Investigation of Third-Grade fluid flow in an inclined Microchannel: Utilizing the Hermite wavelet technique for second law analysis

Microfluidics serves as an interdisciplinary bridge between thermal and engineering fields, offering flexible solutions for addressing heat transport obstacles across diverse sectors. This study explores entropy production in the flow of a third-grade fluid through an inclined microchannel, considering radiation and convective heating effects. The analysis includes various factors such as viscous dissipation, natural convection, Joule heating, magnetic fields, and a uniform heat source/sink. The aim is to assess the energy efficiency of the system by minimizing entropy generation. To achieve this, governing equations are transformed into dimensionless forms using non-dimensional parameters. These equations are then solved using the Hermite wavelet method, a novel approach in this field. The impact of the Biot number on temperature exhibits a dual nature: temperature increases towards the upper plate of the channel while decreasing towards the lower plate. Similarly, entropy generation displays a dual behavior for higher values of Qt and Re, decreasing at the lower plate and increasing at the upper plate. This research offers valuable insights for optimizing energy efficiency in various applications, including pumps, heat exchangers, and energy systems, with potential applications in electronics cooling and renewable energy collection.