Scale Analysis for Optimal Pattern Formation in Flow Systems

Abstract:

The occurrence of flow pattern can be predicted based on constructal law. Scale analysis is a method for deriving the essential information based on the basic principles of fluid flow and heat transfer. It provides order-of-magnitudes but also the form of the functions that describe the quantities understudy. In flow systems, patterns (configuration, design, architecture) arise from competition between competing trends, at least two modes of transport or locomotion: slow (diffusion, walk, etc.) and fast (streams, run, etc.). Optimal patterns mean the best flow access and the best balance between these trends. The study presented here follows from the scale analysis together with constructal and, is illustrated by examples from simple water heating to human locomotion.

• Periodical: Defect and Diffusion Forum (Volume 407)
• Pages: 59-67
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.407.59
• Online since: March 2021
• Authors: Antonio Ferreira Miguel*
• Keywords: Constructal Law, Convection, Diffusion, Scale Analysis, Self-Organization

References

[1] J. G. Charney, On the scale of atmospheric motions, Geofys. Publ. 17 (1948) 1–17.

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

[3] A. Bejan, Simple methods for convection in porous media: scale analysis and the intersection of asymptotes, Int. J. Energy Res. 27 (2003) 859–874.

DOI: 10.1002/er.922

[4] D. Chandra, D. K. Ghosh, D. Sanyal, A scale analysis model for film boiling heat transfer on a vertical flat plate with wide applicability, International Journal of Heat and Mass Transfer 90 (2015) 40-48.

DOI: 10.1016/j.ijheatmasstransfer.2015.06.044

[5] M. Dzodzo, Scaling analysis and relation to EMDAP and BEPU, Nuclear Engineering and Design 353 (2019) 110228.

DOI: 10.1016/j.nucengdes.2019.110228

[6] O. Dounia, O. Vermorel, T. Jaravel, T. Poinsot, Time scale analysis of the homogeneous flame inhibition by alkali metals, Proceedings of the Combustion Institute (2020) in press.

DOI: 10.1016/j.proci.2020.06.030

[7] A. F. Miguel, Natural flow systems: acquiring their constructal morphology. International Journal of Design & Nature and Ecodynamics 5 (2010) 230-241.

DOI: 10.2495/dne-v5-n3-230-241

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

[9] A. F. Miguel, Constructal patterns formation in nature, pedestrian motion and epidemics propagation, in: A. Bejan, G. Merkx (Eds.), Constructal Theory of Social Dynamics, Springer, New York, 2007, pp.85-114.

DOI: 10.1007/978-0-387-47681-0_5

[10] A. Bejan, Advanced Engineering Thermodynamics, John Wiley & Sons, Hoboken, New Jersey, (2016).

[11] A. F. Miguel, A. Bejan, The principle that generates dissimilar patterns inside aggregates of organisms, Journal Physica A 388 (2009) 727-731.

DOI: 10.1016/j.physa.2008.11.013

[12] A. F. Miguel, Constructal pattern formation in stony corals, bacterial colonies and plant roots under different hydrodynamics conditions, Journal of Theoretical Biology 242 (2006) 954-961.

DOI: 10.1016/j.jtbi.2006.05.010

[13] A. F. Miguel, Constructal theory of pedestrian dynamics, Physics Letters A 373 (2009) 1734-1738.

DOI: 10.1016/j.physleta.2009.03.020

[14] A. F. Miguel, The emergence of design in pedestrian dynamics: locomotion, self-organization, walking paths and constructal law, Physics of Life Reviews 10 (2013) 168–190.

DOI: 10.1016/j.plrev.2013.03.007

[15] A. F. Miguel, Entropy generation: a path for understanding human gait patterns and crowd dynamics, International Journal of Exergy 23 (2017) 18-30.

DOI: 10.1504/ijex.2017.084519

[16] A. F. Miguel, A crowd of pedestrian dynamics – the perspective of physics, Physics of Life Review 18 (2016) 37-39.

[17] A.F. Miguel, Key mechanisms behind pedestrian dynamics: individual and collective patterns of motion, Diffusion Foundations 3 (2015) 153-164.

DOI: 10.4028/www.scientific.net/df.3.153

[18] A. F. Miguel, Physics' insights into pedestrian motion and crowd dynamics. Physics of Life Reviews 10 (2013) 206–209.

DOI: 10.1016/j.plrev.2013.05.006

[19] A. F. Miguel, A study of entropy generation in tree-shaped flow structures, International Journal of Heat and Mass Transfer 92 (2016) 349-359.

DOI: 10.1016/j.ijheatmasstransfer.2015.08.067

[20] A. F. Miguel, Toward an optimal design principle in symmetric and asymmetric tree flow networks, Journal of Theoretical Biology 389 (2016) 101-109.

DOI: 10.1016/j.jtbi.2015.10.027

[21] A. Bejan, S. Ziaei, S. Lorente, Evolution: why all plumes and jets evolve to round cross sections, Scientific Reports 4 (2014) 4730.

DOI: 10.1038/srep04730

[22] B. Soni, A. F. Miguel, A. K. Nayak, A mathematical analysis for constructal design of tree flow networks under unsteady flow, Proceedings of the Royal Society A 476 (2020) 20200377.

DOI: 10.1098/rspa.2020.0377