Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

doi:10.1007/s10483-016-2141-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (12): 1587-1596.doi: https://doi.org/10.1007/s10483-016-2141-8

• 论文 • 下一篇

Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

Yanhai LIN¹, Liancun ZHENG², Lianxi MA³

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian Province, China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
3. Department of Physics, Blinn College, Bryan, TX 77805, U. S. A

收稿日期:2016-02-01 修回日期:2016-07-04 出版日期:2016-12-01 发布日期:2016-12-01
通讯作者: Yanhai LIN E-mail:linyanhai999@hqu.edu.cn
基金资助:
Project supported by the Scientific Research Funds of Huaqiao University (No. 14BS310) and the National Natural Science Foundation of China (Nos. 51276014 and 51476191)

Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

Yanhai LIN¹, Liancun ZHENG², Lianxi MA³

1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, Fujian Province, China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
3. Department of Physics, Blinn College, Bryan, TX 77805, U. S. A

Received:2016-02-01 Revised:2016-07-04 Online:2016-12-01 Published:2016-12-01
Contact: Yanhai LIN E-mail:linyanhai999@hqu.edu.cn
Supported by:
Project supported by the Scientific Research Funds of Huaqiao University (No. 14BS310) and the National Natural Science Foundation of China (Nos. 51276014 and 51476191)

摘要/Abstract

摘要：

The effect of internal heating source on the film momentum and thermal transport characteristic of thin finite power-law liquids over an accelerating unsteady horizontal stretched interface is studied. Unlike most classical works in this field, a general surface temperature distribution of the liquid film and the generalized Fourier's law for varying thermal conductivity are taken into consideration. Appropriate similarity transformations are used to convert the strongly nonlinear governing partial differential equations (PDEs) into a boundary value problem with a group of two-point ordinary differential equations (ODEs). The correspondence between the liquid film thickness and the unsteadiness parameter is derived with the BVP4C program in MATLAB. Numerical solutions to the self-similarity ODEs are obtained using the shooting technique combined with a Runge-Kutta iteration program and Newton's scheme. The effects of the involved physical parameters on the fluid's horizontal velocity and temperature distribution are presented and discussed.

关键词: internal heating, non-Newtonian fluid, thermal conductivity, thin film, heat transfer, numerical solution, nonlinear equation, stretching sheet

Abstract:

Key words: thermal conductivity, thin film, non-Newtonian fluid, nonlinear equation, internal heating, stretching sheet, heat transfer, numerical solution

中图分类号:

Yanhai LIN, Liancun ZHENG, Lianxi MA. Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1587-1596.

参考文献

[1] Wang, C. Y. Liquid film on an unsteady stretching surface. Quarterly of Applied Mathematics, 48, 601-610(1990)
[2] Andersson, H. I., Aarseth, J. B., and Dandapat, B. S. Heat transfer in a liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer, 43, 69-74(2000)
[3] Liu, I. C. and Andersson, H. I. Heat transfer in a liquid film on an unsteady stretching sheet. International Journal of Thermal Sciences, 47, 766-772(2008)
[4] Wang, C. Analytic solutions for a liquid film on an unsteady stretching surface. Heat and Mass Transfer, 42, 759-766(2006)
[5] Rashidi, M. M. and Keimanesh, M. Using differential transform method and Padé approximant for solving MHD flow in a laminar liquid film from a horizontal stretching surface. Mathematical Problems in Engineering, 2010, 491319(2010)
[6] Aziz, R. C. and Hashim, I. Liquid film on unsteady stretching sheet with general surface temperature and viscous dissipation. Chinese Physics Letters, 27, 1-4(2010)
[7] Aziz, R. C., Hashim, I., and Alomari, A. K. Thin film flow and heat transfer on an unsteady stretching sheet with internal heating. Meccanica, 46, 349-357(2010)
[8] Dandapat, B. S., Santra, B., and Vajravelu, K. The effects of variable fluid properties and ther-mocapillarity on the flow of a thin film on an unsteady stretching sheet. International Journal of Heat and Mass Transfer, 50, 991-996(2007)
[9] Noor, N. F. M. and Hashim, I. Thermocapillarity and magnetic field effects in a thin liquid film on an unsteady stretching surface. International Journal of Heat and Mass Transfer, 53, 2044-2051(2010)
[10] Aziz, R. C., Hashim, I., and Abbasbandy, S. Effects of thermocapillarity and thermal radiation on flow and heat transfer in a thin liquid film on an unsteady stretching sheet. Mathematical Problems in Engineering, 2012, 127320(2012)
[11] Noor, N. F. M, Abdulaziz, O., and Hashim, I. MHD flow and heat transfer in a thin film on an unsteady stretching sheet by the homotopy analysis method. International Journal for Numerical Methods in Fluids, 63, 357-373(2009)
[12] Liu. I. C. and Megahed, A. M. Numerical study for the flow and heat transfer in a thin liquid film over an unsteady stretching sheet with variable fluid properties in the presence of thermal radiation. Journal of Mechanics, 28, 291-297(2012)
[13] Liu, I. C., Wang, H. H., and Umavathi, J. C. Effect of viscous dissipation, internal heat source/sink, and thermal radiation on a hydromagnetic liquid film over an unsteady stretching sheet. Journal of Heat Transfer, 135, 031701(2013)
[14] Nandeppanavar, M. M., Vajravelu, K., Abel, M. S., Ravi, S., and Jyoti, H. Heat transfer in a liquid film over an unsteady stretching sheet. International Journal of Heat and Mass Transfer, 55, 1316-1324(2012)
[15] Andersson, H. I., Aarseth, J. B., Braud, N., and Dandapat, B. S. Flow of a power-law fluid film on unsteady stretching surface. Journal of Non-Newtonian Fluid Mechanics, 62, 1-8(1996)
[16] Chen, C. Heat transfer in a power-law fluid film over an unsteady stretching sheet. Heat and Mass Transfer, 39, 791-796(2003)
[17] Chen, C. Effect of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. Journal of Non-Newtonian Fluid Mechanics, 135, 128-135(2006)
[18] Chen, C. Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface. Physics Letters A, 370, 51-57(2007)
[19] Wang, C. and Pop, I. Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method. Journal of Non-Newtonian Fluid Mechanics, 138, 161-172(2006)
[20] Abbas, Z., Hayat, T., Sajid, M., and Asghar, S. Unsteady flow of a second grade fluid film over an unsteady stretching sheet. Mathematical and Computer Modelling, 48, 518-526(2008)
[21] Elgazery, N. S. and Hassan, M. A. The effects of variable fluid properties and magnetic field on the flow of non-Newtonian fluid film on an unsteady stretching sheet through a porous medium. Communications in Numerical Methods in Engineering, 24, 2113-2129(2008)
[22] Mahmoud, M. A. A. and Megahed, A. M. MHD flow and heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet with variable fluid properties. Canadian Journal of Physics, 87, 1065-1071(2009)
[23] Huang, K. H., Tsai, R., and Huang, C. H. Chebyshev finite difference approach to modeling the thermoviscosity effect in a power-law liquid film on an unsteady stretching surface. Journal of Non-Newtonian Fluid Mechanics, 165, 1351-1356(2010)
[24] Vajravelu, K., Prasad, K. V., and Ng, C. Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface. Communications in Nonlinear Science and Numerical Simulation, 17, 4163-4173(2012)
[25] Vajravelu, K., Prasad, K. V., and Raju, B. T. Effects of variable fluid properties on the thin film flow of Ostwald-de Waele fluid over a stretching surface. Journal of Hydrodynamics, 25, 10-19(2013)
[26] Lin, Y. H., Zheng, L. C., and Chen, G. Unsteady flow and heat transfer of pseudo-plastic nano-liquid in a finite thin film on a stretching surface with variable thermal conductivity and viscous dissipation. Powder Technology, 274, 324-332(2015)
[27] Lin, Y. H., Zheng, L. C., Zhang, X. X., Ma, L. X., and Chen, G. MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. International Journal of Heat and Mass Transfer, 84, 903-911(2015)
[28] Pop, I., Rashidi, M., and Gorla, R. S. R. Mixed convection to power-law type non-Newtonian fluids from a vertical wall. Polymer-Plastics Technology Engineering, 30, 47-66(1991)
[29] Gorla, R. S. R., Pop, I., and Lee, J. K. Convective wall plume in power-law fluid:second-order correction for the adiabatic wall. Wärme-und Stoffübertragung, 27, 473-479(1992)
[30] Chamkha, A. J. Similarity solution for thermal boundary layer on a stretched surface of a non-Newtonian fluid. International Communications in Heat and Mass Transfer, 24, 643-652(1997)
[31] Zheng, L. C., Zhang, X. X., and Ma, L. X. Fully developed convective heat transfer for power law fluids in a circular tube. Chinese Physics Letters, 25, 195-197(2008)
[32] Zheng, L. C., Lin, Y. H., and Zhang, X. X. Marangoni convection of power law fluids driven by power-law temperature gradient. Journal of the Franklin Institute, 349, 2585-2597(2012)
[33] Lin, Y. H., Zheng, L. C., and Zhang, X. X. Magnetohydrodynamics thermocapillary Marangoni convection heat transfer driven by temperature gradient. Journal of Heat Transfer, 135, 051702(2013)
[34] Chen, X. H., Zheng, L. C., and Zhang, X. X. MHD of power-law fluid on moving surface with power-law velocity and special injection/blowing. Applied Mathematics and Mechanics (English Edition), 35, 1555-1564(2014) DOI 10.1007/s10483-014-1887-6
[35] Lin, Y. H., Zheng, L. C., and Zhang, X. X. Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity. International Journal of Heat and Mass Transfer, 77, 708-716(2014)
[36] Lin, Y. H., Zheng, L. C., and Zhang, X. X. MHD Marangoni boundary layer flow and heat transfer of pseudo-plastic nanofluids over a porous medium with a modified model. Mechanics of Time-Dependent Materials, 19, 519-536(2015)

Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

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