU gives measure of heat exchanger size: NTU e Comparison of LMTD and e-ntu methods f UA C min C T T C T T C T T C T T h h, i h, o c c, o c, i min h, i c, i min h, i c, i NTU C, r C r C C min max

52 LMTD Method Good for design problems when the following data is known:» Inlet and outlet temperatures for hot and cold streams» Mass flow rates for hot and cold streams» All relevant properties for hot and cold streams Compute log mean temperature difference depending on whether parallel flow, counter flow, cross flow or other Determine overall heat transfer coefficient depending on type of flow, geometry and fouling factor Evaluate the necessary heat transfer area

53 e-ntu Method Good for performance check when the following is known:» Inlet temperatures for hot and cold streams» Mass flow rates for hot and cold streams» All relevant properties for hot and cold streams» Overall heat transfer coefficient and area Compute NTU using given data Calculate ratio of heat capacity rates Determine maximum possible heat transfer rate from given temperatures and minimum heat capacity rate Look up e using charts Get the actual heat transfer rate and compute outlet temperatures for hot and cold streams