Laminar Free Convection in Power-law Fluids in a Right Angle Triangular Duct with Heated Base

ABSTRACT

Laminar free convection in power-law fluids in a triangular duct is studied numerically to delineate the effects of the height-to-base ratio of the enclosure (0.2 to 2), power-law index (0.2 to 1.8), Grashof number (10 to 10⁴) and Prandtl number (0.7 to 100). The heat transfer is analyzed for the heated base with the other two walls being cold. Detailed kinematics is characterized by the formation of multiple recirculating zones ranging from two to four cells. Shear rate contours provide additional insights about the variation of the local viscosity in the fluid. Heatlines and the values of the Bejan number over the range of conditions are calculated to delineate the contributions of the entropy generation due to thermal effects and viscous dissipation. At low Grashof and/or Prandtl numbers, conduction dominates the overall heat transfer and this transition between the conduction and convection-dominated regimes is captured in terms of a modified Rayleigh number. The effect of aspect ratio on the Nusselt number is modulated by the values of Grashof and Prandtl numbers and power-law index. The present results have been consolidated via the use of a modified Rayleigh number for estimating the value of average Nusselt number in a new application.

Acknowledgement

Raj Chhabra gratefully acknowledges the award of the JC Bose fellowship to him by the Department of Science and Technology (Govt. of India, New Delhi) for the period 2015 – 2020.

Additional information

Notes on contributors

Sujit Jagnade

Sujit A. Jagnade earned his M.Tech. in Chemical Engineering in 2017 from the Indian Institute of Technology, Kanpur, India. He worked for one year in Finolex Industries limited in 2014–2015. He obtained his bachelor's degree in 2014 from Dr. Babasaheb Ambedkar Technological University, Lonere, India, where he worked on modelling, simulation and design of controller of flow tank system. His master research is focused on computational fluid dynamics. He is now working for Tata Steel Ltd., Jamshedpur.

Lubhani Mishra

Lubhani Mishra is a Ph.D. student in Department of Chemical Engineering at the Indian Institute of Technology Kanpur, India. She obtained her Bachelor's degree in 2013 from UICET, Panjab University, Chandigarh, India where she investigated the process of manufacture of styrene from ethylbenzene as a part of her undergraduate research project. Her doctoral research is focused on the computational fluid dynamics and primarily deals with the role of non-Newtonian rheology on transport phenomenon in complex geometries.

Ashok K. Baranwal

Ashok Kumar Baranwal earned his Ph.D. in Chemical Engineering in 2017 from the Indian Institute of Technology, Kanpur, India. He worked on kinetic analysis of biodiesel formation from Karanja oil and using ion exchange resin catalyst for his master's thesis, and received his M.Tech. in 2011 from the Indian School of Mines Dhanbad, India. He obtained his bachelor's degree in 2009 from the Birsa Institute of Technology Sindri, Dhanbad, India, where he investigated the development of process technology for the manufacture of ferrous sulphate from scrap iron and spent acid. His doctoral research is focused on the computational fluid dynamics. He is currently working as an Assistant Professor at BIT Mesra, Ranchi.

Raj P. Chhabra

Raj Chhabra is a Professor of Chemical Engineering at the Indian Institute of Technology, Kanpur, India. He received his PhD 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 or coauthored three books in the broad field of non-Newtonian fluid mechanics and applied rheology. He serves on the editorial boards of Journal of Non-Newtonian Fluid Mechanics (Elsevier), Heat Transfer-Asian Research (Wiley), Industrial Crops & Products (Elsevier) and the Indian Journal of Chemical Technology. 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 and South Africa.