Hydromagnetic Self-gravitating Stability of Streaming Fluid Cylinder With Longitudinal Magnetic Forces is developed. A general eigenvalue relation is derived studied analytically and results are confirmed numerically. In absence of the effect of the electromagnetic forces interior and exterior the fluid, so the model is only subjected to the capillary force. It is found that the model is unstable in the region 0 < x ≤ 1.07. While it is stable in the region 1.07 ≤ x < ∞. This means that model is just unstable in small domains of axisymmetric perturbation but it stable in all other domains. For very high intensity of magnetic field the model is completely stable for all values of wave lengths. The Lorentz

In this work, we deal with unsteady magnetohydrodynamic allowed convection inflow of blood with a carbon nanotubes model; the single and multiwalled carbon nanotubes of human blood are used as a based fluid. Two numerical methods used to study this model are the weighted average finite difference method and the nonstandard compact finite difference method. The proportional Caputo hybrid operator has been used to fractionalize the proposed model. Stability analysis has been construed by a kind of John von Neumann stability analysis. Numerical results are presented in diverse graphs, which manifest that the method is successful in solving the proposed model.