Skip to main content Accessibility help
×
Home

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

  • Botong Li (a1) (a2), Liancun Zheng (a3), Ping Lin (a3) (a4), Zhaohui Wang (a5) and Mingjie Liao (a3)...

Abstract

This paper presents a relatively simple numerical method to investigate the flow and heat transfer of laminar power-law fluids over a semi-infinite plate in the presence of viscous dissipation and anisotropy radiation. On one hand, unlike most classical works, the effects of power-law viscosity on velocity and temperature fields are taken into account when both the dynamic viscosity and the thermal diffusivity vary as a power-law function. On the other hand, boundary layer equations are derived by Taylor expansion, and a mixed analytical/numerical method (a pseudosimilarity method) is proposed to effectively solve the boundary layer equations. This method has been justified by comparing its results with those of the original governing equations obtained by a finite element method. These results agree very well especially when the Reynolds number is large. We also observe that the robustness and accuracy of the algorithm are better when thermal boundary layer is thinner than velocity boundary layer.

Copyright

Corresponding author

*Corresponding author. Email addresses:plin@maths.dundee.ac.uk (P. Lin), leedonlion408@163.com (B.-T. Li), liancunzheng@ustb.edu.cn (L.-C. Zheng), zwang24@ncsu.edu (Z.-H. Wang), mliao@xs.ustb.edu.cn (M.-J. Liao)

References

Hide All
[1]Moraga, N. O., and Lemus-Mondaca, R. A., Numerical conjugate air mixed convection/non-Newtonian liquid solidification for various cavity configurations and rheological models, Int. J. Heat Mass Transfer, 54 (2011), pp. 5116–25.
[2]Jumah, R.Y., and Mujumdar, A.S., Natural convection heat and mass transfer from a vertical plate with variable wall temperature and concentration to power law fluids with yield stress in a porous medium, Chem. Eng. Commun., 185 (2001), pp. 165–82.
[3]Kim, G. B., and Hyun, J. M., Buoyant convection of power-law fluid in an enclosure filled with heat-generating porous media, Numer. Heat Transfer, Part A: Applications, 45 (2004), pp. 569–82.
[4]Yoshino, M., Hotta, Y., Hirozane, T., and Endo, M., A numerical method for incompressible non-Newtonian fluid flows based on the lattice Boltzmann method, J. Non-Newtonian Fluid Mech., 147(1-2) (2007), pp. 6978.
[5]Tomé, M. F., Grossi, L., Castelo, A., Cuminato, J. A., Mangiavacchi, N., Ferreira, V. G., De Sousa, F. S., and Mckee, S., A numerical method for solving three-dimensional generalized Newtonian free surface flows, J. Non-Newtonian Fluid Mech., 123(2-3) (2004), pp. 85103.
[6]Bataller, R. C., Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation, Phys. Lett. A, 372 (2008), pp. 2431–9.
[7]Prasad, K. V., Abel, S., and Datti, P. S., Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet, Int. J. Non-Linear Mech., 38(5) (2003), pp. 651–7.
[8]Yürüsoy, M., Unsteady boundary layer flow of power-law fluid on stretching sheet surface, Int. J. Eng. Sci., 44 (2006), pp. 325–32.
[9]Cheng, C. Y., Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions, Int. Commun. Heat Mass Transfer, 36(7) (2009), pp. 693–7.
[10]Tai, B. C., and Char, M. I., Soret and Dufour effects on free convection flow of non-Newtonian fluids along a vertical plate embedded in a porous medium with thermal radiation, Int. Commun. Heat Mass Transfer, 37(5) (2010), pp. 480–3.
[11]Ming, C. Y., Zheng, L. C., and Zhang, X. X., Steady flow and heat transfer of the power-law fluid over a rotating disk, Int. Commun. Heat Mass Transfer, 38 (2011), pp. 280–4.
[12]Massoudi, M., Local non-similarity solutions for the flow of a non-Newtonian fluid over a wedge, Int. J. Non-Linear Mech., 36(6) (2001), pp. 961–76.
[13]Wang, S. C., Chen, C. K., and Yang, Y. T., Natural convection of non-Newtonian fluids through permeable axisymmetric and two-dimensional bodies in a porous medium, Int. J. Heat Mass Transfer, 45(2) (2002), pp. 393408.
[14]Sadeghy, K., and Sharifi, M., Local similarity solution for the flow of a ‘second-grade’ viscoelastic fluid above a moving plate, Int. J. Non-Linear Mech., 39(8) (2004), pp. 1265–73.
[15]Olagunju, D. O., Local similarity solutions for boundary layer flow of a FENE-P fluid, Appl. Math. Comput., 173(1) (2006), pp. 593602.
[16]Kairi, R. R., and Murthy, P. V. S. N., Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium, Appl. Math. Comput., 217(20) (2011), pp. 8100–14.
[17]Leveque, R. J., Numerical Methods for Conservation Laws, Birkhauser-Verlag, 1990.
[18]Anderson, J. D., Computational Fluid Dynamics, the Basics with Applications, McGraw-Hill Science/Engineering/Math, 1995.
[19]Arfken, G. B., and Weber, H. J., MathematicalMethods for Physicists, 6th Edition. Elsevier Academic Press, 2005.
[20]Pozrikidis, C., Fluid Dynamics: Theory, Computation, and Numerical Simulation, 2nd Edition. Springer, 2009.
[21]Lin, P., A sequential regularization method for time-dependent incompressible Navier-Stokes equations, SIAM J. Numer. Anal., 34(3) (1997), pp. 1051–71.
[22]Lu, X. L., Lin, P., and Liu, J. G., Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Math. Comput., 77(263) (2008), pp. 1467–94.
[23]Zheng, L. C., Zhang, X. X., and He, J. C., Drag force of non-Newtonian fluid on a continuous moving surface with strong suction/blowing, Chin. Phys. Lett., 20 (2003), pp. 858–61.
[24]Zheng, L. C., Zhang, X. X., and He, J. C., Suitable heat transfer model for self-similar laminar boundary layer in power law fluids, J. Therm. Sci., 13 (2004), pp. 150–54.
[25]Li, B. T., Zheng, L. C., and Zhang, X. X., A new model for flow and heat of a power law fluid in a pipe, Therm. Sci., 15 (2011), pp. 127–30.
[26]Li, B. T., Zheng, L. C., and Zhang, X. X., Comparison between Thermal Conductivity Models on Heat Transfer in Power-law Non-Newtonian Fluids, ASME J. Heat Transfer, 134(4) (2012), 041702.
[27]Zheng, L. C., Zhang, X. X., Boubaker, K., Yücel, U., Gargouri-Ellouze, E., and Yιldιrιm, A., Similarity and BPES comparative solutions to the heat transfer equation for incompressible non-Newtonian fluids: Case of laminar boundary energy equation, Eur. Phys. J. Appl. Phys., 55 (2011), 21102.
[28]Mukhopadhyay, S., and Layek, G. C., Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface, Int. J. Heat Mass Transfer, 51(9-10) (2008), pp. 2167–78.
[29]Cortell, R., Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a power-law fluid past an infinite porous plate, Chem. Eng. Res. Des., 89(1) (2011), pp. 8593.
[30]Mahmoud, M. A. A., Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity, Phys. A: Stat. Mech. Appl., 375(2) (2007), pp. 401–10.
[31]Abel, M. S., and Mahesha, N., Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation, Appl. Math. Modell., 32 (2008), pp. 1965–83.
[32]Abel, M. S., Siddheshwar, P. G., and Mahesha, N., Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source, Int. J. Non-Linear Mech., 44 (2009), pp. 112.
[33]Li, X. K., and Duan, Q. L., Meshfree iterative stabilized Taylor-Galerkin and characteristic-based split (CBS) algorithms for incompressible N-S equations, Comput. Methods Appl. Mech. Engrg., 195 (2006), pp. 6125–45.
[34]Salonen, E. M., and Lindroos, M., On the derivation of boundary-layer equations, Rakenteiden Mekaniikka (J. Struct. Mech.), 42(4) (2009), pp. 187–99.
[35]Denier, J. P., and Dabrowski, P. P., On the boundary-layer equations for power-law fluids, Proc. R. Soc. Lond. A, 460 (2004), pp. 3143–58.
[36]Raptis, A., Perdikis, C., and Takhar, H. S., Effect of thermal radiation on MHD flow, Appl. Math. Comput., 153 (2004), pp. 645–9.
[37]Chen, C. H., Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption, Int. J. Non-Linear Mech., 44 (2009), pp. 596603.
[38]Seddeek, M. A., Finite element method for the effect of various injection parameter on heat transfer for a power-law non-Newtonian fluid over a continuous stretched surface with thermal radiation, Comput. Mater. Sci., 37 (2006), pp. 624–7.
[39]Shi, H. D., Lin, P., Li, B. T., and Zheng, L. C., A Finite Element Method for Heat Transfer of Power-law Flow in Channels with A Transverse Magnetic Field, Math. Meth. Appl. Sci., 37 (2014), pp. 1121–9.
[40]Lin, P., and Liu, C., Simulations of singularity dynamics in liquid crystal flows: A C0 finite element approach, J. Comput. Phys., 215 (2006), pp. 348–62.

Keywords

MSC classification

Related content

Powered by UNSILO

A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Laminar Power-Law Fluids

  • Botong Li (a1) (a2), Liancun Zheng (a3), Ping Lin (a3) (a4), Zhaohui Wang (a5) and Mingjie Liao (a3)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.