This study investigated the problem of radiation effects on the flow heat and mass transfer of magnetohydrodynamic steady laminar Marangoni convection in the boundary layer over a disk in the presence of a linear heat source and first-order chemical reactions. The governing partial differential equations of the disk model were established and transformed to a series of ordinary differential equations via suitable self-similar transformations, which were solved numerically by the shooting technique coupled with Runge-Kutta scheme and Newton’s method. The Marangoni number related to temperature and concentration was derived, the effects of the magnetic Hartmann number, Marangoni number, radiation number, heat source number and chemical reaction number related to velocity, temperature, and concentration profiles were analyzed. The results demonstrate that the Hartmann number and Marangoni number have significant impacts on the heat and mass transfer of the Marangoni boundary layer flow. The temperature tends to increase with heat generation and decrease with heat absorption, and it exhibits a delay phenomenon for significant heat generation cases. Negative/positive chemical reactions tended to increase/decrease the concentration, similar to the effect of heat generation/absorption on the temperature.

中文翻译：

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辐射对圆盘边界层中磁流体动力马兰戈尼流传热传质的影响

本研究调查了在存在线性热源和一级化学反应的情况下，辐射对磁盘边界层中磁流体动力学稳定层流 Marangoni 对流的流动热和质量传递的影响。建立了圆盘模型的控制偏微分方程，并通过适当的自相似变换将其转化为一系列常微分方程，并结合Runge-Kutta格式和牛顿方法进行数值求解。推导了与温度和浓度相关的马兰戈尼数，分析了磁哈特曼数、马兰戈尼数、辐射数、热源数和化学反应数对速度、温度和浓度分布的影响。结果表明，哈特曼数和马兰戈尼数对马兰戈尼边界层流的传热传质有显着影响。温度趋于随着热量的产生而升高，随着热量的吸收而降低，并且在显着的发热情况下表现出延迟现象。负/正化学反应倾向于增加/减少浓度，类似于热量产生/吸收对温度的影响。