This article is concerned with the study of free convective unsteady magnetohydrodynamic flow of the incompressible Oldroyd-B fluid along with chemical reaction. The fluid flows on a vertical plate that is impulsively brought in motion in the presence of a constant magnetic field which is applied transversely on the fluid. The structure has been modeled in the form of governing differential equations, which are then nondimensionalized and solved using a numerical technique, that is, Crank–Nicolson’s scheme to obtain solutions for velocity field, temperature distribution, and concentration profile. These solutions satisfy the governing equations as well as all initial and boundary conditions. The obtained solutions are new, and previous literature lacks such derivations. Some previous solutions can be recovered as limiting cases of our general solutions. The effects of thermophysical parameters, such as Reynolds number, Prandtl number, thermal Grashof number, modified Grashof number, Darcy number, Schmidt number, dissipation function, magnetic field, radiation–conduction, chemical reaction parameter, relaxation and retardation times on the velocity field, temperature, and concentration of fluid, are also examined and discussed graphically.

本文涉及不可压缩的Oldroyd-B流体的自由对流非稳态磁流体动力学流动以及化学反应的研究。流体在垂直板上流动，该垂直板上在存在横向施加在流体上的恒定磁场的情况下被推动运动。该结构已经以控制微分方程的形式建模，然后对其进行了无量纲化并使用一种数值技术进行求解，即使用Crank–Nicolson方案来获得速度场，温度分布和浓度分布的解。这些解决方案满足控制方程式以及所有初始条件和边界条件。所获得的解决方案是新的，并且先前的文献缺乏这种推导。某些先前的解决方案可以作为我们一般解决方案的有限情况加以恢复。热物理参数（例如雷诺数，普朗特数，热格拉斯霍夫数，修正的格拉斯霍夫数，达西数，施密特数，耗散函数，磁场，辐射传导，化学反应参数，弛豫和延迟时间）对速度场的影响，温度和流体浓度也将通过图形检查和讨论。