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Research Papers: Forced Convection

Convection Heat Transfer of Power-Law Fluids Along the Inclined Nonuniformly Heated Plate With Suction or Injection

[+] Author and Article Information
Jize Sui

School of Mechanical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China;
School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China

Liancun Zheng

School of Mathematics and Physics,
University of Science and Technology Beijing,
Beijing 100083, China
e-mail: liancunzheng@ustb.edu.cn

Xinxin Zhang

School of Mechanical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 2, 2014; final manuscript received May 8, 2015; published online September 29, 2015. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 138(2), 021701 (Sep 29, 2015) (8 pages) Paper No: HT-14-1507; doi: 10.1115/1.4031109 History: Received August 02, 2014; Revised May 08, 2015

A comprehensive analysis to convection heat transfer of power-law fluids along the inclined nonuniformly heated plate with suction or injection is presented. The effects of power-law viscosity on temperature field are taken into account in highly coupled velocity and temperature fields. Analytical solutions are established by homotopy analysis method (HAM), and the effects of pertinent parameters (velocity power-law exponent, temperature power index, suction/injection parameter, and inclination angle) are analyzed. Some new interesting phenomena are found, for example, unlike classical boundary layer problem in which the skin friction monotonically increases (decreases) with suction increases (injection increases), but there exists a special region where the skin friction is not monotonic, which is strongly bound up with Prandtl number, which have never been reported before. The nonmonotony occurs in suction region for Prandtl number Npr < 1 and injection region for Npr > 1. Results also illustrate that the velocity profile decreases but the heat convection is enhanced obviously with increasing in temperature power exponent m (generalized Prandtl number Npr has similar effects), the decreases in inclination angle lead to the reduction in convection and heat transfer efficiency.

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References

Farrell, P. V. , Springer, G. S. , and Vest, C. M. , 1983, “ Natural Convection Boundary Layers Adjacent to Pyrolyzing Surfaces,” Combust. Flame, 54(1–3), pp. 1–14. [CrossRef]
Brackenridge, J. B. , and Gilbert, W. P. , 1965, “ An Optical Method for Determining Temperature and Velocity Distributions in Liquids,” J. Appl. Opt., 4(7), pp. 819–821. [CrossRef]
Tsuji, T. , and Nagano, Y. , 1989, “ Velocity and Temperature Measurements in a Natural Convection Boundary Layer Along a Vertical Flat Plate,” Exp. Therm. Fluid Sci., 2(2), pp. 208–215. [CrossRef]
Tsuji, T. , Kajitani, T. , and Nishino, T. , 2007, “ Heat Transfer Enhancement in a Turbulent Natural Convection Boundary Layer Along a Vertical Flat Plate,” Int. J. Heat Fluid Flow, 28(6), pp. 1472–1483. [CrossRef]
Watanabe, T. , 1991, “ Free Convection Boundary Layer Flow With Uniform Suction or Injection Over a Cone,” Acta Mech., 87(1–2), pp. 1–9. [CrossRef]
Watanabe, T. , 1991, “ Forced and Free Mixed Convection Boundary Layer Flow With Uniform Suction or Injection on a Vertical Flat Plate,” Acta Mech., 89(1–4), pp. 123–132. [CrossRef]
Al-Sanea, S. A. , 2004, “ Mixed Convection Heat Transfer Along a Continuously Moving Heated Vertical Plate With Suction or Injection,” Int. J. Heat Mass Transfer, 47(6–7), pp. 1445–1465. [CrossRef]
Deswita, L. , Nazar, R. , Ishak, A. , Ahmad, R. , and Pop, I. , 2010, “ Similarity Solutions for Mixed Convection Boundary Layer Flow Over a Permeable Horizontal Flat Plate,” Appl. Math. Comput., 217(6), pp. 2619–2630. [CrossRef]
Ali, M. , and Al-Yousef, F. , 2002, “ Laminar Mixed Convection Boundary Layers Induced by a Linearly Stretching Permeable Surface,” Int. J. Heat Mass Transfer, 45(21), pp. 4241–4250. [CrossRef]
Schowalter, W. R. , 1960, “ The Application of Boundary-Layer Theory to Power-Law Pseudoplastic Fluids: Similar Solutions,” AIChE J., 6(1), pp. 24–28. [CrossRef]
Acrivos, A. , Shah, M. J. , and Petersen, E. E. , 1960, “ Momentum and Heat Transfer in Laminar Boundary-Layer Flows of Non-Newtonian Fluids Past External Surfaces,” AIChE J., 6(2), pp. 312–317. [CrossRef]
Sahu, A. K. , and Mathur, M. N. , 1996, “ Free Convection in Boundary Layer Flows of Power-Law Fluids Past a Vertical Flat Plate With Suction/Injection,” Indian J. Pure Appl. Math., 27(9), pp. 931–941.
Pop, I. , Rashidi, M. , and Gorla, R. S. R. , 1991, “ Mixed Convection to Power-Law Type Non-Newtonian Fluids From a Vertical Plate,” Polym.-Plast. Technol. Eng., 30(1), pp. 47–66. [CrossRef]
Grosan, T. , and Pop, I. , 2001, “ Free Convection Over a Vertical Flat Plate With a Variable Plate Temperature and Internal Heat Generation in a Porous Medium Saturated With a Non-Newtonian Fluid,” Tech. Mech., 4, pp. 313–318.
Zheng, L. C. , Zhang, X. X. , and Lu, C. Q. , 2006, “ Heat Transfer for Power Law Non-Newtonian Fluids,” Chin. Phys. Lett., 23(12), pp. 3301–3304. [CrossRef]
Li, B. T. , Zheng, L. C. , and Zhang, X. X. , 2011, “ Heat Transfer in Pseudo-Plastic Non-Newtonian Fluids With Variable Thermal Conductivity,” Energy Convers. Manage., 52(1), pp. 355–358. [CrossRef]
Zheng, L. C. , Lin, Y. H. , and Zhang, X. X. , 2012, “ Marangoni Convection of Power Law Fluids Driven by Power-Law Temperature Gradient,” J. Franklin Inst., 349(8), pp. 2585–2597. [CrossRef]
Lin, Y. H. , Zheng, L. C. , and Zhang, X. X. , 2013, “ Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient,” ASME J. Heat Transfer, 135(5), p. 051702. [CrossRef]
Ahmadi, M. , Mostafavi, G. , and Bahrami, M. , 2014, “ Natural Convection From Interrupted Vertical Walls,” ASME J. Heat Transfer, 136(11), p. 112501. [CrossRef]
Wang, C. Y. , and Ng, C.-O. , 2014, “ Natural Convection in a Vertical Slit Microchannel With Superhydrophobic Slip and Temperature Jump,” ASME J. Heat Transfer, 136(3), p. 034502. [CrossRef]
Cho, C.-C. , Chen, C.-L. , Hwang, J.-J. , and Chen, C.-K. , 2014, “ Natural Convection Heat Transfer Performance of Non-Newtonian Power-Law Fluids Enclosed in Cavity With Complex-Wavy Surfaces,” ASME J. Heat Transfer, 136(1), p. 014502. [CrossRef]
Piller, M. , Polidoro, S. , and Stalio, E. , 2014, “ Multiplicity of Solutions for Laminar, Fully-Developed Natural Convection in Inclined, Parallel-Plate Channels,” Int. J. Heat Mass Transfer, 79, pp. 1014–1026. [CrossRef]
Turan, O. , Lai, J. , Poole, R. J. , and Chakraborty, N. , 2013, “ Laminar Natural Convection of Power-Law Fluids in a Square Enclosure Submitted From Below to a Uniform Heat Flux Density,” J. Non-Newtonian Fluid Mech., 199, pp. 80–95. [CrossRef]
Liao, S. J. , 1992, “ The Proposed Homotopy Analysis Technique for the Solution of Non-Linear Problems,” Ph.D. thesis, Shanghai Jiao Tong University, Shanghai.
Liao, S. J. , 2004, “ On the Homotopy Analysis Method for Non-Linear Problems,” Appl. Math. Comput., 147(2), pp. 499–513. [CrossRef]
Liao, S. J. , 2010, “ An Optimal Homotopy-Analysis Approach for Strongly Nonlinear Differential Equations,” Commun. Nonlinear Sci. Numer. Simul., 15(8), pp. 2003–2016. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Convection boundary layer system sketch

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Fig. 2

Velocity profiles for various values of angle φ for pseudoplastic fluids

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Fig. 3

Temperature profiles for various values of angle φ for pseudoplastic fluids

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Fig. 4

Shear stress profiles for various values of angle φ for pseudoplastic fluids

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Fig. 5

The compare of skin friction coefficient Cf and Nusseltnumber Nun between pseudoplastic fluids and Newtonian fluids for various values of φ with the condition Npr = 2, C = 0, and m = 0.5

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Fig. 6

Velocity profiles for various values of C for Newtonian fluids

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Fig. 7

Temperature profiles for various values of C for Newtonian fluids

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Fig. 8

Velocity profiles for various values of C for dilatant fluids

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Fig. 9

Temperature profiles for various values of C for dilatant fluids

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Fig. 10

Variation of skin friction coefficient Cf for different parameter C (from injection to suction variation) with the different cases Npr < 1 (Pr < 1) and Npr > 1 (Pr > 1) for a dilatant fluid at φ = π/2  and  m = 0, respectively. The obvious nonmonotonic variations of Cf are limited by Prandtl number apparently.

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Fig. 11

Variation of Nusselt number Nun for different parameter C (from injection to suction variation) for a dilatant fluid and a Newtonian fluid at φ = π/2  and  m = 0

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Fig. 12

Velocity profiles for various values of m for pseudoplastic fluids

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Fig. 13

Temperature profiles for various values of m for pseudoplastic fluids

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Fig. 14

Velocity profiles for various values of m for dilatant fluids

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Fig. 15

Temperature profiles for various values of m for dilatant fluids

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