HEAT TRANSFER ͳ THEORETICAL ANALYSIS, EXPERIMENTAL INVESTIGATIONS AND INDUSTRIAL SYSTEMS Edited by Aziz Belmiloudi Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems Edited by Aziz Belmiloudi Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. 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ISBN 978-953-307-226-5 free online editions of InTech Books and Journals can be found at www.intechopen.com [...]... follows: T0 = wT0 T1 + T2 + T3 + + T10 10 (14 ) 2 2 2 ⎡⎛ ∂T ⎛ ∂T ⎞ ⎤ ⎞ ⎛ ∂T ⎞ ⎢⎜ 0 wT ⎟ + ⎜ 0 wT ⎟ + + ⎜ 0 wT ⎟ ⎥ =± 10 ⎢⎝ ∂T1 1 ⎠ ⎝ ∂T2 2 ⎠ ⎝ ∂T10 ⎠ ⎥ ⎣ ⎦ w T0 2 2 2 ⎡⎛ 1 ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞ ⎤ = ± ⎢⎜ w T1 ⎟ + ⎜ w T2 ⎟ + + ⎜ w T10 ⎟ ⎥ ⎠ ⎝ 10 ⎠ ⎝ 10 ⎠ ⎥ ⎢⎝ 10 ⎣ ⎦ 1 1 2 (15 ) 2 (16 ) 22 Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems 3 Heat transfer correlations in this chapter... x1, x2, x3, …….xn Thus: P = P ( x1 , x2 , x3 , , xn ) (4) 20 Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems Parameters Uncertainty Tref, sat (°C) 0 .19 xi ±6.96-8.24% ΔT (K) ±0 .19 1 (Tw,out-Tw,in)TS (K) ±0.045 (Tw,in-Tw,out)ph (K) ±0 .13 mref (g s -1) ±0.023 mw,TS (g s -1) ±0.35 mw,pre (g s -1) ±0.38 qTS (W m-2) ±6.55-8.93% qpre (W m-2) 12 -14 . 81% href (W m-2K -1) ... F1 ( X ) 2.83 ⎤ 1 0.9 F1 ( X ) = 0 .15 ⎢ + 0.476 ⎥ Traviss et Nu = Rel Prl F (Re ,Pr ) ⎣X X ⎦ l l 2 al (19 72) F2 = 5Prl + 5ln (1 + 5Prl ) + 2.5ln(0.00 313 Re l 0. 812 ) Rel >11 25 Chato (19 61) Akers and 0.8 1/ 3 Rosson Nu = 0.0265Re eq Prl (19 60) Tandon et Re > 30000 g al (19 95) Re eq = Geq d μl ( Geq = G ⎡ (1 − x ) + x ρ l / ρ g ⎢ ⎣ ⎡ 1 ⎤ Nu = 0.084 Re g 0.67 Prl 1/ 3 ⎢ ⎥ ⎣ Jal ⎦ 1/ 6 Table 2 Annular flow heat. .. Annular flow heat transfer correlations and models Jal = Cpl ΔTsat i fg ) 0.5 ⎤ ⎥ ⎦ 24 Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems 7000 h (W m -2K -1) 6000 5000 4000 Shah (19 79) Dobson and Chato (19 98) Dobson and Chato (19 98) Sweeney (19 96) Cavallini et al (19 74) Bivens and Yokozeki (19 94) Tang et al (2000) Fujii (19 95) Chato (19 61) Traviss et al (19 72) Akers... (19 60) Tandon et al (19 95) +30% 3000 2000 10 00 10 00 -30% 2000 3000 4000 5000 -2 6000 7000 -1 hexp (W m K ) (a) 7000 h (W m -2K -1) 6000 5000 4000 Shah (19 79) Dobson and Chato (19 98) Dobson and Chato (19 98) Sweeney (19 96) Cavallini et al (19 74) Bivens and Yokozeki (19 94) Tang et al (2000) Fujii (19 95) Chato (19 61) Traviss et al (19 72) Akers and Rosson (19 60) Tandon et al (19 95) +30% 3000 2000 -30% 10 00... 0.4 1 + ⎜ ⎟ ⎥ Pred 0.38 ⎝ 1 − x ⎠ ⎥ ⎢ ⎣ ⎦ 0.836 ⎤ ⎡ x ⎞ ⎛ 0.8 0.4 Nu = 0.023Re l Prl 1 + 4.863 ⎜ ( − ln( Pred ) ⎥ ⎟ 1 x⎠ ⎝ ⎢ ⎥ ⎣ ⎦ Tang et al 1. 5 ⎛ 1 + 1. 09 X 0.039 ⎞ 1 (2000) Rel ≤ 12 50 c3= 0.025 c4= 1. 59 Fr = c Re c4 ⎜ ⎟ 3 so l ⎜ ⎟ Ga0.5 X ⎝ ⎠ Rel >12 50 c3= 1. 26 c4= 1. 04 ( Fujii (19 95) Nul = 0. 012 5 Rel ρl / ρ g ) 0,9 ⎛ x ⎞ ⎜ ⎟ 1 x⎠ ⎝ 0.1x + 0.8 Prl 0.63 ⎡ 2.47 ⎤ Nu = 0.023Re l 0.8 Prl 0.4 ⎢ 1. 96... the density range of 1- 3 g/cm3 [12 ] The flow regime changes with density variations and fluidization velocities, but settling chamber provides 8 Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems 0.4 ZSM-5 0.098 mm ZSM-5 0 .15 mm SAPO-34 0.098 mm SAPO-34 0 .15 mm AJI 0.3 0.2 0 .1 0.0 Z (constant) 4 Um = 0.059 m/s 3 2 1 0 1. 0 1. 2 ρ = ρL / ρS 1. 4 1. 6 Fig 6 Effect of... Chemistry Research, 49 (2 010 ) 4 614 -4 619 [11 ] ASTM Standard D-5757-Revised, ASTM, Philadelphia PA, (2006) [12 ] Zeeshan Nawaz*, Tang Xiaoping, Xiaobo Wei and Fei Wei, Attrition behavior of small particles in bimodal particles fluidized bed environment: Influence of density and size ratio, Korean J Chem Eng., 27(4), 10 25 -10 31 (2 010 ) (DOI: 10 .10 07/s 118 14- 010 0240-5) [13 ] Zeeshan Nawaz, Fei Wei and Shahid... 2.0 1. 5 1. 0 8 6 4 2 0.5 0.0 0 18 20 22 24 26 28 30 32 Conversion (%) Fig 9 OPE with respect to yield and selectivity 18 20 22 24 26 28 Conversion (%) 30 32 12 Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems Al-SAPO-34 Cycle I supported Conversion TOS Cycle II Selectivity Cycle III Conversion Selectivity Conversion Selectivity 1 hr 8 hr 1 hr 8 hr 1 hr 8 hr 1 hr... 48 (2009) 7442-7447 14 Heat Transfer - Theoretical Analysis, Experimental Investigations and Industrial Systems [18 ] Zeeshan Nawaz, Tang Xiaoping, Shahid Naveed, Qing Shu and Fei Wei, Experimental Investigation of Attrition Resistance of Zeolite Catalysts in Two Particle Gas-SolidSolid Fluidization System, Pakistan Journal of Scientific & Industrial Research, 53 (2 010 ) 16 9 -17 4 [19 ] Shuiyuan Huang, . HEAT TRANSFER ͳ THEORETICAL ANALYSIS, EXPERIMENTAL INVESTIGATIONS AND INDUSTRIAL SYSTEMS Edited by Aziz Belmiloudi Heat Transfer - Theoretical Analysis, Experimental Investigations. Kneer Heat Transfer to Fluids at Supercritical Pressures 4 81 Igor Pioro and Sarah Mokry Fouling of Heat Transfer Surfaces 505 Mostafa M. Awad Chapter 10 Chapter 11 Chapter 12 Part 3 Chapter 13 Chapter. alt="" Part 1 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Part 2 Chapter 8 Chapter 9 Preface IX Heat Transfer in Micro Systems 1 Integrated Approach for Heat Transfer