Numerical analysis of porous media flow of magnetized Carreau nanofluids in vertical micro-channels subject to thermal radiation and uniform injection/suction

The present study focuses on the flow and heat transfer dynamics of a Carreau nanofluid flowing through a micro-channel. The micro-channel is filled with a porous media and the micro-channel walls are assumed permeable, allowing for fluid injection and suction. The flow is subjected to the heat transfer under effects of thermal radiation and viscous dissipation. In addition to being shear-rate dependent under the Carreau viscosity constitutive model, the fluid viscosity is also considered temperature dependent. A uniform magnetic field is also applied transverse to the main flow direction. The Carreau model is an example of a non-Newtonian fluid model which. The flow and heat transfer dynamics of non-Newtonian nanofluids through porous channels or micro-channels finds wide application, say to, petroleum engineering, heating and cooling processes in engineering and industry, biomedical and biotechnological phenomena, etc. The governing equations form a complex system of coupled and nonlinear partial differential equations (PDEs). The governing system of PDEs is solved via direct numerical simulation using robust and efficient numerical algorithms based on semi-implicit finite difference methods (SIFDM). Qualitative analyses, based on changes to the values of the embedded parameters, are performed on the profiles of the field variables, namely, the main-flow velocity, fluid temperature, and nanoparticle concentration. The principal insights derived from the research reveal that the qualitative behaviour of the main-flow velocity mirrors that of the fluid temperature, i.e., these quantities either both increase or both decrease in response to changes in the values of the embedded parameters. The results illustrate that the following effects are drag-inducing, i.e., lead to a decrease in the main-flow velocity; porous media intensity, transverse magnetic field strength, increased injection/suction cross-flow motion, and higher fluid viscosity. The study also demonstrates the effects of Brownian motion and thermophoresis on the main-flow velocity and fluid temperature. Specifically, it is observed that an increase in either thermophoresis or Brownian motion lead to increases in temperature and velocity. A particularly important result of the study illustrates that shear-thickening Carreau nanofluids are less susceptible to thermal runaway phenomena than Newtonian fluids. The results lead to important conclusions with regards to heat transfer applications. An increase in nanoparticle concentration is linked to a increase in thermophoresis but to a decrease in Brownian motion. Similarly, a decrease in nanoparticle concentration corresponds to a decrease in thermophoresis but to an increase in Brownian motion. It is therefore important in applications to carefully balance the nanoparticle concentration in order to optimize the combined effects of thermophoresis and Brownian motion. For applications which may demand thermal runaway phenomena mitigation, it is crucially important to utilize rheologically appropriate fluids such as sher-thickening Carreau fluids. The present study significantly adds to the existing scientific body of knowledge with regards a systematic analysis of multiple heat transfer effects simultaneously, instead of these effects being examined in isolation as is largely presented in the existing literature.