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**Fluid flow and heat transfer through a vertical cylindrical collapsible tube in the presence of magnetic field and an obstacle.**
*(English)*
Zbl 1468.76077

Summary: In this paper, fluid flow and heat transfer through a Collapsible tube that is vertical with a spherical obstacle and Magnetic fields applied perpendicularly to the main flow has been investigated. The governing equations for this flow are the equations of continuity, motion and energy. The fluid flow through a Collapsible tube present a complex phenomenon due to the interaction of flowing fluid and the tube, hence the equations governing the flow are nonlinear partial differential equations. These equations have been transformed into non-linear ordinary differential equations by introducing a similarity transformation. The resulting equation from the similarity transformation is solved numerically using the Collocation method. The collocation method was implemented in MATLAB by invoking th bvp4c function to obtain the profiles. The simulation results has been presented in form of tables and graphs and also discussed. The effects of varying the Reynolds number, Hartmann number, Eckert number, Unsteadiness parameter, Prandtl number, Grashof number and Thrust constant on fluid temperature, fluid velocity and the rate of heat transfer have been determined. Variation in the various parameters is observed to change the fluid primary velocity, temperature and the rate of heat transfer. This results finds application in physical, biological and applied sciences.

### MSC:

76W05 | Magnetohydrodynamics and electrohydrodynamics |

76M99 | Basic methods in fluid mechanics |

76M55 | Dimensional analysis and similarity applied to problems in fluid mechanics |

80A19 | Diffusive and convective heat and mass transfer, heat flow |

### Keywords:

similarity transformation; collocation method; unsteadiness; transmural pressure; parametric investigation### Software:

Matlab
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\textit{D. Chepkonga} et al., Int. J. Adv. Appl. Math. Mech. 7, No. 1, 62--71 (2019; Zbl 1468.76077)

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