The present work explores the behavior of three-dimensional incompressible viscous fluid flow and heat transfer over the surface of a non-flat stretchable rotating disk. A variable thickness fluid is subjected under the influence of an external variable magnetic field and heat transfer. Navier–Stokes equation is coupled with Maxwell equations to examine the hydrothermal properties of fluid. The basic governing equations of motion are diminished to a system of nonlinear ordinary differential equations using appropriate similarity framework, which are further treated with numerical scheme known as parametric continuation method. The parametric continuation method has combined interesting characteristics of both shooting and implicit finite difference methods. For validity of the present numerical scheme, a comparison with the published work is performed and it is found that the results are in excellent agreement with each other. Numerical and graphical results for the velocity, temperature, and magnetic strength profiles as well as skin fractions and Nusselt number are presented and discussed in detail for various physical parameters. The heat transfer process is reduced with positive increment of no-flatness parameter $\zeta$, while Prandtl number increases the heat transfer rate at the surface of the disk.

本工作探讨了非平面可拉伸转盘表面上三维不可压缩粘性流体流动和传热的行为。可变厚度的流体在外部可变磁场和热传递的影响下受到作用。Navier–Stokes方程与Maxwell方程耦合以检查流体的水热性质。使用适当的相似性框架，将基本的运动控制方程简化为非线性常微分方程组，然后使用称为参数连续法的数值方案对其进行进一步处理。参数连续法结合了射击和隐式有限差分法的有趣特征。为确保本数值方案的有效性，与已发表的作品进行了比较，发现结果彼此之间非常吻合。给出并讨论了各种物理参数的速度，温度和磁强度曲线以及表皮分数和Nusselt数的数字和图形结果。随着不平坦度参数的正增量减少传热过程$\zeta$，而Prandtl数则增加了磁盘表面的传热速率。