Temperature-dependent fluid properties on Ree-Eyring fluid flow through vertically oriented microchannel subject to rhythmic membrane contraction

The present study theoretically investigates the mixed convection flow and heat transfer of a Ree-Eyring non-Newtonian fluid in a vertical channel driven by rhythmic membrane contraction. The main objective of this work is to understand how variable fluid properties, thermal effects, and non-Newtonian behaviour influence fluid motion, pumping performance, and heat transfer in membrane-based microfluidic systems. The pressure gradient induced by a moving membrane, combined with buoyancy forces, drives the fluid through a vertical microchannel. To capture realistic thermal behaviour, temperature-dependent viscosity and thermal conductivity are incorporated into the model. Variable viscosity and variable thermal conductivity are considered to accommodate variable fluid properties. The basic nonlinear equations are then derived using the assumptions of a small Reynolds number, a long wavelength, and the lubrication approximation. Because of the nonlinearity of the governing equations, a regular perturbation technique is developed to obtain semi-analytical expressions for the velocity and temperature distributions. From these obtained velocity and temperature fields, the pressure gradient, skin friction, Nusselt number, flow rate, and stream function were then evaluated. Extensive parametric analysis has been performed in MATLAB R2024b to investigate the influence of variable viscosity, variable thermal conductivity, the heat-source parameter, the Grashof number, and the Ree-Eyring fluid parameter on the flow and thermal characteristics. Results indicate that variable viscosity improves flow behaviour, whereas heat generation and buoyancy forces significantly affect pumping and heat characteristics. The present findings provide useful guidance for the design and optimisation of thermally controlled micro-pumps, MEMS cooling devices, lab-on-chip technologies, and biomedical microchannels that require accurate regulation of fluid flow and heat transfer.