Influence of variable thermal conductivity and dissipation on magnetic Carreau fluid flow along a micro-cantilever sensor in a squeezing regime

Mathematical modeling of squeezing flows finds numerous applications in biological, mechanical, and medical engineering. Sensors feature such flows and can be effectively utilized to control vibrations and regulate lubrication. Magnetic fluids are critical to modern sensor systems. Micro-cantilevers are utilized in biomedical applications as biological, physical, or chemical sensors and operate via the detection of variations in the vibrational frequency or cantilever bending. Hence, a theoretical study is conducted to explore the dissipative flow and thermal characteristics in non-Newtonian boundary layer flow along a micro-cantilever sensor surface suspended in a squeezing regime between parallel plates. To achieve a more refined simulation, the effects of variable thermal conductivity and Joule magnetic dissipation are incorporated. The governing conservation equations for unsteady magnetic Carreau squeezing flow and heat transfer are rendered dimensionless and self-similar via appropriate scaling transformations. Emerging nonlinear coupled boundary value problem is then solved by using RK-4 method. The magnifying Weissenberg parameter decays the flow field. Skin friction is elevated with increasing Carreau power-law index and Weissenberg number. The novelty of the present study is the inclusion of dissipation and thermal conductivity variation effects which extends previous investigations and provides a more accurate appraisal of thermal characteristics in sensor squeezing flows.