In this research study, fluid flow through a cylindrical collapsible tube has been investigated. Of particular interest is the effect of flow parameters on the cross sectional area of a collapsible tube, flow velocity and internal pressure of the fluid. The flow parameters considered are longitudinal tension and volumetric flow rate. The tube is considered collapsible in the transverse direction, taken to be perpendicular to the main flow direction. Collapse happens when external pressure exceeds internal pressure and hence the tube results to a highly noncircular cross sectional area. The fluid flow in consideration is steady and incompressible. Equations governing the flow are non-linear and cannot be solved analytically. Therefore an approximate solution to the equations has been determined numerically. In this case, finite difference method has been used. A computer program has then been used to generate the results which are presented in form of graphs. The results show that the longitudinal tension is directly proportional to both the cross sectional area and internal pressure and inversely proportional to the flow velocity and that change in volumetric flow rate has no effect on the cross sectional area but it is directly proportional to the flow velocity and inversely proportional to the internal pressure.

In the present study, a hydromagnetic non-Newtonian (dilatant) fluid flow in a convergent conduit, in the presence of a variable transverse magnetic field, has been investigated. The governing nonlinear partial differential equations are reduced to system of ordinary differential equations. These equations are solved numerically by the collocation method and implemented in MATLAB. The study determines the flow profiles and the impact of the flow parameters on the flow variables. Joule heating, variable viscosity, viscous dissipation, skin friction, the rate of heat transfer, and the induced magnetic field are taken into account. The obtained results are presented graphically and the impact of varying flow parameters on the skin friction coefficient and the Nusselt number is presented in tabular form. These results indicate that an increase in the Reynolds number, Eckert’s number, and the Joule heating parameter increases the fluid’s velocity, while an increase in the Hartmann number and the unsteadiness parameter decreases the convective heat transfer and the fluid’s velocity. Further, the skin friction coefficient decreases with increase in the Reynolds number, the Hartmann number, and the Joule heating parameter. Therefore, a less viscous fluid is appropriate to facilitate the fluid’s motion, but the presence of high magnetic field reduces the fluid’s motion.

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Abstract:The unsteady, laminar hydro magnetic flow of an incompressible, viscous and electrically conducting Newtonian fluid over a contracting sheet embedded in a porous medium has been investigated. The flow takes place between two parallel flat sheets that are made of an electrically non-conducting material. The fluid is subjected to transverse magnetic field that cuts perpendicularly across the flow in the positive direction of the z-axis. The contracting sheet has a permeable surface while the surface of other sheet is impermeable, each sheet has an isothermal surface and both sheets are kept at different temperature of T W andT ∞ such that the temperature differences within the flow are sufficiently small. The effect of varying various parameters on the velocity and temperature profiles has been discussed. The coupled non-linear partial differential equations governing the flow have been solved numerically using the finite difference method because of its accuracy, stability and convergence. The results that are obtained are then presented graphically and observations have been discussed. Changes in various parameters have been observed to alter the velocity profiles and temperature profiles.