Abstract
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.