Abstract: Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.
Abstract: A numerical approach of the effectiveness of numerous
parameters on magnetohydrodynamic (MHD) natural convection
heat and mass transfer problem of a dusty micropolar fluid in
a non-Darcy porous regime is prepared in the current paper.
In addition, a convective boundary condition is scrutinized into
the micropolar dusty fluid model. The governing boundary layer
equations are converted utilizing similarity transformations to a
system of dimensionless equations to be convenient for numerical
treatment. The resulting equations for fluid phase and dust phases
of momentum, angular momentum, energy, and concentration with
the appropriate boundary conditions are solved numerically applying
the Runge-Kutta method of fourth-order. In accordance with the
numerical study, it is obtained that the magnitude of the velocity
of both fluid phase and particle phase reduces with an increasing
magnetic parameter, the mass concentration of the dust particles, and
Forchheimer number. While rises due to an increment in convective
parameter and Darcy number. Also, the results refer that high values
of the magnetic parameter, convective parameter, and Forchheimer
number support the temperature distributions. However, deterioration
occurs as the mass concentration of the dust particles and Darcy
number increases. The angular velocity behavior is described by
progress when studying the effect of the magnetic parameter and
microrotation parameter.
Abstract: This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number Pr, magnetic field parameter M, Peclet number Pe, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.
Abstract: Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.
Abstract: The problem of thermal convection in temperature and
magnetic field sensitive Newtonian ferromagnetic liquid is studied
in the presence of uniform vertical magnetic field and throughflow.
Using a combination of Galerkin and shooting techniques the critical
eigenvalues are obtained for stationary mode. The effect of Prandtl
number (Pr > 1) on onset is insignificant and nonlinearity of
non-buoyancy magnetic parameter M3 is found to have no influence
on the onset of ferroconvection. The magnetic buoyancy number, M1
and variable viscosity parameter, V have destabilizing influences on
the system. The effect of throughflow Peclet number, Pe is to delay
the onset of ferroconvection and this effect is independent of the
direction of flow.
Abstract: High-speed transportation is a growing concern. To develop high-speed rails and to increase high-speed efficiencies, the idea of Hyperloop was introduced. The challenge is to overcome the difficulties of managing friction and air-resistance which become substantial when vehicles approach high speeds. In this paper, we are presenting the methodologies of the capsule design which got a design concept innovation award at SpaceX competition in January, 2016. MATLAB scripts are written for the levitation and propulsion calculations and iterations. Computational Fluid Dynamics (CFD) is used to simulate the air flow around the capsule considering the effect of the axial-flow air compressor and the levitation cushion on the air flow. The design procedures of a single-sided linear induction motor are analyzed in detail and its geometric and magnetic parameters are determined. A structural design is introduced and Finite Element Method (FEM) is used to analyze the stresses in different parts. The configuration and the arrangement of the components are illustrated. Moreover, comments on manufacturing are made.
Abstract: Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of elliptic cross
section under the influence of magnetic field and constant pressure
gradient has been obtained in this paper. Initially, the flow is
generated by a constant pressure gradient. After attaining the steady
state, the pressure gradient is suddenly withdrawn and the resulting
fluid motion in a tube of elliptical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
the first stage is a steady motion in tube under the influence of a
constant pressure gradient, the second stage concern with an unsteady
motion. The problem is solved employing separation of variables
technique. The results are expressed in terms of a non-dimensional
porosity parameter, magnetic parameter and elastico-viscosity
parameter, which depends on the Non-Newtonian coefficient. The
flow parameters are found to be identical with that of Newtonian case
as elastic-viscosity parameter, magnetic parameter tends to zero, and
porosity tends to infinity. The numerical results were simulated in
MATLAB software to analyze the effect of Elastico-viscous
parameter, porosity parameter, and magnetic parameter on velocity
profile. Boundary conditions were satisfied. It is seen that the effect
of elastico-viscosity parameter, porosity parameter and magnetic
parameter of the bounding surface has significant effect on the
velocity parameter.
Abstract: Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of spherical cross
section under the influence of magnetic field and constant pressure
gradient has been obtained in this paper. Initially, the flow is
generated by a constant pressure gradient. After attaining the steady
state, the pressure gradient is suddenly withdrawn and the resulting
fluid motion in a tube of spherical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
the first stage is a steady motion in tube under the influence of a
constant pressure gradient, the second stage concern with an unsteady
motion. The problem is solved employing separation of variables
technique. The results are expressed in terms of a non-dimensional
porosity parameter (K), magnetic parameter (m) and elasticoviscosity
parameter (β), which depends on the Non-Newtonian
coefficient. The flow parameters are found to be identical with that of
Newtonian case as elastic-viscosity parameter and magnetic
parameter tends to zero and porosity tends to infinity. It is seen that
the effect of elastico-viscosity parameter, porosity parameter and
magnetic parameter of the bounding surface has significant effect on
the velocity parameter.
Abstract: Exact solution of an unsteady flow of elastico-viscous
electrically conducting fluid through a porous media in a tube of
elliptical cross section under the influence of constant pressure
gradient and magnetic field has been obtained in this paper. Initially,
the flow is generated by a constant pressure gradient. After attaining
the steady state, the pressure gradient is suddenly withdrawn and the
resulting fluid motion in a tube of elliptical cross section by taking
into account of the transverse magnetic field and porosity factor of
the bounding surface is investigated. The problem is solved in twostages
the first stage is a steady motion in tube under the influence of
a constant pressure gradient, the second stage concern with an
unsteady motion. The problem is solved employing separation of
variables technique. The results are expressed in terms of a nondimensional
porosity parameter (K), magnetic parameter (m) and
elastico-viscosity parameter (β), which depends on the Non-
Newtonian coefficient. The flow parameters are found to be identical
with that of Newtonian case as elastic-viscosity parameter and
magnetic parameter tends to zero and porosity tends to infinity. It is
seen that the effect of elastico-viscosity parameter, magnetic
parameter and the porosity parameter of the bounding surface has
significant effect on the velocity parameter.
Abstract: The present analysis considers the steady stagnation point flow and heat transfer towards a permeable shrinking sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow and a local heat generation within the boundary layer, with a heat generation rate proportional to (T-T)p Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the stretching/shrinking parameter λ, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value λc whose value depends on the value of M, K, and s. In the presence of internal heat absorption (Q
Abstract: An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.
Abstract: The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.
Abstract: Unsteady magnetohydrodynamics (MHD) boundary
layer flow and heat transfer over a continuously stretching surface in
the presence of radiation is examined. By similarity transformation,
the governing partial differential equations are transformed to a set of
ordinary differential equations. Numerical solutions are obtained by
employing the Runge-Kutta-Fehlberg method scheme with shooting
technique in Maple software environment. The effects of
unsteadiness parameter, radiation parameter, magnetic parameter and
Prandtl number on the heat transfer characteristics are obtained and
discussed. It is found that the heat transfer rate at the surface
increases as the Prandtl number and unsteadiness parameter increase
but decreases with magnetic and radiation parameter.
Abstract: This paper presents an approach which is based on the
use of supervised feed forward neural network, namely multilayer
perceptron (MLP) neural network and finite element method (FEM)
to solve the inverse problem of parameters identification. The
approach is used to identify unknown parameters of ferromagnetic
materials. The methodology used in this study consists in the
simulation of a large number of parameters in a material under test,
using the finite element method (FEM). Both variations in relative
magnetic permeability and electrical conductivity of the material
under test are considered. Then, the obtained results are used to
generate a set of vectors for the training of MLP neural network.
Finally, the obtained neural network is used to evaluate a group of
new materials, simulated by the FEM, but not belonging to the
original dataset. Noisy data, added to the probe measurements is used
to enhance the robustness of the method. The reached results
demonstrate the efficiency of the proposed approach, and encourage
future works on this subject.
Abstract: A conjugate heat transfer for steady two-dimensional
mixed convection with magnetic hydrodynamic (MHD) flow of an
incompressible quiescent fluid over an unsteady thermal forming
stretching sheet has been studied. A parameter, M, which is used to
represent the dominance of the magnetic effect has been presented in
governing equations. The similar transformation and an implicit
finite-difference method have been used to analyze the present
problem. The numerical solutions of the flow velocity distributions,
temperature profiles, the wall unknown values of f''(0) and '(θ (0) for
calculating the heat transfer of the similar boundary-layer flow are
carried out as functions of the unsteadiness parameter (S), the Prandtl
number (Pr), the space-dependent parameter (A) and
temperature-dependent parameter (B) for heat source/sink and the
magnetic parameter (M). The effects of these parameters have also
discussed. At the results, it will produce greater heat transfer effect
with a larger Pr and M, S, A, B will reduce heat transfer effects. At
last, conjugate heat transfer for the free convection with a larger G has
a good heat transfer effect better than a smaller G=0.
Abstract: A steady two-dimensional magnetohydrodynamics
flow and heat transfer over a stretching vertical sheet influenced by
radiation and porosity is studied. The governing boundary layer
equations of partial differential equations are reduced to a system of
ordinary differential equations using similarity transformation. The
system is solved numerically by using a finite difference scheme
known as the Keller-box method for some values of parameters,
namely the radiation parameter N, magnetic parameter M, buoyancy
parameter l , Prandtl number Pr and permeability parameter K. The
effects of the parameters on the heat transfer characteristics are
analyzed and discussed. It is found that both the skin friction
coefficient and the local Nusselt number decrease as the magnetic
parameter M and permeability parameter K increase. Heat transfer
rate at the surface decreases as the radiation parameter increases.