The brain is a complex system suffering exergy and energy exchange. The analysis of entropy can be used in brain analysis and its diseases while gold nanoparticles are vital in the treatment of cancer. Sequel to the nature of the thermo-physical property of the blood and usefulness of gold nanoparticles over curved shrinking/stretched surfaces; noting is known on the dynamics of transient blood conveying gold nanoparticles when entropy generation and Lorentz force are significant. Therefore, a transient problem of irreversibility analysis (entropy generation/s law analysis) is studied in this work. Blood is taken as base fluid, a counter example of Casson fluid containing a suspension of gold nanoparticles over a curved shrinking/stretched surface. A formulation type of Tiwari-Das is utilized with modification in viscosity. Here, the approach of entropy is underlined as a dominant device for the scrutiny of the function of the brain, in line with Saint Thomas Aquinas's philosophical and theological approach. The influences of viscous dissipation with joule heating are also invoked. The problem is modeled initially in the shape of PDEs and then renovates these equations into ODEs through similarity variables. The Lobatto IIIA formula (known as bvp4c) is employed to obtain multiple results. The importance of numerous emerging parameters is stimulated for the temperature distribution and the velocity profile as well as the temperature gradient and drag force. Also, the entropy generation is computed for various flow constraints. The results signifying that the entropy augments with radiation and dissipation effects. Thus, entropy can be significant in the artificial process in the analysis of brain function. In addition, the velocity and the temperature augment due to the inclusion of gold nanoparticles in blood flow.

大脑是一个复杂的系统，需要进行火用和能量交换。熵的分析可用于大脑分析及其疾病，而金纳米粒子在癌症治疗中至关重要。血液的热物理性质和金纳米粒子在弯曲的收缩/拉伸表面上的有用性的后续；当熵产生和洛伦兹力显着时，关于输送金纳米颗粒的瞬态血液的动力学是已知的。因此，在这项工作中研究了不可逆分析（熵生成/s 定律分析）的瞬态问题。以血液为基础流体，这是 Casson 流体的一个反例，它包含在弯曲的收缩/拉伸表面上的金纳米颗粒悬浮液。使用 Tiwari-Das 的配方类型并改变粘度。这里，熵的方法被强调为审查大脑功能的主要工具，与圣托马斯阿奎那的哲学和神学方法一致。还调用了焦耳加热的粘性耗散的影响。该问题最初以 PDE 的形式建模，然后通过相似性变量将这些方程更新为 ODE。Lobatto IIIA 公式（称为 bvp4c）用于获得多个结果。许多新出现的参数对于温度分布和速度分布以及温度梯度和阻力的重要性被激发。此外，熵生成是针对各种流约束计算的。结果表明熵随着辐射和耗散效应而增加。因此，熵在分析大脑功能的人工过程中可能很重要。此外，由于在血流中包含金纳米粒子，速度和温度增加。