An oscillating hydromagnetic non-Newtonian flow in a rotating system

AbstractAn exact solution of an oscillatory boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and the other at rest, is developed. The fluid and the plates are in a state of solid body rotation with constant angular velocity about the z-axis normal to the plates. The fluid is assumed to be second grade, incompressible, and electrically conducting. A uniform transverse magnetic field is applied. During the mathematical analysis, it is found that the steady part of the solution is identical to that of viscous fluid. The structure of the boundary layers is also discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered

Resonant oscillations of a plate in an electrically conducting rotating Johnson-Segalman fluid

AbstractAn analysis of hydromagnetic flow is examined in a semi-infinite expanse of electrically conducting rotating Johnson-Segalman fluid bounded by nonconducting plate in the presence of a transverse magnetic field and the governing equations are modeled first time. The structure of the velocity distribution and the associated hydromagnetic boundary layers are investigated including the case of resonant oscillations. It is shown that unlike the hydrodynamic situation for the case of resonance, the hydromagnetic steady solution satisfies the boundary condition at infinity. The inherent difficulty involved in the hydrodynamic resonance case has been resolved in the presence analysis

Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation

Background: Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature. Methods: The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t), the Grashof number (Gr), the Prandtl number (Pr), and the phase angle (ωt). Skin friction and the Nusselt number are also evaluated. Results: The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver–Stehfest algorithm. Conclusion: The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number (Pr), and the phase angle (ωt)

MHD free convection-radiation interaction in a porous medium - part I : numerical investigation

A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement

Oscillatory dissipative conjugate heat and mass transfer in chemically-reacting micropolar flow with wall couple stress : a finite element numerical study

High temperature non-Newtonian materials processing provides a stimulating area for process engineering simulation. Motivated by emerging applications in this area, the present article investigates the time-dependent free convective flow of a chemically-reacting micropolar fluid from a vertical plate oscillating in its own plane adjacent to a porous medium. Thermal radiative, viscous dissipation and wall couple stress effects are included. The Rosseland diffusion approximation is used to model uni-directional radiative heat flux in the energy equation. Darcy’s model is adopted to mimic porous medium drag force effects. The governing two-dimensional conservation equations are normalized with appropriate variables and transformed into a dimensionless, coupled, nonlinear system of partial differential equations under the assumption of low Reynolds number. The governing boundary value problem is then solved under physically viable boundary conditions numerically with a finite element method based on the weighted residual approach. Graphical illustrations for velocity, micro-rotation (angular velocity), temperature and concentration are obtained as functions of the emerging physical parameters i.e. thermal radiation, viscous dissipation, first order chemical reaction parameter etc. Furthermore, friction factor (skin friction), surface heat transfer and mass transfer rates have been tabulated quantitatively for selected thermo-physical parameters. A comparison with previously published paper is made to check the validity and accuracy of the present finite element solutions under some limiting cases and excellent agreement is attained. Additionally, a mesh independence study is conducted. The model is relevant to reactive polymeric materials processing simulation

Finite element analysis of rotating oscillatory magneto-convective radiative micropolar thermo-solutal flow

Micropolar fluids provide an alternative mechanism for simulating micro-scale and molecular fluid mechanics which require less computational effort. In the present paper, a numerical analysis is conducted for the primary and secondary flow characterizing dissipative micropolar convective heat and mass transfer from a rotating vertical plate with oscillatory plate velocity, adjacent to a permeable medium. Owing to high temperature, thermal radiation effects are also studied. The micropolar fluid is also chemically-reacting, both thermal and species (concentration) buoyancy effects and heat source/sink are included. The entire system rotates with uniform angular velocity about an axis normal to the plate. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. The partial differential equations governing the flow problem are rendered dimensionless with appropriate transformation variables. A Galerkin finite element method is employed to solve the emerging multi-physical components of fluid dynamics problem are examined for a variety of parameters including rotation parameter, radiation-conduction parameter, micropolar coupling parameter, Eckert number (dissipation), reaction parameter, magnetic body force parameter and Schmidt number. A comparison with previously published article is made to check the validity and accuracy of the present finite element solutions under some limiting case and excellent agreement is attained. The current simulations may be applicable to various chemical engineering systems, oscillating rheometry, and rotating MHD energy generator near-wall flows

Finite element computation of magnetohydrodynamic nanofluid convection from an oscillating inclined plate with radiative flux, heat source and variable temperature effects

The present work describes finite element computations for radiative magnetohydrodynamic convective Newtonian nanofluid flow from an oscillating inclined porous plate with variable temperature. Heat source/sink and buoyancy effects are included in the mathematical model. The problem is formulated by employing Tiwari-Das nanofluid model and two water - based nanofluids with spherical shaped metal nano particles as copper and alumina are considered. The Brinkman and Maxwell-Garnetts models are used for the dynamic viscosity and effective thermal conductivity of the nanofluids respectively. An algebraic flux model, the Rosseland diffusion approximation is adopted to simulate thermal radiative flux effects. The dimensionless, coupled governing partial differential equations are numerically solved via the finite element method with weak variational formulation by imposing initial and boundary conditions with a weighted residual scheme. A grid independence study is also conducted. The finite element solutions are reduced to known previous solutions in some limiting cases of the present investigation and are found to be in good agreement with published work. This investigation is relevant to electromagnetic nanomaterial manufacturing processes operating at high temperatures where radiation heat transfer is significant

Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model

Nonlinear, steady-state, viscous flow and heat transfer between two stretchable rotating disks spinning at dissimilar velocities is studied with a non-Fourier heat flux model. A non-deformable porous medium is intercalated between the disks and the Darcy model is employed to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the Von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless dimensionless parameters i.e. Prandtl number, upper disk stretching, lower disk stretching, permeability, non-Fourier thermal relaxation and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to to rotating disk bioreactors in chemical engineering

Mixed convection flow of viscous and second grade fluids due to non–coaxial rotation

Unsteady flow of viscous and second grade fluids in non-coaxial rotation past a vertical oscillating disk have been studied by a number of researchers due to wide applications in boundary layer control, food processing, mixer machines and cooling turbine blades. Therefore, in this research, heat and mass transfer of viscous and second grade fluids were studied. The effect of magnetohydrodynamics (MHD) flow through a porous medium was considered. The main purpose of this study was to obtain the exact solutions for four problems of non-coaxial rotating flow. Two problems were studied for viscous fluid, whereas another two problems were studied for second grade fluid. All problems were considered in mixed convection flow and without magnetic and porosity effects. Appropriate non-dimensional variables were used to simplify the governing equations into non-dimensional equations along with initial and boundary conditions. Through this non-dimensional process, the non-dimensional parameters such as Grashof number, modified Grashof number, Prandtl number, Schmidt number, velocity of oscillation, magnetic, porosity and second grade fluid were obtained. The exact solutions for velocity, temperature and concentration expressions were obtained by using Laplace transform technique. From these corresponding expressions, the skin friction, Nusselt number and Sherwood number were calculated. The solutions were plotted graphically to discuss the influence of non-dimensional parameters in velocity, temperature and concentration profiles. Results show that, velocity profile with magnetic effect is lower compared to velocity without magnetic effect, whereas the velocity with heat and mass transfer phenomena is higher than just a heat transfer. It is also observed that velocity of second grade fluid solutions is always lower compared to the velocity of viscous fluid. All the obtained results are compared with published results and found to be in good agreement, validating the obtained solutions. The exact solutions obtained in this thesis provide an interesting and complete benchmark to verify numerical schemes for solving different complex flow situations