Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated. Magnetic field is applied in vertical direction to the disk. Temperature equation is assisted with Joule heating effect. Governing system of PDE's is transformed to dimensionless form by suitable variables. One of the numerical techniques known as finite difference scheme is adopted to tackle the given dimensionless partial differential system. This method results in a system of simple algebraic equations. The unknown function is analyzed inside domain of interest. In this technique of solution, a system is subdivided into many smaller parts called finite elements. The obtained simpler algebraic equations are then assembled to form a system of equations which governs the original problem. Variational method is used to get approximate solution by reducing the error function. Behaviors of pertinent variables on surface drag force, temperature, velocity and heat transfer rate are shown graphically. The obtained outcomes guarantee that velocity decreases for Hartmann number while it enhances with Reynolds number. Temperature increases for higher Prandtl, Eckert and Hartmann numbers. Skin friction boosts for larger values of Hartmann number. Nusselt number enhances with Hartmann number.

研究了由于可拉伸的旋转盘引起的随时间变化的粘性流体流动。磁场在垂直方向上施加到磁盘上。温度方程式具有焦耳热效应。PDE的控制系统通过适当的变量转换为无量纲形式。采用一种称为有限差分方案的数值技术来解决给定的无量纲偏微分系统。这种方法导致了一个简单的代数方程组。在感兴趣的域内分析未知函数。在这种解决方案技术中，系统被细分为许多称为有限元的较小部分。然后将获得的较简单的代数方程组组装起来，形成一个控制原始问题的方程组。使用变分法通过减少误差函数来获得近似解。以图形方式显示了有关表面阻力，温度，速度和传热速率的相关变量的行为。所获得的结果保证了Hartmann数的速度降低，而雷诺数则增加。较高的Prandtl，Eckert和Hartmann数会导致温度升高。皮肤摩擦会增加Hartmann数的值。Nusselt数随Hartmann数而增加。皮肤摩擦会增加Hartmann数的值。Nusselt数随Hartmann数而增加。皮肤摩擦会增加Hartmann数的值。Nusselt数随Hartmann数而增加。