Nanofluids are the fluid suspensions in nanoparticles. A considerable enhancement in their features is less nanoparticle concentrations. Various studies on nanofluids focused on representing their performance with respect to the functions — here enhancing straight heat transfer was critical, like that in nuclear reactors, transportation, different industrial settings, biology, food and electronics. Hence, this consideration analyzes the utilization of the novel mathematical method, called the bvp4c method by viscous heat energy research in Buongiorno-modeled nanoliquid confined by the apt permeable plate along with slip mechanism. The thermophoresis and Brownian dispersion affects are again assumed. This transfer of solutal and thermal energy was dependent on the appreciable effect on heat source, variable chemical reactions and nonlinear thermal radiation. The dimensional model of partial differential equations (PDEs), applied to precise related applications, had been adapted into ordinary differential equations (ODEs). This modified Nusselt number decreases with increasing viscous heating, thermal radiation, thermophoresis parameter and Brownian motion, always it rises due to increasing temperature ratio parameter. The validation of the outcomes was attained with past solutions by free convectional flow and non-magnetic research. There are many functions in petroleum industries and engineering like electroplating, chemical processing of substantial metals and solar water heaters.

纳米流体是纳米颗粒中的流体悬浮液。其功能的一个显着增强是纳米颗粒浓度较低。关于纳米流体的各种研究都集中在表现它们在功能方面的性能——在这里，增强直接传热至关重要，就像在核反应堆、运输、不同工业环境、生物学、食品和电子领域中的传热一样。因此，本研究分析了新型数学方法（称为 bvp4c 方法）的利用，该方法通过粘性热能研究在由合适的渗透板和滑移机制约束的 Buongiorno 模型纳米液体中进行。再次假设热泳和布朗色散影响。这种溶液和热能的传递取决于对热源、可变化学反应和非线性热辐射的明显影响。应用于精确相关应用的偏微分方程（PDE）的量纲模型已被改编为常微分方程（ODE）。该修正努塞尔数随着粘性加热、热辐射、热泳参数和布朗运动的增加而减小，但总是由于温度比参数的增加而增加。结果的验证是通过自由对流和非磁性研究过去的解决方案来实现的。在石油工业和工程中具有许多功能，如电镀、大量金属的化学处理和太阳能热水器。