Thermomagnetic peristaltic Casson flow in a microchannel containing a Darcy–Brinkman porous medium under the influence of oscillatory, thermal radiation, slip and heat source effects

The objective of this article is to study mathematically the magnetohydrodynamic (MHD) unsteady non-Newtonian oscillatory blood flow and heat transfer in microchannels containing a Darcy–Brinkman porous medium. The Casson fluid model is deployed. Additionally, the effects of heat source, nonlinear thermal radiation and Hall current are included. Convective heating and slip at the internal boundaries of the microchannel are also examined. Utilising a set of non-dimensional variables, the governing partial differential equations and associated boundary conditions are transformed into a non-dimensional form. By solving the transformed model, exact solutions are obtained. Graphical representations depict the influence of different physical characteristics on the velocity and temperature patterns. In addition, this study incorporated a parametric analysis to demonstrate the impacts of key parameters on Nusselt number and wall shear stress. Increased values of thermal radiation and Casson rheological parameters produce intensified velocity fields. Blood flow is also controlled by modulating the intensity of the external magnetic field and the regulation of the blood temperature is achieved by modifying its thermal conductivity. With an increment in thermal Biot number (Bh) (stronger convective heating at the microchannel walls) there is a uniform increase in temperatures. With the elevation in the Hall parameter, more complex streamline patterns are generated and there is an increase in the magnitude of trapped boluses. An increment in Grashof number (Gr), i.e. stronger thermal buoyancy force, accelerates the flow. Elevation in the Nusselt number is produced with a stronger heat source (S). With greater frequency (ω), the blood flow is more strongly modified by periodic fluctuations in the driving pressure and this produces an elevated amplitude of velocity oscillations, thereby increasing the average velocity of the blood. Increasing slip (\(\gamma )\) generates significant flow deceleration in the microchannel. This work, which focusses on the thermal radiation in the blood flow, will significantly influence therapeutic strategies for hyperthermia. Specifically, the analysis provides a good foundation for more sophisticated computational fluid dynamics (CFD) studies and will enhance our understanding and management of blood flow and heat transfer in, for example, arterial hemodynamics.