1. Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 11 Heat Exchangers

2. Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Heat Exchangers, NTU-  Method Where we’ve been …… Analysis of heat exchangers using log mean temperature difference (LMTD) Where we’re going: Computation of heat exchanger performance compared to the theoretical maximum possible for the flow conditions and HX type and size.

3. Heat Transfer Su Yongkang School of Mechanical Engineering # 3 Heat Exchangers, NTU-  Method KEY POINTS THIS LECTURE Concept of heat exchanger effectiveness,  based on the ratio of fluid heat capacity, C. Concept of heat exchanger Number of Transfer Units, NTU Application of NTU-  method to predict the performance of a given heat exchanger Text book sections: §11.4 – 11.5

4. Heat Transfer Su Yongkang School of Mechanical Engineering # 4 For a condensing vapor For an evaporating liquid What if C h = C c in a counterflow HX? Recall earlier discussion x T In Out x T x T

5. Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Heat exchanger effectiveness Maximum possible heat transfer rate for any given inlet temperatures and flow rates occurs in a infinitely long counterflow HX Length of heat exchanger Maximum

6. Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Heat exchanger effectiveness (Cont’d) Define: Heat exchanger effectiveness,  Actual heat transfer, q, can be determined from simple energy balance Thus: If the heat exchanger effectiveness were known, then the actual heat transferred could be found from:

7. Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Number of Transfer Units Define: Number of Transfer Units, NTU NTU depends on both the heat exchanger design (UA) and the operating conditions (C min ). Define: Capacity Ratio, Cr Effectiveness is a function of capacity ratio and the NTU Relationships between , NTU and Cr can be computed. Tables 11.3 and 11.4 and Figures 11.14 – 11.19 in textbook

8. Heat Transfer Su Yongkang School of Mechanical Engineering # 8 NTU -  Tables Parallel flow Counter flow

9. Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Summary of Solution Method Typical scenario for using  -NTU method: Given: Find: Solution method: 1.Determine UA for this heat exchanger 1.Find 2.Find 2.Calculate 3.Determine  from tabulated formulas or plots 4.Compute actual heat transfer 5.Find outlet temperatures from

10. Heat Transfer Su Yongkang School of Mechanical Engineering # 10 Calculation Methodology Performance calculation: Given: Find: Solution method: NTU Design problems: Given: Find: Solution method: LMTD

11. Heat Transfer Su Yongkang School of Mechanical Engineering # 11 Example #1 Situation: Light lubricating oil (cp=2090 J/kg-K) is cooled with water in a small heat exchanger. Oil flow = 0.5 kg/s, inlet T = 375 K Water flow = 0.2 kg/s, inlet T = 280 K Part 1: If desired outlet temperature of the oil is 350 K, and you know the estimated overall heat transfer coefficient, U = 250 W/m²-K, from manufacturer’s data for this type of HX Find: Required heat transfer area for a parallel flow HX and compare to the area needed for a counter flow HX. Solution Method? LMTD

12. Heat Transfer Su Yongkang School of Mechanical Engineering # 12 Example (Cont’d) Solution, Part 1: For parallel flow, For counter flow,

13. Heat Transfer Su Yongkang School of Mechanical Engineering # 13 Example (Cont’d) Solution, Part 1 (Cont’d): Now, compute the required area Parallel flow Counter flow Part 2: Use  -NTU method to determine the required NTU and heat transfer area for parallel and counter flow Solution Method?

14. Heat Transfer Su Yongkang School of Mechanical Engineering # 14 Example (Cont’d) Solution, Part 2: To determine the minimum heat capacity rate, Then The effectiveness is

15. Heat Transfer Su Yongkang School of Mechanical Engineering # 15 Example (Cont’d) Solution, Part 2: With It follows from Figure 11.14 and 11.15 that

16. Heat Transfer Su Yongkang School of Mechanical Engineering # 16 Example #2 The oil in an engine is cooled by air in a cross-flow heat exchanger where both fluids are unmixed. Atmospheric air enters at 303K and 0.53 kg/s. Oil at 0.026 kg/s enters at 348K and flows through a tube of 10-mm diameter. Assuming fully developed flow and constant wall heat flux, estimate the oil-side heat transfer coefficient. If the overall convection coefficient is 53 W/m 2.K and the total heat transfer area is 1m 2, determine the effectiveness. What is the exit temperature of the oil?

17. Heat Transfer Su Yongkang School of Mechanical Engineering # 17

18. Heat Transfer Su Yongkang School of Mechanical Engineering # 18

19. Heat Transfer Su Yongkang School of Mechanical Engineering # 19 Heat Exchangers, NTU-  Method KEY POINTS THIS LESSON Defined heat exchanger effectiveness,  Defined term Number of Transfer Units, NTU Defined the Capacity Ratio, Cr Identified methods to determine relation between , NTU and Cr (Table formulas or charts)

20. Heat Transfer Su Yongkang School of Mechanical Engineering # 20 Appendix The maximum possible heat transfer rate. From the energy conservation, If the fluid having the larger heat capacity rate were to experience the maximum possible temperature change, the other fluid would experience a larger temperature change. That is: If and ? impossible