Effect of Non-Newtonian Fluid Behavior on Forced Convection from a Cluster of Four Circular Cylinders in a Duct, Part II: Bingham Plastic Fluids

Abstract

Extensive results are reported on the flow and heat transfer for Bingham plastic fluids for the same configuration as in Part I over the ranges: Reynolds number $\left(5\mathrm{}-\mathrm{}200\right),$ Prandtl number $\left(1-100\right),$ and Bingham number $\left(0.01-100\right)$ and the gap ratio $\left(0.3\mathrm{}-\mathrm{}0.7\right).$ At small Bingham numbers, the results deviate a little from that in Newtonian fluids except for the pockets of unyielded material. With the increasing fluid yield stress, the flow field consists of preferred flow channels between the inlet and outlet ports with high shear zones which directly influence the drag and Nusselt number. Depending upon the extent of fluid yielding, the drag on the middle cylinder can be higher by up to ∼100% or lower by up to ∼90% than that on the upstream cylinder. Similarly, the strong back flow observed at low Bingham numbers and high Reynolds numbers in the rear of the downstream cylinder leads to negative drag. In sparse arrays, the drag of upstream and downstream cylinders is comparable but that on the middle cylinder is always smaller. Similarly, the average heat transfer coefficient for each successive cylinder decreases with respect to the upstream cylinder. For the upper and downstream cylinder, this ratio is about 28-65% depending upon the kinematic conditions. In most cases, the first cylinder offers the maximum heat transfer.

Acknowledgment

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.