Life-span of classical solutions for one-dimensional hydromagnetic flow

The paper concerns Cauchy,problem for one-dimensional hydromagnetic dynamics with dissipative terms. When the dissipation coefficient is equal to zero it is shown that the smooth solutions develop shocks in the finite time if the initial amounts of entropy and magnetic field are smaller than those of sound waves; when it is larger than zero, and the initial amounts of entropyI this dissipation coefficient and the magnetic field in each period are smaller than those of sound Waves, then the smooth solutions blow up in the finite time. Moreover, the life-span of the smooth solution is given.

On Inherent Irreversibility in a Reactive Hydromagnetic Channel Flow

This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a transversely imposed magnetic field.Using a perturbation method coupled with a special type of Hermite-Pade' approximation technique,the simplified governing non-linear equation is solved and the important properties of overall flow structure including velocity field,temperature field and thermal criticality conditions are derived which essentially expedite to obtain expressions for volumetric entropy generation numbers,irreversibility distribution ratio and the Bejan number in the flow field.

Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo–Christov Heat Diffusion Theory

Heat transport phenomenon of two-dimensional magnetohydrodynamie Casson fluid flow by employing Cattaneo-Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Fhrther, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo-Christov heat diffusion model when matched with the profiles obtained for Fourier＇s theory of heat flux.

Influence of temperature dependent heat source/sink on transient MHD free convective flow in an infinite rigid impermeable vertical cylinder with chemical reaction

It is increasingly apparent that the inclusion of mass transfer aspects,together with certain thermal conditions,in the momentum and energy equations governing MHD flows leads to a numbers of real life applications.Keeping this in view,we have attempted an exact analysis of heat and mass transfer aspects in transient hydromagnetic free convective flow of an incompressible viscous fluid through a vertical pipe under an externally applied magnetic field,assuming presence of chemical reaction and heat source/sink.The governing PDEs,which simplify to a set of 3 linear ODEs in the physical set up considered here,have been solved using Laplace transform technique,with solutions for key physical variables presented in the term of Bessel and modified Bessel functions.The influence of governing non-dimensional parameters,namely,Hartmann number,Schmidt number,source/sink parameter,Prandtl number and chemical reaction parameter,has been illustrated on the developing velocity and some concentration profiles.Some important quantities of engineering interest-surface skin friction and volumetric flow rates-have been computed too and analysed.Some notable finding worth mentioning are:(a)heat source presence causes higher fluid velocity as compared to the heat sink;(b)all important surface shear stress can be suitably controlled,among others,by chemical reaction parameter and Schmidt number.The key challenge of this study has been to obtain exact closed-form solutions of the field equations,including cumbersome Laplace inverses.This study finds innovative applications in the emerging fields such as magnetic materials processing,chemical processes,solar energy systems,etc.

Peristaltic transport of a conducting Jeffrey fluid in an inclined asymmetric channel

Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ1, the Froude number Fr, the perturbation parameter 5, the angle of inclination θ and the phase difference Ф. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.