Rheological study of Hall current and slip boundary conditions on fluid–nanoparticle phases in a convergent channel

Purpose: the purpose of this theoretical study was to analyze the heat transfer in the fluid–particle suspension model under the effects of a porous medium, magnetic field, Hall effects, and slip boundary conditions in a convergent channel with the addition of electrokinetic phenomena. The Darcy–Brinkman (non-Darcy porous medium) model was used to assess the effects of the porous medium. Methodology: the rheological equations of both models were transformed into a dimensionless form to obtain the exact solutions of the fluid and particle phase velocities, pressure gradient, volumetric flow rate, stream function, temperature distribution, and heat-transfer rate. To obtain an exact solution to the models, the physical aspects of the parameters are discussed, analyzed, and reported through graphs, contour plots, and in tabular form. Findings: mixing in hafnium particles in a viscous fluid provide 1.2% more cooling compared to with a regular fluid. A reduction of the streamlines was observed with the contribution of the slip condition. The utilization of the Darcy parameters upgraded both the fluid flow and temperature profiles, while the heat-transfer rate decreased by up to 3.3% and 1.7% with the addition of a magnetic field and porous medium, respectively. Originality: the current study is an original work of the authors and has not been submitted nor published elsewhere.