Numerical Study of an Unsteady Electro-Osmotic Flow of Reactive Third-Grade Fluid through a Microchannel Having Asymmetric Convective Cooling

The study analyzes the fluid-dynamical and thermodynamical behavior of a viscous and incompressible third-grade fluid flowing upwards through a vertical microchannel. The flow is driven by a combination of three forces, namely an adverse pressure gradient, buoyancy forces, and electroosmosis. The fluid is subjected to exothermic reactions modeled under Arrhenius kinetics, and the fluid viscosity is assumed temperature dependent as modeled via a Nahme law. The vertical walls of the microchannel are subjected to convective cooling, modeled via Newton's law of cooling. The resultant system of nonlinear coupled partial differential equations is solved numerically using robust semi-implicit finite difference methods. The results primarily demonstrate, as expected, that both the flow velocity and fluid temperature increase with time, from the zero initial states, until steady states are reached—provided the exothermic reactions are kept low enough to avoid thermal runaway and hence allow for the attainment of steady states. Additionally, and as expected, both the flow velocity and fluid temperature are enhanced in response to increases in the buoyancy driving forces. The more pertinent results show that increased non-Newtonian character of the fluid as well as increased electroosmotic characteristic are both flow retarding. Furthermore, we observe that the presence of non-Newtonian character in the fluid also leads to better mitigation of the thermal runaway phenomena than corresponding Newtonian fluids.