Exact solutions for the unsteady rotational flow of a generalized second grade fluid through a circular cylinder

Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t = 0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis with a time dependent angular velocity Ωt. The solutions that have been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for the ordinary second grade and Newtonian fluids, performing the same motion, are obtained as special cases of our general solution

Unsteady newtonian and non-newtonian fluid flows in the circular tube in the presence of magnetic field using caputo-fabrizio derivative

This thesis investigates analytically the magnetohydrodynamics (MHD) transport of Newtonian and non-Newtonian fluids flows inside a circular channel. The flow was subjected to an external electric field for the Newtonian model and a uniform transverse magnetic field for all models. Pressure gradient or oscillating boundary condition was employed to drive the flow. In the first model Newtonian fluid flow without stenotic porous tube was considered and in the second model stenotic porous tube was taken into account. The third model is concerned with the temperature distribution and Nusselt number. The fourth model investigates the non-Newtonian second grade fluid velocity affected by the heat distribution and oscillating walls. Last model study the velocity, acceleration and flow rate of third grade non-Newtonian fluid flow in the porous tube. The non-linear governing equations were solved using the Caputo-Fabrizio time fractional order model without singular kernel. The analytical solutions were obtained using Laplace transform, finite Hankel transforms and Robotnov and Hartley’s functions. The velocity profiles obtained from various physiological parameters were graphically analyzed using Mathematica. Results were compared with those reported in the previous studies and good agreement were found. Fractional derivative and electric field are in direct relation whereas magnetic field and porosity are in inverse relation with respect to the velocity profile in Newtonian flow case. Meanwhile, fractional derivative and Womersely number are in direct relation whereas magnetic field, third grade parameter, frequency ratio and porosity are in inverse relation in third grade non-Newtonian flow case. In the case of second grade fluid, Prandtl number, fractional derivative and Grashof number are in direct relation whereas second grade parameter and magnetic field are in inverse relation. The fluid flow model can be regulated by applying a sufficiently strong magnetic field

Modelling and design of a dual channel magnetorheological damper

© Cranfield UniversityA limitation with the current analytical models for predicting the performance of a magnetorheological (MR) damper is that they fail to capture the hysteretic variation of force versus velocity variation correctly. This can significantly underestimate the damper force and overestimate the dynamic range of the device. In this work a transient analytical fluid dynamics model is developed by using a combination of Laplace and Weber transform and Duhamel’s superposition of velocity boundary condition, to overcome these limitations. The solution of the system of nonlinear simultaneous equations, obtained by applying mass flow balance, velocity compatibility conditions and force equilibrium of Bingham plastic plug flow, gives the damper force. This method is shown to generate direct and inverse model of an MR device. The proposed model has been validated against a commercially available MR damper at low speed, to a range of test signals. The mean error using the above model has been shown to be 5% for all the test signals. This compares well with three conventional models which give; transient constant velocity model 35%, quasi static model 35% and phenomenological model 35%. The phenomenological model gives 10% mean error for a sinusoidal input signal. The application of the proposed analytical model has been demonstrated by the design of a novel dual channel damper. The design of the electromechanical components has been shown to be np-hard problem and the optimisation using genetic algorithm has been applied to minimise the volume and electrical time constant. The performance of the dual channel damper has been simulated for various combinations of values of shear yield stress for two channels. Compared to the conventional single channel damper the novel design is shown to give 30% higher damper force, 50% improved dynamic range and limits the effect of transients to within 10% of the damper force. The dual channel damper is an effective solution to resist the onset of turbulent flow in the channels up to 20m/s piston velocity