In this study, we investigated dual solutions for the influence of chemical reaction and radiation effect on axisymmetric flow of magneto-Cross nanomaterial towards a radially shrinking disk on taking account of stagnation point. The governing expressions which describe the assumed flow are reduced to ordinary differential equations by opting suitable similarity variables. The dual solutions on the performance of dimensionless velocity, thermal, concentration gradients, skin friction, rate of heat and mass transfer with the impact of relevant parameters are studied using suitable graphs. Result outcomes reveal that, upsurge in Brownian motion parameter improves the thermal gradient in case of both the solution but, converse trend is detected in concentration gradient. The uplift of thermophoresis parameter boosts up the concentration gradient in both branch solution but reverse trend is noticed in concentration profile for inclined values of Schmidt number. Further, dual nature of solutions exists only for certain range of shrinking parameter.

中文翻译：

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磁交叉纳米材料向径向收缩盘的轴对称流动的临界值

在这项研究中，我们研究了化学反应和辐射效应对考虑驻点的磁交叉纳米材料向径向收缩盘的轴对称流动的影响的双重解决方案。通过选择合适的相似性变量，描述假设流动的控制表达式被简化为常微分方程。使用合适的图表研究了无量纲速度、热、浓度梯度、表面摩擦、传热和传质速率以及相关参数的影响的双重解。结果表明，布朗运动参数的上升改善了两种溶液的热梯度，但在浓度梯度中检测到相反的趋势。热泳参数的升高提高了两个分支溶液中的浓度梯度，但在施密特数倾斜值的浓度分布中发现了相反的趋势。此外，解的双重性质只存在于一定范围的收缩参数。