Analysis of a channel-confined non-Newtonian shear-thinning flow past a pair of mildly heated side-by-side square cylinders

References

• R. P. Chhabra, and J. F. Richardson, Non-Newtonian Flow and Applied Rheology. Burlington: Butterworth-Heinemann, 2009.
   Google Scholar
• M. M. Zdravkovich, “Review of flow interference between two circular cylinders in various arrangements,” J. Fluids Eng., vol. 99, no. 4, pp. 618, 1977. DOI: 10.1115/1.3448871.
   Web of Science ®Google Scholar
• D. Sumner, “Two circular cylinders in cross-flow: A review,” J. Fluids Struct., vol. 26, no. 6, pp. 849, 2010. DOI: 10.1016/j.jfluidstructs.2010.07.001.
   Web of Science ®Google Scholar
• H. M. Spivack, “Vortex frequency and flow pattern in the wake of two parallel cylinders at varied spacing normal to an airstream,” J. Aeronautical Sci., vol. 13, no. 6, pp. 289, 1946. DOI: 10.2514/8.11375.
   Google Scholar
• C. H. K. Williamson, “Evolution of a single wake behind a pair of bluff bodies,” J. Fluid Mech., vol. 159, no. 1, pp. 1, 1985. DOI: 10.1017/S002211208500307X.
   Google Scholar
• F. H. Harlow, and J. E. Fromm, “Dynamics and heat transfer in the von Kármán wake of a rectangular cylinder,” Phys. Fluids, vol. 7, no. 8, pp. 1147, 1964. DOI: 10.1063/1.1711354.
   Web of Science ®Google Scholar
• E. M. Sparrow, and L. Lee, “Analysis of mixed convection about a horizontal cylinder,” Int. J. Heat Mass Transfer, vol. 19, no. 2, pp. 229, 1976. DOI: 10.1016/0017-9310(76)90118-6.
   Web of Science ®Google Scholar
• R. N. Kieft, C. C. M. Rindt, A. A. van Steehoven, and G. J. F. van Heijst, “On the wake structure behind a heated horizontal cylinder in cross-flow,” J. Fluid Mech., vol. 486, pp. 189, 2003. DOI: 10.1017/S0022112003004567.
   Web of Science ®Google Scholar
• S. Sen, S. Mittal, and G. Biswas, “Flow past a square cylinder at low Reynolds number,” Int. J. Numer. Methods Fluids, vol. 67, no. 9, pp. 1160, 2011. DOI: 10.1002/fld.2416.
   Web of Science ®Google Scholar
• M. M. Alam, Y. Zhou, and X. W. Wang, “The wake of two side-by-side cylinders,” J. Fluid Mech., vol. 669, pp. 432, 2011. DOI: 10.1017/S0022112010005288.
   Web of Science ®Google Scholar
• M. M. Alam, and Y. Zhou, “Intrinsic features of flow around two side-by-side square cylinders,” Phys. Fluids, vol. 25, no. 8, pp. 085106, 2013. DOI: 10.1063/1.4817670.
   Web of Science ®Google Scholar
• R. Yuan, M. Wu, and Z. Huang, “Steady mixed convective flow and heat transfer from tandem square cylinders in a horizontal channel,” Numer. Heat Transfer, Part A, vol. 71, no. 10, pp. 1023, 2017. DOI: 10.1080/10407782.2017.1330921.
   Web of Science ®Google Scholar
• Z. Wang, Z. Huang, W. Zhang, and G. Xi, “A multidomain chebyshev pseudo-spectral method for fluid flow and heat transfer from square cylinders,” Numer. Heat Transfer, Part A, vol. 68, no. 3, pp. 224, 2015. DOI: 10.1080/10407790.2015.1033320.
   Web of Science ®Google Scholar
• D. Chatterjee, and S. K. Gupta, “Convective transport around rows of square cylinders arranged in a staggered fashion at moderate Reynolds number,” Numer. Heat Transfer, Part A, vol. 68, no. 4, pp. 388, 2015. DOI: 10.1080/10407782.2014.986004.
   Web of Science ®Google Scholar
• M. J. Shah, E. E. Petersen, and A. Acrivos, “Heat transfer from a cylinder to a Power-law non-Newtonian fluid,” AIChe J., vol. 8, no. 4, pp. 542, 1962. DOI: 10.1002/aic.690080425.
   Web of Science ®Google Scholar
• R. W. Serth, and K. M. Kiser, “A solution of the two-dimensional boundary-layer equations for an Ostwald-de Waele fluid,” Chem. Eng. Sci., vol. 22, no. 7, pp. 945, 1967. DOI: 10.1016/0009-2509(67)80159-3.
   Web of Science ®Google Scholar
• P. M. Coelho, and F. T. Pinho, “Vortex shedding in cylinder flow of shear-thinning fluids I. identification and demarcation of flow regimes,” J. Non-Newtonian Fluid Mech., vol. 110, no. 2-3, pp. 143, 2003. DOI: 10.1016/S0377-0257(03)00007-7.
   Web of Science ®Google Scholar
• P. M. Coelho, and F. T. Pinho, “Vortex shedding in cylinder flow of shear-thinning fluids II. flow characteristics,” J. Non-Newtonian Fluid Mech., vol. 110, no. 2-3, pp. 177, 2003. DOI: 10.1016/S0377-0257(03)00008-9.
   Web of Science ®Google Scholar
• P. M. Coelho, and F. T. Pinho, “Vortex shedding in cylinder flow of shear-thinning fluids III. pressure measurements,” J. Non-Newtonian Fluid Mech., vol. 121, pp. 55, 2004. DOI: 10.1016/S0377-0257(04)00134-X.
   Web of Science ®Google Scholar
• I. Lashgari, J. O. Pralits, F. Giannetti, and L. Brandt, “First instability of the flow of shear-thinning and shear-thickening fluids past a circular cylinder,” J. Fluid Mech., vol. 701, pp. 201, 2012. DOI: 10.1017/jfm.2012.151.
   Web of Science ®Google Scholar
• P. Sivakumar, R. P. Bharti, and R. P. Chhabra, “Effect of power-law index on critical parameters for power-law flow across an unconfined circular cylinder,” Chem. Eng. Sci., vol. 61, no. 18, pp. 6035, 2006. DOI: 10.1016/j.ces.2006.05.031.
   Web of Science ®Google Scholar
• R. P. Bharti, R. P. Chhabra, and V. Eswaran, “Two-dimensional steady Poiseuille flow of power-law fluids across a circular cylinder in a plane confined channel: Wall effects and drag coefficients,” Ind. Eng. Chem. Res., vol. 46, no. 11, pp. 3820, 2007.
   Web of Science ®Google Scholar
• A. K. Dhiman, R. P. Chhabra, and V. Eswaran, “Steady flow of power-law fluids across a square cylinder,” Chem. Eng. Res. Des., vol. 84, no. 4, pp. 300, 2006. DOI: 10.1205/cherd05017.
   Web of Science ®Google Scholar
• A. K. Dhiman, R. P. Chhabra, and V. Eswaran, “Steady flow across a confined square cylinder: Effects of power-law index and blockage ratio,” J. Non-Newtonian Fluid Mech., vol. 148, no. 1-3, pp. 141, 2008. DOI: 10.1016/j.jnnfm.2007.04.010.
   Web of Science ®Google Scholar
• A. K. Sahu, R. P. Chhabra, and V. Eswaran, “Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder,” J. Non-Newtonian Fluid Mech., vol. 160, no. 2-3, pp. 157, 2009. DOI: 10.1016/j.jnnfm.2009.03.010.
   Web of Science ®Google Scholar
• A. K. Sahu, R. P. Chhabra, and V. Eswaran, “Two-dimensional laminar flow of a power-law fluid across a confined square cylinder,” J. Non-Newtonian Fluid Mech., vol. 165, no. 13-14, pp. 752, 2010. DOI: 10.1016/j.jnnfm.2010.03.011.
   Web of Science ®Google Scholar
• A. K. Sahu, R. P. Chhabra, and V. Eswaran, “Forced convection heat transfer from a heated square cylinder to power law fluids in the unsteady flow regime,” Numer. Heat Transfer, Part A, vol. 56, no. 2, pp. 109, 2009. DOI: 10.1080/10407780903107147.
   Web of Science ®Google Scholar
• A. K. Sahu, R. P. Chhabra, and V. Eswaran, “The effect of a blockage on forced convection heat transfer from a heated square cylinder to power-law fluids,” Numer. Heat Transfer, Part A, vol. 58, no. 8, pp. 641, 2010. DOI: 10.1080/10407782.2010.516696.
   Web of Science ®Google Scholar
• M. Bouaziz, S. Kessentini, and S. Turki, “Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder,” Int. J. Heat Mass Transfer, vol. 53, no. 23-24, pp. 5420, 2010. DOI: 10.1016/j.ijheatmasstransfer.2010.07.014.
   Web of Science ®Google Scholar
• S. Shibu, R. P. Chhabra, and V. Eswaran, “Power law fluid flow over a bundle of cylinders at intermediate Reynolds number,” Chem. Eng. Sci., vol. 56, no. 19, pp. 5545, 2001. DOI: 10.1016/S0009-2509(01)00161-0.
   Web of Science ®Google Scholar
• N. Mangadoddy, R. Prakash, R. P. Chhabra, and V. Eswaran, “Forced convection in cross flow of power law fluids over a tube bank,” Chem. Eng. Sci., vol. 59, no. 11, pp. 2213, 2004. DOI: 10.1016/j.ces.2004.01.054.
   Web of Science ®Google Scholar
• A. A. Soares, J. M. Ferreira, and R. P. Chhabra, “Steady two-dimensional non-Newtonian flow past an array of long circular cylinders up to Reynolds number 500: A numerical study,” Can. J. Chem. Eng., vol. 83, no. 3, pp. 437, 2008.
   Google Scholar
• N. S. K. Chaitanya, and A. K. Dhiman, “Non-Newtonian power-law flow and heat transfer across a pair of side-by-side circular cylinders,” Int. J. Heat Mass Transfer, vol. 55, no. 21-22, pp. 5941, 2012. DOI: 10.1016/j.ijheatmasstransfer.2012.06.005.
   Web of Science ®Google Scholar
• A. Agrawal, L. Djenidi, and R. A. Antonia, “Investigation of flow around a pair of side-by-side square cylinders using the lattice Boltzmann method,” Comput. Fluids, vol. 35, no. 10, pp. 1093, 2006. DOI: 10.1016/j.compfluid.2005.05.008.
   Web of Science ®Google Scholar
• A. Valencia, and R. Paredes, “Laminar flow and heat transfer in confined channel flow past square bars arranged side-by-side,” Heat Mass Transfer, vol. 39, no. 8-9, pp. 721, 2003. DOI: 10.1007/s00231-002-0356-1.
   Web of Science ®Google Scholar
• A. V. V. S. Durga Prasad, and A. K. Dhiman, “CFD analysis of momentum and heat transfer around a pair of square cylinders in side-by-side arrangement,” Heat Transfer Eng., vol. 35, no. 4, pp. 398, 2014. DOI: 10.1080/01457632.2013.828561.
   Web of Science ®Google Scholar
• A. Sanyal, and A. Dhiman, “Effect of forced convection heat transfer over side-by-side square cylinders in a steady confined flow regime,” J. Comput. Appl. Mech., vol. 11, pp. 197, 2016.
   Google Scholar
• A. K. Saha, K. Muralidhar, and G. Biswas, “Investigation of two- and three-dimensional models of transitional flow past a square cylinder,” J. Eng. Mech., vol. 129, no. 11, pp. 1320, 2003. DOI: 10.1061/(ASCE)0733-9399(2003)129:11(1320).
   Web of Science ®Google Scholar
• A. Sanyal, and A. Dhiman, “Wake interactions in a fluid flow past a pair of side-by-side square cylinders in presence of mixed convection,” Phys. Fluids, vol. 29, no. 10, pp. 103602, 2017. DOI: 10.1063/1.5005118.
   Web of Science ®Google Scholar
• A. Sanyal, and A. Dhiman, “Effect of thermal buoyancy on a fluid flowing past a pair of side-by-side square bluff-bodies in a low-Reynolds number flow regime,” Phys. Fluids, vol. 30, no. 6, pp. 063603, 2018. DOI: 10.1063/1.5025652.
   Web of Science ®Google Scholar
• A. Daniel, and A. Dhiman, “Aiding-buoyancy mixed convection from a pair of side-by-side heated circular cylinders in power-law fluids,” Ind. Eng. Chem. Res., vol. 52, no. 48, pp. 17294, 2013. DOI: 10.1021/ie4027742.
   Web of Science ®Google Scholar
• C. Norberg, “Flow around rectangular cylinders: Pressure forces and wake frequencies,” J. Wind Eng. Ind. Aerodyn., vol. 49, no. 1-3, pp. 187, 1993. DOI: 10.1016/0167-6105(93)90014-F.
   Web of Science ®Google Scholar
• P. Burattini, and A. Agrawal, “Wake interaction between two side-by-side square cylinders in channel flow,” Comput. Fluids, vol. 77, pp. 134, 2013. DOI: 10.1016/j.compfluid.2013.02.014.
   Web of Science ®Google Scholar
• R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena. New York: Wiley, 1960.
   Google Scholar
• N. Sharma, A. K. Dhiman, and S. Kumar, “Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers,” Int. J. Heat Mass Transfer, vol. 55, no. 9-10, pp. 2601, 2012. DOI: 10.1016/j.ijheatmasstransfer.2011.12.034.
   Web of Science ®Google Scholar
• K. Muralidhar, and T. Sundarajan, Computational Fluid Flow and Heat Transfer. Kanpur: Alpha Science International Ltd, 2003.
   Google Scholar
• ANSYS User Manual. Canonsburg, PA: Ansys Inc, 2009.
   Google Scholar
• A. K. Gupta, A. Sharma, R. P. Chhabra, and V. Eswaran, “Two-dimensional steady flow of a power law fluid past a square cylinder in a plane channel: Momentum and heat transfer characteristics,” Ind. Eng. Chem. Res., vol. 42, no. 22, pp. 5674, 2003. DOI: 10.1021/ie030368f.
   Web of Science ®Google Scholar
• M. D. Atkins, L. Dala, and T. Kim, “Time-averaged behavior of gap flow between two side-by-side circular cylinders,” Aiaa J., vol. 54, no. 9, pp. 2742, 2016. DOI: 10.2514/1.J054638.
   Google Scholar
• S. A. Kumar, M. Mathur, A. Sameen, and S. A. Lal, “Effects of Prandtl number on the laminar cross flow past a heated cylinder,” Phys. Fluids, vol. 28, pp. 113603, 2016. DOI: 10.1063/1.4966937.
   Web of Science ®Google Scholar
• M. Asif, and A. Dhiman, “Analysis of laminar flow across a triangular periodic array of heated cylinders,” J. Braz. Soc. Mech. Sci. Eng., vol. 40, pp. 350, 2018.
   Web of Science ®Google Scholar
• F. P. Incropera, A. L. Knox, and J. R. Maughan, “Mixed-convection flow and heat transfer in the entry region of a horizontal rectangular duct,” J. Heat Transfer, vol. 109, no. 2, pp. 434, 1987. DOI: 10.1115/1.3248100.
   Web of Science ®Google Scholar
• X. Yang, and A. Zebib, “Absolute and convective instability of a cylinder wake,” Phys. Fluids A, vol. 1, no. 4, pp. 689, 1989. DOI: 10.1063/1.857362.
   Web of Science ®Google Scholar
• G. I. Taylor, and A. E. Green, “Mechanism of the production of small eddies from large ones,” Proc. Roy. Soc. Lond. A, vol. 158, pp. 499, 1936.
   Google Scholar
• J. Weiss, “The dynamics of enstrophy transfer in two-dimensional hydrodynamics,” Physica D, vol. 48, no. 2-3, pp. 273, 1991. DOI: 10.1016/0167-2789(91)90088-Q.
   Web of Science ®Google Scholar
• H. J. Kim, and P. A. Durbin, “Investigation of the flow between a pair of circular cylinders in the flopping regime,” J. Fluid Mech, vol. 196, pp. 431, 1988. DOI: 10.1017/S0022112088002769.
   Web of Science ®Google Scholar
• S. R. Kumar, A. Sharma, and A. Agrawal, “Simulation of flow around a row of square cylinders,” J. Fluid Mech., vol. 606, pp. 369, 2008. DOI: 10.1017/S0022112008001924.
   Web of Science ®Google Scholar
• S. H. Strogatz, Non-Linear Dynamics and Chaos. Massachusetts: Perseus Book Publishing, 1994.
   Google Scholar
• D. Chatterjee, and G. Biswas, “Dynamic behavior of flow around rows of square cylinders kept in staggered arrangement,” J. Wind Eng. Ind. Aerodyn., vol. 136, pp. 1, 2015. DOI: 10.1016/j.jweia.2014.10.019.
   Web of Science ®Google Scholar
• D. Chatterjee, and B. Mondal, “Effect of thermal buoyancy on vortex shedding behind a square cylinder in cross flow at low Reynolds numbers,” Int. J. Heat Mass Transfer, vol. 54, no. 25-26, pp. 5262, 2011. DOI: 10.1016/j.ijheatmasstransfer.2011.08.016.
   Web of Science ®Google Scholar
• W. J. Marner, and H. K. McMillian, “Combined free and forced laminar non-Newtonian convection in a vertical tube with constant wall temperature,” Chem. Eng. Sci., vol. 27, no. 3, pp. 473, 1972. DOI: 10.1016/0009-2509(72)87003-9.
   Web of Science ®Google Scholar
• Sanyal, A., and Dhiman A. ‘Control of wake interactions for a flow past a pair of side-by-side square bluff-bodies in a thermally stratified flow field,’ presented at the Proceedings of 7th Conference on Bluff Body Wakes and Vortex-Induced Vibrations, (Marseille, 2018), pp. 71.
   Google Scholar