In this article, combined effects of magnetohydrodynamics (MHD) heat transfer flow under the influence of slip over a moving flat plate are investigated. Effects of entropy generation are also examined. A set of non-dimensional resulting equations are solved by means of Bvp4c Matlab package. The role of flow parameters like magnetic parameter and slip parameter on flow velocity profile and temperature profile are presented and elaborated through graphs. The expressions for entropy generation and flow against Bejan number are also examined. The obtained results reveal that for various values of slip parameter, the Bejan number (Be) decreases for λ > 1, whereas opposite behaviour is noted for λ < 1.

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Using the vortex filament model and the Gross Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantised vortex lines in helium II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, Kelvin waves of large amplitude are generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.

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In this paper we determine the velocity, the energy and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number w, given by the ratio of the number of meridian wraps to that of the longitudinal wraps. We find that for w < 1 vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for w > 1 knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by the writhe contribution. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, that are found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid 4 He.