Numerical Study of the Effect of Reynolds Number and Aspect Ratio in Heat Transfer from Elliptical Tubes to Viscoplastic Fluids Employing Constructal Design

Abstract:

The present work aims to obtain geometries that ease the heat transfer from elliptical section tubes to cross flow of viscoplastic fluids. The Construtal Design method is applied to obtain aspect ratios between the axes of the elliptic sections that maximize the Nusselt number. The tubes elliptical section area is fixed, but the aspect ratio between their axes is free to change in order to optimize this geometry for different Reynolds numbers (Re). The viscoplastic fluid behavior is modeled using the Herschel-Bulkley constitutive equation for the viscosity function. The governing differential equations are solved numerically by the finite volume method. The values of the dimensionless numbers, Prandtl (Pr), modified Bingham (Bn^*) and flow index (n), were kept constant and equal to 1, 1 and 0.4, respectively. The Reynolds number was varied from 1 to 40. The results obtained show that increasing the number of Reynolds results in a greater heat transfer. In addition, the optimal aspect ratio is smaller the greater the Reynolds number is. It was found that, as the aspect ratio grows, heat transfer increases due to flow acceleration, but also decreases due to the low strain rate zone downstream the tube, which possesses recirculation and unyielded material. The balance between these effects gives the optimum point.

• Periodical: Defect and Diffusion Forum (Volume 372)
• Pages: 142-151
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.372.142
• Online since: March 2017
• Authors: Lober Hermany, Rafael José Klein, Flavia Schwarz Franceschini Zinani, Liércio André Isoldi, Elizaldo Domingues dos Santos, Luiz Alberto Oliveira Rocha
• Keywords: Constructal Law, Non-Newtonian Fluids, Tube Bundles

References

[1] Zukauskas, A. Heat transfer from tubes in crossflow, Advances in Heat Transfer, v. 18, pp.87-159, (1987).

DOI: 10.1016/s0065-2717(08)70118-7

[2] Zhang, W.; Samtaney, R. Numerical simulation and global linear stability analysis of low-Re past a heated circular cylinder., International Journal of Heat and Mass Transfer, v. 98, pp.584-595, (2016).

DOI: 10.1016/j.ijheatmasstransfer.2016.03.058

[3] Bharti, R. P.; Sivakumar, P.; Chhabra R. P. Forced Convection Heat Transfer from an elliptical cylinder to power-law fluids, International Journal of Heat and Mass Transfer, v. 51, pp.1838-1853, (2008).

DOI: 10.1016/j.ijheatmasstransfer.2007.06.032

[4] Thakur, P.; Mittal, S.; Tiwari, N.; Chhabra, R.P. The motion of a rotating circular cylinder in a stream of Bingham plastic fluid, Journal of Non-Newtonian Fluid Mechanics, v. 235, pp.29-46, (2016).

DOI: 10.1016/j.jnnfm.2016.06.013

[5] Rao, P.K.; Sasmal, C.; Sahu, A.K.; Chhabra, R.P.; Eswaran, V. Effect of power-law fluid behavior on momentum and heat transfer characteristics of an inclined square cylinder in steady flow regime., International Journal of Heat and Mass Transfer, v. 54, pp.2854-2867, (2011).

DOI: 10.1016/j.ijheatmasstransfer.2011.03.013

[6] Nirmalkar, N.; Bose, A.; Chhabra, R.P. Free convection from a heated circular cylinder in Bingham plastic fluids., International Journal of Thermal Science. v. 83, pp.33-44, (2014).

DOI: 10.1016/j.ijthermalsci.2014.04.004

[7] Rao, P. K.; Sahu, A. K.; Chhabra, R. P. Flow of newtonian and power-law fluids past an elliptical cylinder, a numerical study., Industrial and Engineering Chemistry Research, v. 49, pp.6649-6661, (2010).

DOI: 10.1021/ie100251w

[8] Bejan, A.; Lorente S. Constructal law of design and evaluation: physics, biology, technology and society., Journal of Applied Physics, v. 113, (2013).

DOI: 10.1063/1.4798429

[9] Bejan, A. Constructal-theory network of conducting paths for cooling a heat generating volume., International Journal of Heat and Mass Transfer, v. 40, pp.799-816, 1997a.

DOI: 10.1016/0017-9310(96)00175-5

[10] Bejan, A. How nature takes shape., Mechanical Engineering, vol. 119, p.90, 1997b.

[11] Bejan, A.; Zane J.P. Design in nature,. Doubleday, New York, (2012).

[12] Bello-Ochende, T.; Bejan, A. Constructal multi-scale cylinders in cross-flow., International Journal of Heat and Mass Transfer, v. 48, pp.1373-1383, (2005).

DOI: 10.1016/j.ijheatmasstransfer.2004.10.013

[13] Bejan, A., Shape and Structure, from Engineering to Nature. Cambridge University Press, Cambridge, (2000).

[14] Bejan, A. & Lorente, S., Design with Constructal Theory. Wiley, Hoboken, (2008).

[15] Bird R.B., Armstrong R.C., Hassager O. Dynamics of polymeric liquids., Vol. 1: Fluid mechanics. John Wiley and Sons Inc., New York, (1987).

DOI: 10.1002/aic.690340623

[16] Slattery, J., C. Advanced Transport Phenomena, Cambridge University Press, New York, (1999).

[17] Atapattu, D.D.; Chhabra, R.P.; Uhlherr, P.H.T. Creeping sphere motion in Herschel-Bulkley fluids: flow field and drag, Journal of Non-Newtonian Fluid Mechanics, v. 59, pp.245-265, (1995).

DOI: 10.1016/0377-0257(95)01373-4

[18] Silva, J.P. Como calcular a área e o perímetro de uma elipse?, Revista Eletrônica Paulista de Matemática, v. 3, n. 1, pp.2-6, (2014).

DOI: 10.21167/cqdvol3201423169664jps0206

[19] Patankar, S. V. Numerical Heat Transfer and Fluid Flow., McGraw-Hill, New York, (1980).

[20] Nirmalkar, N.; Chhabra, R. P. Momentum and heat transfer from a heated circular cylinder in Bingham plastic fluids., International Journal of Heat and Mass Transfer, v. 70, pp.564-577, (2014).

DOI: 10.1016/j.ijheatmasstransfer.2013.11.034