235 r. sengupta
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This document summarizes a study on assessing the thermal performance of semicircular fins under forced air convection and its application to air preheaters. The study finds that semicircular fins have greater thermal efficiency compared to circular fins of the same volume due to their larger surface area. Mathematical models are developed to analyze heat transfer in the fins and an air preheater. Various parameters like number of fins, pipe size, air velocity and temperature are examined. The results show that larger preheat can be achieved using semicircular fins, providing potential for higher energy efficiency.
235 r. sengupta
- 1. Assessment of thermal performance of semicircular fins under forced air convection : Application to air preheater Rajarshi Sengupta Under the supervision of Dr. Rajat Chakraborty Chemical Engineering Department Jadavpur University ICAER 2013
- 2. Motivation Improved performance of air preheaters increase boiler efficiency. Boiler efficiency increases by 1% for every 22oC rise in combustion air temperature. Better design of heat exchangers lead to increased thermal efficiency and reduced costs. Key to the improved design of existing thermal systems is enhancing the heat transfer between hot and cold streams. Enhancement can be done by improvisations of the extended surfaces.
- 3. Brief Overview Mathematical modeling Efficiency comparison Application to air preheaters
- 5. Assumptions of the model Two directional heat conduction. Insulated tip. Thermal conductivity of fin is constant. Negligible thermal contact resistance between pipe wall and fin. Heat is lost only by convection. No loss by radiation. Curvature of fin base can be neglected. Heat transfer coefficient is a function of Reynolds number and Prandtl number.
- 6. Front and side view Side view Front view Chakraborty et al. (2011)
- 7. Control volume and the Differential equation The control volume is shown below The partial differential equation the describes heat conduction is 2 T x2 (1) 2 T y2 2h (T Ta ) 0 kf B ...
- 8. The heat transfer coefficient is given as hd kair 1 3 C (Re)n (Pr) (2) The boundary conditions are : x 0, r y x r, y 0, x r, y 0, y r, x 0, y r, x 0, r,T T x T y T x T y 0 0 0 0 Tb …
- 9. Solution Using separation of variables, the temperature profile obtained is T Ta Tb Ta 4 n 0 ( 2n 1) cosh p 4 n 0 cosh ( 2n 1) cosh p …(3) py r cosh tanh p sinh tanh p sinh (2n 1) 2 4 p px r pr r 2 m2 …(4) r (r x ) The efficiency is calculated )as 2h(T T dxdy 2 2 0 .5 a 0 ( r 2 x 2 ) 0.5 2 2 0.5 r (r x ) 2h(Tb 0 ( r 2 x 2 ) 0 .5 Ta ) dxdy sin px r sin ( 2n 1) y 2r ( 2n 1) x 2r
- 10. Approximated temperature profile T Ta T Tb m2 x3 1 3r 1 0.0044m 2 m2 x2 2 m2 1 2 r2 0.0347m 4 m 2 2 2 …(6) x y 6 …(7) Where 2 m 2 2hr kf B h = heat transfer coefficient r = radius of semicircular fin kf= thermal conductivity of fin B = thickness of fin …(8)
- 11. Comparing the efficiency of a semicircular fin with a circular fin Constraint – Same volume of material Relations between radii of the fins r 2 R2 180 R1 sin f R12 R2 = Radius of circular fin R1 = Radius of tube f r2 2 …(9) …(10)
- 12. Variation of fin radii with no. of semicircular fins 35 Nominal diameter of pipe = 40mm 30 Radius of fin (mm) 25 20 Radius of semicircular fin 15 Radius of circular fin 10 5 0 4 6 8 No. of semicircular fins 10
- 13. Variation of fin radii with pipe size 80 No. of semicircular fins = 6 70 Radius of fin (mm) 60 50 Radius of semicircular fin 40 30 Radius of circular fin 20 10 0 25 32 40 50 65 Nominal Diameter (mm) 80 90
- 14. EFFICIENCY COMPARISON AND INFLUENCE OF VARIOUS FACTORS ON EFFICIENCY
- 15. No. of semicircular fins 100 Efficiency (%) 95 90 85 SF CF 80 75 4 5 6 7 8 No. of semi-circular fins 9 10
- 16. Pipe size 95 SF CF Efficiency (%) 90 85 80 75 70 0.02 0.03 0.04 0.05 0.06 0.07 Nominal diameter (m) 0.08 0.09
- 18. Base temperature 100 SF CF 98 96 Efficiency (%) 94 92 90 88 86 84 82 80 420 430 440 450 460 Base Temperature (K) 470 480
- 19. Thermal conductivity of the fin 100 SF CF 98 96 Efficiency (%) 94 92 90 88 86 84 82 80 100 105 110 115 120 125 Thermal conductivity of fin material (W/mK) 130
- 21. The system Inline arrangement of finned tubes with 8 rows and 4 columns. Tube side fluid – condensing steam. Shell side fluid – ambient air. Ambient air inlet temperature – 25 o C
- 22. Schematic of the preheater Air Flow Heat Transfer (Holman J. P.)
- 23. Heat transfer inside the preheater Heat is transferred both from the finned and unfinned surface. Over unit length, the amount of heat transferred is m1m2 h (2 r 2 f ) N 2 R1 (1 NB ) (Tb Ta ) …(11) Assuming no loss of heat, the exit air temperature is ATb (mair c p 0.5 A)Ta1 Ta 2 mair c p 0.5 A …(12) where m1m2 h (2 r 2 ) fN A 2 R1 (1 NB )
- 24. Predicted exit air temperatures Exit air temperature depends on a couple of physical and geometrical parameters. The effect of these have been studied. Exit air temperature for the circular and semicircular fins have been compared.
- 25. Effect of fin spacing 90 SF CF 80 Exit Air Temperature (oC) 70 60 50 40 30 4 5 6 7 8 Fin spacing (mm) 9 10
- 26. Effect of tube pitch 100 SF CF 90 80 Exit Air Temperature (oC) 70 60 50 40 30 0.2 0.25 0.3 0.35 Tube pitch (m) 0.4 0.45
- 27. Effect of pipe size 130 SF CF 120 110 Exit Air Temperature (oC) 100 90 80 70 60 50 40 30 0.02 0.03 0.04 0.05 0.06 Nominal Diameter (m) 0.07 0.08 0.09
- 28. Effect of air velocity 100 SF CF 90 80 Exit air temperature (oC) 70 60 50 40 30 1.5 2 2.5 Air velocity (m/s) 3
- 29. Concluding remarks Semicircular fins show a greater thermal efficiency as compared to a circular fin of same volume. A larger amount of preheat can be achieved owing to the larger surface area. Great energy savings can be accomplished by incorporating this design. This has the potential for high energy efficiency and sustainable development.
- 30. References Razelos, P. (2003) A critical review of extended surface heat transfer, Heat Transfer Eng., 24(6), pp. 11–28. Chakraborty R. and Sirkar A. (2011) Efficiency comparison between circular and semicircular fins circumscribing circular pipes, Journal of Heat Transfer, 133 / 044501-1. Khaled A.-R.A. (2007) Heat transfer enhancement in hairy fin systems, Applied Thermal Engineering, 27, pp. 250-257. Kundu B. and Das P.K. (2007) Performance analysis and optimization of elliptic fins circumscribing a circular tube, International Journal of Heat and Mass Transfer, 50, pp. 173180. Chen Han-Taw and Hsu Wei-Lun (2008) Estimation of heat transfer characteristics on a vertical annular circular fin of finned tube heat exchangers in forced convection, International Journal of Heat and Mass Transfer, 51, pp. 1920-1932.
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