Dissipative flow features of Carreau nanofluid with thermal radiation inside plane wall channel: Jeffery-Hamel analysis

Sohail Rehman ^a,*, Hashim ^b, Fuad A.M. Al-Yarimi ^c, Sultan Alqahtani ^d, Mohammed Awad ^e

a. Department Mechanical Engineering, School of Material Sciences and Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA
         b. Department of  Mathematics and Statistics, University of Haripur, Haripur 22620, Pakistan
         c. Department of Computer Science, King Khalid University, Muhayel Aseer, Saudi Arabia
         d. College of Engineering, Mechanical Engineering Department, King Khalid University, Abha, Saudi Arabia
         e. Department of Information Systems, King Khalid University, Muhayel Aseer, Saudi Arabia

Abstract: The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls. Thermal and concentration characteristics due to enthalpy change, activation energy, and non-linear thermal radiation have been examined in the presence of buoyancy forces. The channel walls for both temperature and volumetric fraction are assumed to be isothermal. The instability mechanism of nanofluids is reported using a two-phase nanofluid model, which works reasonably well for nanoparticle concentrations below a certain threshold. A Jeffery-Hamel (J-H) flow model is developed by assuming an incompressible purely radial flow of Carreau nanofluids with heat and mass transportation. Using the suitable non-dimensional variables, the resulting nonlinear partial differential equations are turned into a system of ordinary differential equations. The modified governing equations are then numerically solved using the built-in boundary value problem solver bvp4c, on the template form of commercial software MATLAB. The impacts of material, geometrical and thermophysical parameters governing the J-H problem are discussed and illustrated. Results indicate that higher buoyance forces incline the velocity profiles in converging enclosure, while a slight reduction is perceived in opposing forces. A significant decrease of wall heat transmission is reflected for larger values of activation energy and radiation parameter. For endorsing this communication, a comparison analysis is established with existing research and noticed a remarkable agreement. Practically, the flow inside converging and diverging channels are deployed in nuclear reactors that use plate-type nuclear energies, high heat-flux condensed heat exchangers, high-performance micro-electronic cooling systems, jets, rockets nozzles, and jet propulsion inlet.

Keywords: Nanofluids; Buoyancy forces; Converging/diverging channels; Thermal radiation; Activation energy; Carreau fluid

https://doi.org/10.1016/j.jppr.2023.02.007