In this article, we aim to analyze the dual solutions for the flow of non-Newtonian material (Carreau fluid) over a radially shrinking surface. Magnetohydrodynamics fluid is considered. Concept of Stefan Boltzmann constant and mean absorption coefficient is used in the mathematical modeling of energy expression. Mass transfer is discussed. The upper and lower branch solutions for the Sherwood number, skin friction coefficient, and Nusselt number are calculated for different pertinent flow variables. Appropriate transformation variables are employed for reduction of partial differential equations system into ordinary differential equations. Dual solutions are obtained for the non-dimensional concentration, temperature, velocity, gradient of concentration, gradient of temperature, and gradient of velocity. The critical values for each upper and lower solutions are obtained for the case of gradient of velocity, gradient of temperature, and gradient of concentration. It is formed that concentration and temperature fields display same impact regarding both upper and lower branch solutions for velocity ratio and temperature ratio parameters.

在本文中，我们旨在分析径向收缩表面上非牛顿材料（卡洛流体）流动的双重解。考虑了磁流体动力学流体。Stefan Boltzmann常数和平均吸收系数的概念用于能量表达的数学建模。讨论了传质。对于不同的相关流量变量，计算舍伍德数，皮肤摩擦系数和努塞尔数的上，下分支解。采用适当的变换变量将偏微分方程组简化为常微分方程组。对于无量纲浓度，温度，速度，浓度梯度，温度梯度和速度梯度，可以获得对偶解。在速度梯度，温度梯度和浓度梯度的情况下，获得每个上下解决方案的临界值。对于速度比和温度比参数，浓度和温度场对上支路和下支路显示出相同的影响。