Entropy generation in Casson-Williamson-Powell-Eyring hybrid ferrofluid flow in a microchannel: Adomian decomposition and deep neural networks approaches

Abstract Entropy generation is a fundamental concept in thermodynamics that measures the irreversibility of a process. Understanding the principles of entropy generation is crucial for optimizing thermal management and improving the efficiency of any thermal system. Its applications span a wide range, including heat exchangers, turbomachinery, chemical reactors, microfluidic devices, and many others. This study investigates the fluid flow and energy loss in the flow of three non-Newtonian fluids in a microchannel. The dynamical model incorporates the rheological behaviour of the three distinct fluids without the need for separate, independent mathematical models. These fluids Casson, Williamson, and Powell-Eyring are hybridized with a nanoparticle ferrofluid. The homogenization process is achieved using the Tiwari-Das model. Due to the magnetic body forces in the conservation of energy equation, the generation of entropy is taken into account from three sources: heat loss due to heat transfer, heat loss due to magnetic flow, and heat loss due to viscous dissipation. The solutions of the model equations are approximated using two solution techniques: the Adomian decomposition and deep neural network methods, and the results are compared with Maplesoft’s fourth-order Runge–Kutta (RK4). The solutions of these three methodologies serve as benchmarks for each other. The solutions obtained from each method agree, thus validating the accuracy of the results. The study indicates that the Williamson fluid is the most sensitive to flow changes with varying Reynolds numbers. Although increasing the Reynolds number reduces flow rates near the wall to zero for all fluids, there is a transition near the upper region where higher Reynolds numbers enhance the flow rates of all fluids. Increasing the Brinkman number raises the entropy generation rate for all fluids while inversely affecting the Bejan number across all fluids. Adding more nanoparticles will impede fluid flow and enhance fluid heat transfer. Graphical abstract Flow chart of the study structure