DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) https://hdl.handle.net/10539/20256 2021-10-16T18:37:07Z Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis. https://hdl.handle.net/10539/20434 Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis. Freidoonimehr, N.; Rashidi, M.M.; Abelman, S.; Lorenzini, G. The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number. 2016-04-26T00:00:00Z Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions. https://hdl.handle.net/10539/20433 Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions. Naz, R.; Mahomed, F.M. We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass density g(x), and the applied load denoted by f(u), a function of transverse displacement u(t,x). The complete Lie group classification is obtained for different forms of the variable lineal mass density g(x) and applied load f(u). The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms of g(x). For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature when g(x) is constant with variable applied load f(u). For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions. 2015-01-01T00:00:00Z Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation. https://hdl.handle.net/10539/20432 Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation. Khan, M.; Abelman, S.; Mahomed, F.M. The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates.The exact steady-state solution for the nonlinear problem is obtained.Thereduction of the nonlinear initial value problem is carried out by using a similarity transformation.The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented. 2015-01-01T00:00:00Z Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM. https://hdl.handle.net/10539/20431 Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM. Rashidi, M.M.; Freidoonimehr, N.; Momoniat, E.; Rostami, B. In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics. 2015-08-12T00:00:00Z