Effect of Non-Newtonian Fluid Behavior on Forced Convection from a Cluster of Four Circular Cylinders in a Duct, Part I: Power-Law Fluids

Abstract

Forced convection heat transfer in power-law fluids has been investigated numerically around four identical circular cylinders in a diamond array in a square enclosure. For the laminar flow, the governing equations have been solved numerically over the following ranges of parameters: Reynolds number (5 − 200), Prandtl number (0.7 − 100), power-law index (0.2 − 2) and center-to center gap between cylinders (0.3 − 0.7) to elucidate their influence. The detailed kinematics and engineering parameters are influenced by the gap between the cylinders via the development of multiple secondary flow regions and/or the splitting of incoming fluid stream. The drag on the trailing cylinders with reference to the lead cylinder can be up to ± ∼ 80% higher or lower depending upon the gap between the cylinders, power-law index and Reynolds numbers. In compact arrays, the drag becomes slightly negative due to the reverse flow for certain combinations of power-law index (< 1) and high Reynolds numbers (100 and 200). Similarly, the heat transfer affected by the subsequent cylinders ranges from 50-60% for the second cylinder which drops to ∼10% for the last cylinder. Finally, the functional dependence of the Nusselt number has been consolidated in terms of Reynolds number, Prandtl number, power-law index and the gap ratio.

Acknowledgements

The award of a JC Bose Fellowship (SERB, Department of Science and Technology, Government of India, New Delhi) to RPC for the period 2015-2020 is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Mohit Trivedi

Mohit Trivedi is a doctoral student at the Department of Chemical Engineering in the Indian Institute of Technology, Kanpur, India. He obtained his bachelor’s degree in Chemical Engineering in 2012 from C. S. J. M. University, Kanpur, India, where he worked on the modeling, and design of slurry-based reactor for high density Polyethylene production.

Neelkanth Nirmalkar

Neelkanth Nirmalkar earned his Ph.D. in Chemical Engineering from the Indian Institute of Technology Kanpur. Following a post-doctoral research experience in the Department of Chemical Engineering, The University of Birmingham, UK, he joined IIT Ropar in 2019 as an Assistant Professor in the Department of Chemical Engineering. His research interests include non-Newtonian fluid mechanics and heat transfer in multiphase flows. In recent years, he has been investigating complex fluids and flow, heat transfer in nanofluids, heat transfer in phase change materials and the stability of bulk nanobubbles with potential applications in mineral processing, and water treatment.

Anoop K. Gupta

Anoop Kumar Gupta is an Assistant Professor in the Department of Chemical and Biochemical Engineering at the Indian Institute of Technology Patna, India. He graduated from HBTI Kanpur, India in 2010 and obtained his Master’s degree in Chemical Engineering from the Indian Institute of Technology Guwahati, India. In 2017, he received his Ph.D. degree in Chemical Engineering from the Indian Institute of Technology, Kanpur, India. He has worked as a postdoctoral research fellow in the National University of Singapore for 1.5 years. His research interests include computational fluid dynamics and heat transfer, non-Newtonian fluid rheology, discrete phase modeling, phase change materials and thermal management of lithium-ion batteries.

Rajendra P. Chhabra

Raj Chhabra retired as a Professor of Chemical Engineering from the Indian Institute of Technology Kanpur, India and he is currently the Head of Department of Chemical Engineering at the Indian Institute of Technology Ropar, Punjab. He earned his Ph.D. from Monash University, Melbourne, Australia in 1980. The primary focus of his research has been in the field of non-Newtonian fluid mechanics including multi-phase flows in pipes, particulate flows and bluff-body flows. He has published extensively in this area and has authored and coauthored three books in the field of non-Newtonian fluid mechanics and applied rheology. He serves on the editorial boards of Journal of non-Newtonian Fluid Mechanics (Elsevier), and Industrial Crops & Products (Elsevier). He is a fellow of the Indian National Academy of Engineering and of the Indian National Science Academy. He has been a visiting professor at several universities in Australia, USA, Canada, France, Poland, Japan, China and South Africa.