Nanofluid two phase model analysis in existence of induced magnetic field

The heat generation/absorption and thermo-diffusion on an unsteady free convective MHD flow of radiating and chemically reactive second grade fluid near an infinite vertical plate through a porous medium and taking the Hall current into account have been studied. Assume that the bounding plate has a ramped temperature with a ramped surface concentration and isothermal temperature with a ramped surface concentration. The analytical solutions for the governing equations are obtained by making use of the Laplace transforms technique. The velocity, temperature, and concentration profiles are discussed through graphs. We also found that velocity, temperature, and concentration profiles in the case of ramped temperature with ramped surface concentrations are less than those of isothermal temperature with ramped surface concentrations. Also, the expressions of the skin friction, Nusselt number, and Sherwood number are obtained and represented computationally through a tabular form.

Hall effects on unsteady MHD flow of second grade fluid through porous medium with ramped wall temperature and ramped surface concentration

Melting heat transfer in boundary layer stagnation-point flow of nanofluid toward a stretching sheet with induced magnetic field

In this paper, the influence of induced magnetic field on free convection of Al2O3-water nanofluid on permeable plate by means of Koo-Kleinstreuer-Li (KKL) model is reported. Impact of Brownian motion, along with the properties of nanofluid, are also taken into account. The resulting equations are solved utilizing Runge-Kutta integration method. Obtained results are examined for innumerable energetic parameters, namely Al2O3 volume fraction, suction parameter, and Hartmann and magnetic Prandtl numbers. Results indicate that the velocity profile reduces with rise of the suction parameter and magnetic Prandtl and Hartmann numbers but it increases with addition of nanoparticles. Shear stress enhances with rise of suction parameter, magnetic Prandtl and Hartmann numbers. Temperature gradient improves with augment of suction parameter.

Influence of Induced Magnetic Field on Free Convection of Nanofluid Considering Koo-Kleinstreuer-Li (KKL) Correlation

Heat transfer—A review of 2005 literature

An exact solution is presented for the hydromagnetic natural convection boundary layer flow past an infinite vertical flat plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained for the non-dimensional velocity (u), non-dimensional induced magnetic field component (B
 x
 ) and wall frictional shearing stress i.e. skin friction function (τ
 x
 ) as functions of dimensionless transverse coordinate (η), Grashof free convection number (G
 r
 ) and the Hartmann number (M). The bulk temperature in the boundary layer (Θ) is also evaluated and shown to be purely a function of M. The Rayleigh flow distribution (R) is derived and found to be a function of both Hartmann number (M) and the buoyant diffusivity parameter (ϑ
 *). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region and intensifies with greater magnetic field i.e. larger Hartman number M, for constant buoyant diffusivity parameter ϑ
 *. The induced magnetic field (B
 x
 ), is elevated in the vicinity of the plate surface with a rise in free convection (buoyancy) parameter G
 r
 , but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.

Hydromagnetic free convection flow with induced magnetic field effects

Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters Asymptotic behavior of the solution is analyzed for large M
 2 (Hartmann number squared) and K
 2 (rotation parameter) The heat transfer aspect is considered also with Joule and viscous heating effects present Boundary layers arise close to the channel walls for large K
 2, ie strong rotation of the channel For slowly rotating systems (small K
 2), Hall current parameter (m) reduces primary mass flow rate (Q
 x
 /R
 ρ
 v) Heat transfer rate at the upper plate (d
 θ/d
 η)
 η=1 decreases, while at the lower plate (d
 θ/d
 η)
 η=−1 increases, with increase in either K
 2 or m For constant values of the rotation parameter, K
 2, heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Oscillatory MHD Couette flow of electrically conducting fluid between two parallel plates in a rotating system in the presence of an inclined magnetic field is considered when the upper plate is held at rest and the lower plate oscillates non-torsionally . An exact solution of the governing equations has been obtained by using Laplace transform technique. Asymptotic behavior of the solution is analyzed for M 2 ≪1, K 2 ≪1 and ω ≪1 and for large M 2, K 2 and ω. Numerical results of velocities are depicted graphically and the frictional shearing stresses are presented in tables. It is found that a thin boundary layer is formed near the lower plate, for large values of rotation parameter K 2, Hartman number M 2 and frequency parameter ω. The thickness of this boundary layer increases with increase in inclination of the magnetic field with the axis of rotation.

Oscillatory Couette flow in the presence of an inclined magnetic field

We have studied the unsteady Couette flow of a viscous incompressible fluid confined between parallel plates, rotating with an uniform angular velocity about an axis normal to the plates. The flow is induced by the motion of the upper plate and the fluid and plates rotate in unison with the same constant angular velocity. An exact solution of the governing equations have been obtained for small and large time τ by applying Laplace transform technique. It is found that the primary velocity decreases with increase in rotation parameter for small as well as large time. It is interesting to note that a back flow occurs in the region 0.0 ⩽ η ⩽ 0.7 for large time with increase in K when K = 4 and 5. The secondary velocity increases in magnitude for small time with increase in rotation parameter. It is observed that the secondary velocity increases in magnitude for small values of rotation parameter. On the other hand, for large values of rotation parameter K 2 , it decreases near the stationary plate and increases near the moving plate. The shear stress due to primary flow decreases with increase in rotation parameter K 2 . On the other hand, it increases due to secondary flow with increase in rotation parameter for small time. It is noticed that for large time there exists separation in the primary and secondary flows due to high rotation.

S. K. Ghosh

Papers

Hydromagnetic free convection flow with induced magnetic field effects

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Oscillatory Couette flow in the presence of an inclined magnetic field

Unsteady Couette flow in a rotating system