Closed-form solutions are presented for the transient hydromagnetic flow in a rotating channel with inclined applied magnetic field under the influence of a forced oscillation. Magnetic Reynolds number is large enough to permit the inclusion of magnetic induction effects. The Maxwell displacement current effect is also included and simulated via a dielectric strength parameter. The governing momentum and magnetic induction conservation equations are normalized with appropriate transformations and the resulting quartet of partial differential equations are solved exactly. A parametric study is performed of the influence of oscillation frequency parameter (ω), time (T), inverse Ekman number, i.e. rotation parameter (K2), square of the Hartmann magnetohydrodynamic (MHD) parameter (M2), and magnetic field inclination (θ) on the primary and secondary induced magnetic field components (bx, by) and velocity components (u, v) across the channel. Network solutions are also obtained to validate the exact solutions and shown to be in excellent agreement. Applications of the study arise in planetary plasma physics and rotating MHD induction power generators and also astronautical flows.

Transient hydromagnetic flow in a rotating channel permeated by an inclined magnetic field with magnetic induction and Maxwell displacement current effects

The effect of an inclined magnetic field in the peristaltic flow of a Jeffrey fluid with variable thermal conductivity is discussed. The temperature dependent thermal conductivity of fluid in an asymmetric channel is taken into account. A dimensionless nonlinear system subject to a long wavelength and a low Reynolds number is solved. The explicit expressions of the stream function, the axial velocity, the pressure gradient, and the temperature are obtained. The effects of all physical parameters on peristaltic transport and heat transfer characteristics are observed from graphical illustrations. The behaviors of θ ∈ [0, π/2] and θ ∈ [π/2, π] on fluid flow and heat transfer are found to be opposite. Further, the size of trapped bolus is greater for the case of the inclined magnetic field (θ ≠ π/2) than that for the case of the transverse magnetic field (θ = π/2). The heat transfer coefficient decreases when the constant thermal conductivity (Newtonian) fluid is changed to the variable thermal conductivity (Jeffrey) fluid.

Heat transfer analysis in peristaltic flow of MHD Jeffrey fluid with variable thermal conductivity

Unsteady hydromagnetic flow of a viscous incompressible electrically conducting fluid confined between rotating parallel plate non-conducting channel flow under the influence of an oscillating pressure gradient permeated by anuniform transverse magnetic field of which induced magnetic field is taken into account, is studied. The solution in dimensionless form contains four flow parameters viz., α m , E , P m and ω are, respectively, the magnetic interaction parameter, Ekman number, magnetic Prandtl number and frequency parameter. Asymptotic behaviour of the solution is analysed for large ω. The numerical results of velocity, induced magnetic field and shear stress are shown graphically and the mean sectional velocities are presented numerically.

Unsteady Hydromagnetic Flow in a Rotating Channel with Oscillating Pressure Gradient

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system in the presence of an inclined magnetic field taking Hall current into account is studied. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel. Exact solution of the governing equations is obtained by Laplace transform technique. The expression for the shear stress at the moving plate is also derived. Asymptotic behavior of the solution is analyzed for small and large values of time t to highlight (i) the transient approach to the final steady state flow and (ii) the effects of Hall current, magnetic field, rotation and angle of inclination of magnetic field on the flow-field. It is found that Hall current and rotation tend to accelerate fluid velocity in both the primary and secondary flow directions. Magnetic field has retarding influence on the fluid velocity in both the primary and secondary flow directions. Angle of inclination of magnetic field has accelerating influence on the fluid velocity in both the primary and secondary flow directions.

https://jafmonline.net/JournalArchive/download?file_ID=15365&issue_ID=208

Effects of Hall Current and Rotation on Unsteady MHD Couette Flow in the Presence of an Inclined Magnetic Field

The magnetohydrodynamic (MHD) Couette flow of two immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied electric and inclined magnetic field has been investigated in the paper. Both fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations, and closed-form solutions are obtained in both fluid regions of the channel. Separate solutions with appropriate boundary conditions for each fluid have been obtained, and these solutions have been matched at the interface using suitable matching conditions. The analytical results for various values of the Hartmann number, the angle of magnetic field inclination, loading parameter, and the ratio of fluid heights have been presented graphically to show their effect on the flow and heat transfer characteristics.

/pdf/flow-and-heat-transfer-of-two-immiscible-fluids-in-the-4oixhppjxt.pdf

S.K. Ghosh

Papers

Unsteady hydromagnetic flow in a rotating channel in the presence of inclined magnetic field

A note on steady and unsteady hydromagnetic flow in a rotating channel in the presence of inclined magnetic field