Numerical analysis of MHD flow in coaxial stretching and rotating cylinders with viscous effect

The effects of viscous force on magnetohydrodynamic flow in coaxial cylinders are discussed in this article. The inner cylinder stretches linearly along the axis, while the outer cylinder rotates with some fixed angular velocity. The movement of the fluid between these concentric cylinders depends on the stretching of the inner cylinder and the outer cylinder's rotation. Understanding this type of flow is crucial for applications in engineering and industrial processes, such as magnetic materials processing and fluid transport in rotating machinery. The inner cylinder's surface is also considered slippery, that is, the first order slip condition is incorporated on the internal cylinder surface. The impact of viscous dissipation is also calculated in the current study. After using suitable transformations, we turn mass conservation, Navier-stokes, and energy equations into dimensionless ordinary differential equations. Meanwhile, the numerical solutions of these equations are conducted via the shooting method. The numerical outcomes are graphically presented by varying the values of some certain parameters like the curvature parameter, the gap between the cylinders, the magnetic parameter, the slip parameter, and so forth. It is noted that the expanding gap size enhances the velocity of the fluid, accompanied by a rise in the fluid temperature. Additionally, the findings indicate that cylinders with a smaller gap exhibit a higher heat flux rate. The novelty of this work lies in the combined effects of viscous dissipation, slip conditions, and MHD on flow and heat transfer, offering insights beyond what has been previously explored in the literature.