Laminar natural convection of power-law fluid in a differentially heated inclined square cavity

Laminar natural convection of power-law fluid in a differentially heated inclined square cavity

Horimek Abderrahmane  Noureddine Brahim  Benkhchiba Abdelfatah  Ait-Messaoudene Nouereddine 

Laboratoire de Développement en Mécanique et Matériaux (LDM2) Djelfa University, Algeria

Department of Mechanical Engineering, Faculty of Engineering University of Hail, KSA

Corresponding Author Email: 
Horimek_aer@yahoo.fr
Page: 
261-281
|
DOI: 
https://doi.org/10.3166/ACSM.41.261-281
Received: 
|
Accepted: 
|
Published: 
31 December 2017
| Citation

OPEN ACCESS

Abstract: 

The objective of this work is the study the problem of laminar natural convection, for a power-law fluid, in a differentially heated square cavity, to which a clockwise or counterclockwise inclinations are attributed compared to the classical case (ϕ=0°). A finite volume code was used to make the simulations. The study was divided into several parts in order to distinguish the effects of the different widely-varied’ parameters included (Rayleigh number Ran [10+3→10+6], rheological index n [0.6→1.8], inclination angle ϕ [-90°→90°] and Prandtl number Prn [10→10+4]) independently and combined. The obtained results showed the increase of dynamic and thermal fields disturbances for increasing Ran and/or decreasing n especially for a counterclockwise inclination (over a range of variation), with improvement of the heat exchange coefficient, particularly at high Prn. The opposite will occur when Ran decreases and/or n increases and becomes clearer for a clockwise inclination. In addition, an optimal angle for a counterclockwise inclination is recorded (highest mean heat transfer coefficient). This angle is influenced by Ran increase and n decrease. Recommended ranges of inclination angles leading to highest heat transfer rate are finally given depending on problem parameters. The industrial exploitation of the recommended ranges, undoubtedly allows benefits of efficiency and/or economy

Keywords: 

natural convection, square cavity, inclination angle, power-law fluid, prandtl number

1. Introduction
2. Problem description
3. Resolution procedure
4. Results and discussion
5. Conclusions
  References

Hamady F. J., lloyd J. R., Yang H. Q., Yang K. T. (1989). Study of local natural convection heat transfer in an inclined enclosure. International Journal of Heat and Mass Transfer, Vol. 32, No. 9. pp. 1697-1708. http://dx.doi.org/1016/0017-9310(89)90052-5

Horimek A., Ait-Messaoudene N., Aich W., Aichouni M., Kolsi L., Ghernaout J. (2015). Laminar forced convection of a pseudoplastic thermodependent fluid in an annular horizontal duct. Arab Gulf Journal of Scientific Research, Vol. 33, no. 4, pp. 125-137. http://dx.doi.org/1007/978-3-319-70950-5_7

Horimek A., Noureddine B., Benkhchiba A., Ait-Messaoudene N. (2016). Natural convection for an Oswald-De-Waele fluid inside a differentially heated square cavity. International Conference on Mechanics and Energy (ICME'2016), Hammamet, Tunisia, reference. ICME2016-85.

Huelsz G., Rechtman R. (2013). Heat transfer due to natural convection in an inclined square cavity using the lattice Boltzmann equation method. International Journal of Thermal Science, Vol. 65, pp. 111-119. http://dx.doi.org/1016/j.ijthermalsci.2012.09.009

Kaddiri M., Naїmi M., Raji A., Hasnaoui M. (2012). Rayleigh-Benard convection of non-Newtonian power-law fluids temperature-dependent viscosity. ISRN Thermodynalics, Vol. 2012, No. 614712-10. http://dx.doi.org/5402/2012/614712

Khezzar L., Siginer D., Vinogradov I. (2011). Natural convection in inclined two dimensional rectangular cavities. Heat and Mass Transfer, Vol. 48, No. 2, pp. 227-239. http://dx.doi.org/1007/s00231-011-0876-7

Khezzar L., Siginer D., Vinogradov I. (2012). Natural convection of power law fluids in inclined cavities. International Journal of Thermal Science, Vol. 53, pp. 8-17. http://dx.doi.org/1016/j.ijthermalsci.2011.10.020

Koca A., Oztop H.F., Varol Y. (2007). The effects of Prandtl number on natural convection in triangular enclosures with localized heating from below. International Communication in Heat Mass Transfer, Vol. 34, pp. 511-519. http://dx.doi.org/1016/j.icheatmasstransfer.2007.01.006

Lamsaadi M., Naimi M., Hasnaoui M. (2006). Natural convection heat transfer in shallow horizontal rectangular enclosures uniformly heated from the side and filled with non-Newtonian power law fluids. Energy Conversion and Management, Vol. 47, No. 15-16, pp. 2535-2551. http://dx.doi.org/1016/j.enconman.2005.10.028

Lamsaadi M., Naimi M., Hasnaoui M., Mamou M. (2006). Natural convection in a vertical rectangular cavity filled with a non-Newtonian power law fluid and subjected to a horizontal temperature gradient. Numerical Heat Transfer, Part A, Vol. 49, No. 10, pp. 969-990. http://dx.doi.org/1080/10407780500324988

Ng M. L., Hartnett J. P. P. (1986). Natural convection in power law fluids. International Communication in Heat and Mass Transfer, 13, no. 1, pp. 115-120. http://dx.doi.org/1016/0735-1933(86)90078-3

Ohta M., Ohta M., Akiyoshi M., Obata E. (2002). A numerical study on natural convective heat transfer of pseudoplastic fluids in a square cavity. Numerical Heat Transfer, Part A, Vol. 41, No. 4, pp. 357- 372. http://dx.doi.org/1080/104077802317261218

Ostrach S. (1972). Natural convection in enclosures. in: J.PP. Harnett, T.F. Irvine (Eds.), Advances in Heat Transfer, 8. Academic Press, London.

Ozoe H., Churchill S.W. (1972). Hydrodynamic stability and natural convection in Ostwald-De Waele and Ellis fluids: the development of a numerical solution. AIChE Journal, Vol. 18, No. 6, pp. 1196-1207. http://dx.doi.org/1002/aic.690180617

Patankar S. V. (1982), Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC.

Raisi A. (2016). Natural convection of non-Newtonian fluids in a square cavity with a localized heat source. Journal of Mechanical Engineering, Vol.62, No. 10, pp. 553-564.

Rasoul J., Prinos P. P. (1997). Natural convection in an inclined enclosure. International Journal of Numerical Method for Heat and Fluid Flow, Vol. 7, No. 5, pp. 438-478. http://dx.doi.org/1108/09615539710187783

Turan O., Poole R. J., Chakraborty N. (2011). Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls. International Journal of Heat and Fluid Flow, Vol. 33, No. 1, pp. 131-146. http://dx.doi.org/1080/01457632.2014.852870

Turan O., Sachdeva A., Chakraborty N., Poole R. J. (2011). Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant wall temperatures. Journal of Non-Newtonian Fluid Mechanics, Vol. 166, No 17-18, pp. 1049-1063. http://dx.doi.org/1016/j.jnnfm.2011.06.003

Turan O., Sachdeva A., Poole R. J., Chakraborty N. (2012). Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant wall heat flux. Journal of Heat Transfer ASME, Vol. 134, No. 12, pp. 122504-122515. http://dx.doi.org/1016/j.jnnfm.2011.06.003

Turan O., Sachdeva A., Poole R. J., Chakraborty N. (2013). Aspect ratio and boundary conditions effects on laminar natural convection of power-law fluids in a rectangular enclosure with differentially heated side walls. International Journal of Heat and Mass Transfer, Vol. 60, pp. 722-738. http://dx.doi.org/1016/j.ijheatmasstransfer.2013.01.017

Vinogradov I., Khezzar L., Signiner D. (2011). Heat transfer of non-Newtonian dilatant power law fluids in square and rectangular cavities. Journal of Applied fluid Mechanics, Vol. 4, No. 3, pp. 37-42.

Yener Y., Kakac S., Pramuanjaroenkij A. (2013). Convective Heat Transfer, Third Edition. Boca Raton: CRC Press.

Yigit S., Graham T., Poole R. J., Chakraborty N. (2016). Numerical investigation of steady-state laminar natural convection of power-law fluids in square cross-sectioned cylindrical annular cavity with differentially-heated vertical walls. International Journal of Numerical Method for heat and fluid flow, Vol. 26, No. 1, pp. 85-107.

Yigit S., Poole R. J., Chakraborty N. (2013). Laminar natural convection of Bingham fluids in inclined differentially heated square enclosures subjected to uniform wall temperatures. Journal of Heat Transfer, Vol. 137, No. 5, p. 052504-12. http://dx.doi.org/1080/01457632.2016.1239937