The present study delves into the flow characteristics of a couple stress fluid under the influence of electromagnetic fields in a micro-circular-tube with a slippery inner surface. This investigation considers the flow to be actuated by pressure gradient, electromagnetic force, and induced streaming potential field with slip boundary condition. Mathematical model is developed to determine the solution of the Poisson-Boltzmann equation (incorporating the Debye-Hückel approximation) for the electric potential within the electric double layer and the momentum equation for fluid flow under employing physically relevant boundary conditions. The analytical expressions for velocity, streaming potential, electroviscous effect, and efficiency of electrokinetic energy conversion are scrutinized. Further, the numerical solution is computed for the energy equation by employing finite difference method. The key findings of present investigation reveal that a higher non-Newtonian parameter leads to an enhancement in the velocity distribution, streaming potential field, and efficiency of electrokinetic energy conversion. In contrast, the electroviscous effect shows a contrasting behavior. Also, an electric field makes the temperature go up as the Hartmann number increases. But when there's no electric field, the temperature goes down. The discovery has wide-ranging implications for chemical processing and mixing, biochip construction for drug delivery, and biomedical engineering innovations.

中文翻译：

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耦合应力流体通过圆形微通道的电磁流体动力流动的传热和动电能量转换效率研究

本研究深入研究了具有光滑内表面的微圆管中电磁场影响下的耦合应力流体的流动特性。本研究认为流动是由压力梯度、电磁力和滑移边界条件下的感应流势场驱动的。开发数学模型以确定双电层内电势的泊松-玻尔兹曼方程（结合德拜-休克尔近似）的解以及采用物理相关边界条件下的流体流动动量方程。仔细研究了速度、流动势、电粘性效应和动电能量转换效率的解析表达式。进一步，采用有限差分法计算能量方程的数值解。本研究的主要发现表明，较高的非牛顿参数会导致速度分布、流动势场和动电能量转换效率的增强。相反，电粘性效应表现出相反的行为。此外，随着哈特曼数的增加，电场使温度升高。但当没有电场时，温度就会下降。这一发现对化学加工和混合、用于药物输送的生物芯片构建以及生物医学工程创新具有广泛的影响。