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Wei ZHANG Botong LI Liangliang ZHU Liancun ZHENG


This paper completes a numerical research on steady momentum and heat transfer in power-law fluids in a channel. Weakly compressible laminar fluids are studied with no slip at the walls and uniform wall temperatures. The full governing equations are solved by continuous finite element method. Three thermal conductivity models are adopted in this paper, that is, constant thermal conductivity model, thermal conductivity varying as a function of temperature gradient, and a modified temperature-gradient-dependent thermal conductivity model. The results are compared with each other and the physical characteristics for values of parameters are also discussed in details. It is shown that the velocity curve from the solution becomes straight at higher power-law index. The effects of Reynolds numbers on the dilatant fluid and the pseudo-plastic look similar to each other and their trends can be easily predicted. Furthermore, for different models, the temperature curves also present pseudo-plastic and dilatant properties.

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How to Cite
ZHANG, Wei et al. ON HEAT TRANSFER OF WEAKLY COMPRESSIBLE POWER-LAW FLOWS. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2148>. Date accessed: 14 dec. 2017. doi: https://doi.org/10.2298/TSCI150701187L.
Received 2017-03-02
Accepted 2017-03-13
Published 2017-03-13


[1] Schowalter, W., The Application of Boundary-Layer Theory to Power-Law Pseudoplastic Fluids: Similar Solutions, American Inst. Chem. Eng. J., 6(1960), pp.24-28.
[2] Acrivos, A., et.al., Momentum and Heat Transfer in Laminar Boundary-Layer Flows of Non-Newtonian Fluids past External Surfaces, American Inst. Chem. Eng. J., 6(1960), pp.312-317.
[3] Wang, T., Mixed Convection from a Vertical Plate to Non-Newtonian Fluids with Uniform Surface Heat Flux, Int. Commu. Heat Mass Trans., 3(1995), 22, pp.369-380.
[4] Wang, T., Mixed Convection Heat Transfer from a Vertical Plate to non-Newtonian Fluids, Int. J. Heat Fluid Flow, 1(1995),16, pp.56-61.
[5] Hady, F., Mixed Convection Boundary-layer Flow of Non-Newtonian Fluids on a Horizontal Plate, Appl. Math. Compu., 68(1995), pp.105-112.
[6] Venerus, D., Laminar Capillary Flow of Compressible Viscous Fluids, J. Fluid Mech., 555 (2006), pp.59-80.
[7] Vinay, G., et.al., Numerical Simulation of Weakly Compressible Bingham Flows: the Restart of Pipeline Flows of Waxy Crude Oils, J. Non-Newtonian Fluid Mech., 136 (2006), pp.93-105.
[8] Georgiou, G., The Time-dependent, Compressible Poiseuille and Extrudate-swell Flows of a Carreau Fluid with Slip at the Wall, J. Non-Newtonian Fluid Mech., 109 (2003), pp.93-114.
[9] Guo, Z., Wu, X., Compressibility Effect on the Gas Flow and Heat Transfer in a Microtube, Int. J. Heat Mass Trans., 40 (1997), pp.3251-3254.
[10] Georgiou, G., Crochet, M., Time-dependent Compressible Extrudate-swell Problem with Slip at the Wall, J. Rheol., 38 (1994), pp.1745-1755.
[11] Georgiou, G., Crochet, M., Compressible Viscous Flow in Slits with Slip at the Wall, J. Rheol., 38 (1994), pp.639-654.
[12] Belblidia, F., et.al., Stabilised Computations for Viscoelastic Flows under Compressible Considerations, J. Non-Newtonian Fluid Mech., 134 (2006), pp.56-76.
[13] Taliadorou, E., et.al., Perturbation Solutions of Poiseuille Flows of Weakly Compressible Newtonian Liquids, J. Non-Newtonian Fluid Mech., 163 (2009), pp.25-34.
[14] Howell, T., et.al., Momentum and Heat Transfer on a Continuous Moving Surface in Power Law Fluid, Int. J. Heat Mass Trans., 40(1997), pp.1853-1861.
[15] Rao, J., et.al., Momentum and Heat Transfer in a Power-law Fluid with Arbitrary Injection/Suction at a Moving Wall, Int. J. Heat Mass Trans., 42(1999), pp.2837-2847.
[16] Gorla, R., et.al., Convective Wall Plume in Power-law Fluid: Second-order Correction for the Adiabatic Wall, Warme-und Stoffubertragung, 27(1992), pp.473-479.
[17] Shi, H., et.al., A Finite Element Method for Heat Transfer of Power-law Flow in Channels with A Transverse Magnetic Field, Math. Methods in the Appl. Sci.,37(2014), 8, pp.1121-1129.
[18] Lin, P., Liu, C., Simulations of Singularity Dynamics in Liquid Crystal Flows: A C0 Finite Element Approach, J. Compu. Phys., 215 (2006), pp.348-362.
[19] Zheng, L., et.al., Heat Transfer of Power Law Non-Newtonian, Chin. Phys. Lett., 23(2006), pp.3301-3304.
[20] Zheng, L., et.al., Fully Developed Convective Heat Transfer for Power Law Fluids in a Circular Tube, Chin. Phy. Lett., 25(2008), pp.195-197.
[21] Li, B., et.al., A Mixed Analytical/Numerical Method for Velocity and Heat Transfer of Power-law Fluids with High Reynolds Number, Nume. Math.: Theory Methods Applications, in press.