The present paper is an extension of the work done by Fang and Tao (2012) in the presence of a magnetic field. The external magnetic field is applied normal to a stretchable disk surface and heat is transferred from the disk surface to the ambient fluid which gives a new family of unsteady viscous flow over a stretchable rotating disk with deceleration. The Navier–Stokes equations and the energy equation admit similarity solutions depending on unsteadiness parameter. The resulting set of highly nonlinear ordinary differential equations are solved numerically. Two solution branches are found due to the effect of unsteadiness parameter for several values of magnetic parameter and stretching parameter. The effects of pertinent flow parameters on the shear stresses on radial and tangential directions, Nusselt numbers, torque, dimensionless velocity and temperature profiles are shown graphically for both the solution branches and their physical interpretation are discussed in detail. Emphasis has been laid to check the stability of dual solution branches. The stability is tested by the sign of the smallest eigenvalue, and our analysis reveals that the lower solution branches are unstable.

本文是对存在磁场的Fang和Tao（2012）所做工作的扩展。外部磁场垂直于可拉伸磁盘表面施加，热量从磁盘表面传递到环境流体，从而在带减速的可拉伸旋转磁盘上产生了新的不稳定粘性流。Navier–Stokes方程和能量方程根据不稳定参数接受相似解。对所得的一组高度非线性的常微分方程进行数值求解。由于磁参数和拉伸参数的几个值的不稳定参数的影响，找到了两个解分支。相关的流动参数对径向和切向方向上的剪应力，努塞尔数，扭矩，图形化地显示了溶液分支的无量纲速度和温度分布图，并详细讨论了它们的物理解释。已经着重检查双重解决方案分支的稳定性。通过最小特征值的符号测试稳定性，我们的分析表明较低解的分支是不稳定的。