Present work addresses the heat/mass transfer mechanism for higher order mixed convective flow of Williamson nanofluid impinging over a nonlinear bidirectional elongating surface with power-law heat/mass fluxes. For scientific relevancy, we also investigated the combined influence of chemical reaction, nonlinear emission of radiation and hydro-magnetic environment on the flow pattern. Novel combination of scaling transformations has been instigated to metamorphose the principal equations into a set of highly nonlinear coupled ordinary-differential equations and then Keller-Box method (KBM) has been utilized to attain the solution of modeled problem. Convergence of the solution has been discussed via grid independence methodology. Controls of sundry dominant parameters on temperature and concentration variations have been discussed via various plots, whereas variations in heat/mass transfer rates are explained through tabular arrangements. Our analysis shows that the Nusslet number and the Sherwood number are developed up-to 38% with the positive estimations of power-law index $0.1\le n\le 0.5$, whereas thermal gradient $\theta \text{'}(0)$ is reduced up-to 5% with the appraisal of thermo-migration of nanoparticles $0.4\le N_t\le 0.8$. Rate of heat transference is improved up-to 24% and the rate of mass transference is improved up-to 5% with the inclusion of nonlinear thermal radiation aspects $1.1\le {\theta }_w\le 1.5$. The validation of the solution has been made by comparing the results for restricted cases with the available literature.

目前的工作解决了威廉姆森纳米流体的高阶混合对流流冲击具有幂律热/质量通量的非线性双向伸长表面的热/质量传递机制。为了科学相关性，我们还研究了化学反应、辐射的非线性发射和水磁环境对流型的综合影响。提出了标度变换的新组合，将主要方程变形为一组高度非线性耦合的常微分方程，然后利用 Keller-Box 方法 (KBM) 获得建模问题的解。已经通过网格独立性方法讨论了解决方案的收敛性。已经通过各种图表讨论了对温度和浓度变化的各种主要参数的控制，而通过表格排列来解释热/质量传递率的变化。我们的分析表明，在幂律指数的正估计下，Nusslet 数和 Sherwood 数得到了高达 38% 的发展$0.1\le n\le 0.5$, 而热梯度 $\theta \text{'}(0)$ 通过评估纳米颗粒的热迁移，减少高达 5% $0.4\le N_{吨}\le 0.8$. 由于包含非线性热辐射方面，传热率提高了 24%，传质率提高了 5%$1.1\le {\theta }_{瓦}\le 1.5$. 通过将限制案例的结果与可用文献进行比较，对解决方案进行了验证。