Thermal analysis using Prandtl nanofluid in a non-uniform channel: Computational paradigm focusing on complex cilia waves

Abstract

Applications of complex cilia waves may play a vital role in advancing medicine, robotics, fluid dynamics, and environmental technologies. By simulating the synchronized movements of cilia, researchers are developing efficient systems for fluid manipulation, propulsion, and drug delivery. Non-Newtonian nanofluids enhance thermal properties, enable precise flow control, and adapt effectively to complex systems. This work elaborates rheological and thermal aspects of MHD non-Newtonian nanofluids with complex metachronal wave. This investigation aims to enrich engineering design procedures by implementing second-order velocity slip and thermal slip conditions. A mathematical model is presented for cilia induce transport of a Prandtl fluid with nanofluid axioms through a non-uniform ciliated micro-channel by applying magnetic field, second-order velocity slip and thermal slip at the boundaries. Formulation for the physiological fluid transport is made and equations of motion are simplified with pertinent flow scenarios. The solution of the physical fluid transport is carried out with novel BVP5C technique in the MATLAB and computational manipulations are validated with Artificial Neural Network. It has been observed that the nanofluid transport is enhanced at the boundaries by making slip parameters strong, size of the trapped bolus is reduced with Prandtl fluid parameters suggested that this parameter may give driving force to nanofluid flow. Temperature of the nanofluid is significantly raised with the implementation of thermal slip and reduced with variable thermal conductivity. Concentration of the nanofluid is surged with variable thermal conductivity and is declined with Biot number. The pumping phenomenon is lifted with Prandtl fluid parameters and may be controlled with velocity slip, and Darcy parameters, also heat transfer coefficient is affected with Prandtl fluid parameters.