# ON HEAT TRANSFER OF WEAKLY COMPRESSIBLE POWER-LAW FLOWS

## Main Article Content

## Abstract

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.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2148>. Date accessed: 26 june 2017. doi: https://doi.org/10.2298/TSCI150701187L.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-13

Published 2017-03-13

## References

[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.