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 and , 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.

中文翻译：

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倾斜微通道中三级流体流动的研究：利用 Hermite 小波技术进行第二定律分析


微流体作为热学和工程领域之间的跨学科桥梁，为解决不同领域的热传输障碍提供灵活的解决方案。本研究探讨了三级流体流过倾斜微通道时的熵产生，考虑了辐射和对流加热效应。分析包括各种因素，例如粘性耗散、自然对流、焦耳热、磁场和均匀热源/散热器。目的是通过最小化熵的产生来评估系统的能源效率。为了实现这一点，使用无量纲参数将控制方程转换为无量纲形式。然后使用埃尔米特小波法（该领域的一种新颖方法）求解这些方程。毕奥数对温度的影响表现出双重性质：温度朝通道的上板增加，而朝下板减少。类似地，对于较高的 和 值，熵生成显示出双重行为，在下板处减少，在上板处增加。这项研究为优化各种应用（包括泵、热交换器和能源系统）的能源效率提供了宝贵的见解，并在电子冷却和可再生能源收集方面具有潜在的应用。