Unsteady MHD Natural Convective Flow of a Rotating Walters’-B Fluid Over an Oscillating Plate with Fluctuating Wall Temperature and Concentration

Abstract

In the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.

Steady MHD mixed convection flow of a viscoelastic fluid over a magnetized convectively heated vertical surface with Hall current and induced magnetic field effects

“…On using the zeroth-and first-order solutions for the induced magnetic fields (28) and (30) in Equation 20…”

“…Furthermore, it is assumed that the Boussinesq and boundary layer approximations hold good. In light of the above made assumptions and approximations, the system of equations describing the steady mixed convection flow of a viscoelastic fluid over a magnetized convectively heated vertical surface with Hall current and induced magnetic field effects are given by Garg et al 22 and Singh et al 28 …”

“…Analysis of the dynamics of the viscoelastic fluid in the presence of magnetic field is of great importance in practical point of view because of its tremendous applications in gas reservoirs, petroleum drilling, and production of complex multiphase products, such as paints, inks, and ceramic pastes. Motivated by huge industrial applications, recently deep and extensive investigations were carried out by researchers 20‐30 to analyze the motion of viscoelastic fluid under the effect of external magnetic field considering various flow situations. The thermophysical aspects of magnetohydrodynamic (MHD) viscoinelastic fluid over a stretching surface were recently presented by Hussain et al 31 The study of convective heat and mass transfer in a MHD flow regime is important because of its usage in various natural phenomena and engineering applications, such as plasma studies, porous insulations, spreading of pollutants, and so forth.…”

Hall and ion‐slip effects on MHD free convection flow of rotating Jeffrey fluid over an infinite vertical porous surface

“…Singh et al 42 discussed the mixed convection hydromagnetic flow of an incompressible, electrically and thermally conducting and chemically reacting viscoelastic fluid through a vertical porous channel filled with a porous medium in addition to the effects of Hall and ion‐slip currents, rotation, heat radiation, and chemical reaction. The unsteady MHD boundary layer flow of a rotating Walter's B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration, taking Hall and ion‐slip effects into consideration, is discussed by Singh et al 43 Singh et al 44 presented an analytical study on an unsteady MHD boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with an oscillating freestream, taking Hall and ion‐slip currents into account. An analysis for the steady hydromagnetic mixed convective generalized Couette flow between two infinite parallel plates of arbitrary electrical conductivities and finite thicknesses, filled with a porous medium, in the presence of a uniform transverse magnetic field in a rotating system with the Hall effect has been presented by Singh et al 45 The mixed convection hydromagnetic flow of a viscous, incompressible, and electrically and thermally conducting fluid in a rotating channel, taking Hall current into account, was studied by Seth and Singh 46 …”

Hall and induced magnetic field effects on convective flow of viscoelastic fluid within an inclined channel with periodic surface conditions

“…In practical point of view this subject is important due to production of complex multiphase products such as inks, paints and ceramic liquids. Stimulated from the diverse applications the eminent researchers [25][26][27][28][29][30][31][32][33][34][35][36] discussed the behaviour of viscoelastic fluid flow in the presence of magnetic field considering various flow configurations. In many industrial applications such as solar chimneys, ventilation devices and cooling systems where the heated surfaces are inclined, the angular location is important to study the convective heat transfer.…”