Values Of Magnetic Field Parameter Research Articles

Finite element analysis of mixed convection flow in a trapezoidal cavity with non-uniform temperature

A two dimensional flow analysis in a cavity shaped isosceles trapezium is carried out. Non-parallel sides of a trapezium are adiabatic. A varying sinusoidal temperature is applied to the lower wall while the upper wall is at constant temperature. Upper wall of the cavity moves with a velocity η0 in the positive x-direction. Also, B0 is constant magnetic field of strength aligned in the same x-direction and Newtonian fluid is considered. The values of magnetic field parameter used are Ha=0,50, the Richardson number is Ri=0.1,1,10, Re=100 is Reynolds number used for the analysis, the amplitude of sinusoidal temperature is m=0.25,0.5,1. The impacts of different leading parameters are analyzed by plotting streamlines for flow fields and isotherm contours for temperature of the flow dynamics. The graphs that signify the variation of average Nusselt number and local Nusselt number are sketched for both lower and upper walls of the cavity. Result indicated that with constant temperature the top wall of the boundary layer thickness decreases as Richardson number Ri increases and for bottom wall with variable temperature. The Nusselt number gets higher with an increment in the amplitude of the oscillation of temperature function. Furthermore, the study revealed that the average Nusselt number gets reduced as the intensity of magnetic field is enhanced. The variation in transit of heat at the bottom wall is similar but the maximum value of heat transfer at the bottom wall shows a variation from 3.8 to 20 when Ha=0 and from 3 to 18 when Ha=50. The accuracy of the present numerical algorithms is also established.

Finite element method solution of mixed convection flow of Williamson nanofluid past a radially stretching sheet

AbstractThis computation reports the mixed convection flow of Williamson fluid past a radially stretching surface with nanoparticles under the effect of first‐order slip and convective boundary conditions. The coupled nonlinear ordinary differential equations (ODEs) are obtained from the partial differential equations, which are derived from the conservation of momentum, energy, and species. Then, utilizing suitable resemblance transformation, these ODEs were changed into dimensionless form and then solved numerically by means of a powerful numerical technique called the Galerkin finite element method. The effect of different parameters on velocity, temperature, and concentration profiles is inspected and thrashed out in depth by graphs and tables. The upshots exhibit that the velocity profile augments as the values of concentration buoyancy and mixed convection parameters are engorged. Also, the results demonstrated that both temperature and concentration profiles are improved with an enhancement in values of thermophoresis parameters. The outcomes also indicate that for finer values of magnetic field parameter and thermophoresis parameter, the numerical value of local Nusselt and Sherwood numbers is reduced.

A comparative study of Al2O3 and TiO2 nanofluid flow over a wedge with non-linear thermal radiation

PurposeThe purpose of this study is to analyze the impact of chemical reaction and thermal radiation on mixed convection flow, heat and mass transfer characteristics of nanofluid through a wedge occupied with water–TiO2 and water–Al2O3 made nanofluid by considering velocity, temperature and concentration slip conditions in present investigation.Design/methodology/approachUsing acceptable similarity transformations, the prevailing partial differential equations have been altered into non-linear ordinary differential equations and are demonstrated by the diverse thermophysical parameters. The mathematical model is solved numerically by implementing Galarkin finite element method and the outcomes are shown in tables and graphs.FindingsThe temperature and concentration fields impede as magnetic field parameter improves in both water–Al2O3 and water–TiO2 nanofluid. While there is contradiction in the velocity field as the values of magnetic field parameter rises in both nanofluids. The non-dimensional velocity rate, rate of temperature and rate of concentration rise with improved values of Weissenberg number.Originality/valueNanofluid flows past wedge-shaped geometries have gained much consideration because of their extensive range of applications in engineering and science, such as, magnetohydrodynamics, crude oil extraction, heat exchangers, aerodynamics and geothermal systems. Virtually, these types of nanofluid flows happen in ground water pollution, aerodynamics, retrieval of oil, packed bed reactors and geothermal industries.

Nonlinear radiative flow of nanofluid in presence of gyrotactic microorganisms and magnetohydrodynamic

PurposeThis paper aims to explore the study of magnetohydrodynamic viscous fluid flow past on a stretching cylinder with nonlinear thermal radiation having gyrotactic microorganisms.Design/methodology/approachAppropriate transformations reduce the nonlinear partial differential equation to ordinary ones. Subsequent nonlinear equations are calculated to get convergent series solutions.FindingsFluid velocity declines for elevating values of magnetic field parameter. For larger values of curvature parameter near the cylinder temperature reduces.Originality/valueTo the best of the authors’ knowledge, magnetohydrodynamic boundary layer flow of viscous fluid by nonlinear stretching cylinder with nonlinear thermal radiation having gyrotatic microorganisms is not studied yet. The purpose is to study this.

Nonlinear convection flow of Williamson nanofluid past a radially stretching surface

In the current study, a non-linear convection flow of Williamson nanofluid past a radially stretching surface under the application of electric field has been inspected. The simplified joined non-linear ordinary differential equations are acquired from the partial differential equations which are formulated from the flow problems and then, are altered into dimensionless form employing appropriate resemblance transformation and also, the multivariate nonlinear terms are linearised with the help of Taylor series expansion technique. Then ensuing nonlinear ordinary partial differential equations with matching boundary conditions are solved numerically by utilizing spectral Quasilinearization method (SQLM). The influence of pertinent parameters on different flow fields are probed and conferred in depth by means of numerous plots and tables. The outcomes demonstrate that the velocity profile f′(η) enlarges as the value of electric field E1, buoyancy λ and nonlinear convection λ1 parameters are upgraded. Also, both temperature and concentration profiles augment with a boost in values of magnetic field and thermopherasis parameters. The results also signify that, for bigger values of magnetic field parameter M, the numerical value of local Nusselt number and Sherwood number are declined.

Effects of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation

In the present work, two-dimensional mixed convection Casson fluid flow past an infinite plate in a porous medium is performed under the effects of a uniform magnetic field. Characteristics of heat transfer and mass transfer are analyzed with non-linear thermal radiation, cross-diffusion, chemical reaction, heat generation and, heat absorption. The governing partial differential equations are remodeled into ordinary differential equations using similarity transformation. The homotopy analysis method is implemented to solve the governing dimensionless system of ordinary differential equations. The behavior of different physical parameters is shown graphically. The numerical values of Skin friction, Nusselt number, and Sherwood number are presented in a tabular form. Obtained outcomes are compared with earlier studies in the special case and strong agreement is noted. From graphical representation, it is concluded that velocity and temperature distribution increases with the mixed convection parameter and buoyancy force parameter. An increasing value of Casson fluid parameter, magnetic field parameter, chemical reaction parameter, and diffusion-thermo parameter tends to reduced velocity and temperature profiles. In most of the engineering and real-world problems, skin friction is not desirable, so it can be decreased by decreasing the values of magnetic field parameter, non-linear thermal radiation parameter, heat generation parameter, and temperature ratio parameter.

Chemical Reaction and Melting Heat Effects on MHD Free Convective Radiative Fluid Flow Past a Continuous Moving Plate in the Presence of Thermo-Physical Parameters

This study focuses on the analytical solution for the chemical reaction and melting heat transfer effects on MHD steady two-dimensional laminar viscous incompressible radiating boundary layer flow over a flat plate in the presence of variable fluid properties and Soret effect. The presence of viscous dissipation is also put into consideration at the plate under the influence of uniform transverse magnetic field. A mathematical model is developed to investigate the heat transfer characteristics occurring during the melting process due to a stretching sheet. The model contains nonlinear coupled partial differential equations which have been transformed into a system of ordinary differential equation via suitable similarity variables and then solved analytically by employing the Homotopy analysis method (HAM). The convergence of the series solution is established. The impact of various controlling parameters on the flow, heat and mass transfer characteristics are analyzed and discussed in detail through graphs and tables. The velocity and temperature depreciate with increase in radiation parameter and variable viscosity parameter. It is observed that for rising values of magnetic field parameter, variable viscosity parameter, and Prandtl number, the local skin friction increases while a reverse effect is seen in the case of Grashof number and melting parameter. It is found that the temperature decreases as the thermal radiation and melting parameter increase.

Scrutinization of thermal stratification, nonlinear thermal radiation and quartic autocatalytic chemical reaction effects on the flow of three-dimensional Eyring-Powell alumina-water nanofluid

PurposeThe purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell 36 nm alumina-water nanofluid within the thin boundary layer in the presence of quartic autocatalytic kind of chemical reaction effects, and to unravel the effects of a magnetic field parameter, random motion of the tiny nanoparticles and volume fraction on the flow.Design/methodology/approachThe chemical reaction between homogeneous (Eyring-Powell 36 nm alumina-water) bulk fluid and heterogeneous (three molecules of the catalyst at the surface) in the flow of magnetohydrodynamic three-dimensional flow is modeled as a quartic autocatalytic kind of chemical reaction. The electromagnetic radiation which occurs within the boundary layer is treated as the nonlinear form due to the fact that Taylor series expansion may not give full details of such effects within the boundary layer. With the aid of appropriate similarity variables, the nonlinear coupled system of partial differential equation which models the flow was reduced to ordinary differential equation boundary value problem.FindingsA favorable agreement of the present results is obtained by comparing it for a limiting case with the published results; hence, reliable results are presented. The concentration of homogeneous bulk fluid (Eyring-Powell nanofluid) increases and decreases with ϕ and Pr, respectively. The increase in the value of magnetic field parameter causes vertical and horizontal velocities of the flow within the boundary layer to decrease significantly. The decrease in the vertical and horizontal velocities of Eyring-Powell nanofluid flow within the boundary layer is guaranteed due to an increase in the value of M. Concentration of homogeneous fluid increases, while the concentration of the heterogeneous catalyst at the wall decreases with M.Originality/valueConsidering the industrial applications of thermal stratification in solar engineering and polymer processing where the behavior of the flow possesses attributes of Eyring-Powell 36 nm alumina-water, this paper presents the solution of the flow problem considering 36 nm alumina nanoparticles, thermophoresis, stratification of thermal energy, Brownian motion and nonlinear thermal radiation. In addition, the aim and objectives of this paper fill such vacuum in the industry.

Mass Transfer Flow of MHD Radiative Tangent Hyperbolic Fluid Over a Cylinder: A Numerical Study

The current paper focuses on the numerical solution of MHD flow of tangent hyperbolic fluid towards a stretching cylinder with thermal radiation. The modeled non-dimensional governing flow equations are changed to ordinary differential equations by utilizing the similarity transformations. The resultant system is then solved numerically by adapting the efficient finite difference technique known as Keller-Box scheme. The impacts of certain emerging parameters like power law index, curvature parameter, Weissenberg number, velocity slip parameter, magnetic field parameter, radiation parameter, Prandtl number and Schmidt number on dimensionless velocity, temperature and concentration profiles are examined and discussed in a detailed manner. Also, the physical results for the skin friction coefficient, local Nusselt number, and local Sherwood number are analyzed with the aid of tables. The obtained results in the present study are checked with previously available literature and found good agreement. It is revealed that the velocity declines for higher values of velocity slip parameter. Further, the fluid temperature enhances with escalating values of magnetic field parameter.

Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution

In this paper, the effects of magnetic field, nonlinear thermal radiation and homogeneous-heterogeneous quartic autocatalysis chemical reaction on an electrically conducting (36 nm) alumina-water nanofluid containing gyrotactic-microorganism over an upper horizontal surface of a paraboloid of revolution is presented. The case of unequal diffusion coefficients of reactant A (bulk-fluid) and reactant B (catalyst at the surface) in the presence of bioconvection is presented. In this article, a new buoyancy induced model for nanofluid flow along an upper horizontal surface of a paraboloid of revolution is introduced. The viscosity and thermal conductivity are assumed to vary with volume fraction and suitable models for the case 0% ≤ ϕ ≤ 0.8% are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for a limiting case. The influence of pertinent parameters are illustrated graphically and discussed. It is found that at any values of magnetic field parameter, the local skin friction coefficient is larger at high values of thickness parameter while local heat transfer rate is smaller at high values of temperature parameter.

Magneto-hydrodynamic mixed convection of a non-Newtonian power-law nanofluid past a moving vertical plate with variable density

Present paper investigates the magnetohydrodynamic boundary layer mixed convection flow over a moving vertical plate in a non-Newtonian power-law nanofluid with variable density. The governing partial differential equations are transformed into a ordinary differential equations by suitable similarity transformations. The system of coupled non-linear ordinary differential equations are solved numerically using variational finite element method. The solutions for the flow and heat transfer characteristics are computed numerically for various values of flow controlling parameters. Investigation predict that an increase in the values of magnetic field parameter and thermophoresis parameter is to enhance the temperature and nanoparticle volume fraction profiles. Increasing power-law index reduces the velocity, temperature and nanoparticle volume fraction profiles. An increase in the Brownian motion and Lewis number is reduces the nanoparticle volume fraction profiles and temperature field is decreases with increasing Pradtl number. An increase in power-law index and thermophoresis is found to be increase in the skin friction co-efficient but decrease in the heat transfer co-efficient.

Numerical investigation of magnetic field effects on entropy generation in viscous flow over a stretching cylinder embedded in a porous medium

The impact of presence of magnetic field on entropy generation in flow and heat transfer of viscous fluid over a horizontal stretching cylinder embedded in a porous medium has been theoretically studied. The problem is modeled mathematically and the governing partial differential equations are converted into non-linear differential equations by using suitable similarity transformations. Numerical solution of the transformed equations is obtained using the matlab built-in routine bvp4c. The velocity profiles, temperature distribution, local entropy generation number and Bejan number are plotted for various values of magnetic field parameter, curvature parameter, permeability parameter, Prandtl number, Eckert number, temperature exponent and group parameter. Moreover, the effects of these pertinent parameters on skin friction coefficient and local Nusselt number are also presented through tables. A brief discussion has been given about the impact of these physical parameters on thermo-physical properties.

Radiation, Heat Generation and Viscous Dissipation Effects on MHD Boundary Layer Flow for the Blasius and Sakiadis Flows with a Convective Surface Boundary Condition

This study is devoted to investigate the radiation, heat generation viscous dissipation and magnetohydrodynamic effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow), and about a moving plate in a quiescent ambient fluid (Sakiadis flow) both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique alongside with the forth order of Runge-Kutta method and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Magnetic field parameter M, Grashof number Gr, Prandtl number Pr, radiation parameter NR, Heat generation parameter Q, Convective parameter

Viscous-resistive ADAF with a general large-scale magnetic field

We have studied the structure of hot accretion flow bathed in a general large-scale magnetic field. We have considered magnetic parameters $ \beta_{r,\varphi,z}[=c^2_{r,\varphi,z}/(2c^2_{s})] $, where $ c^2_{r, \varphi, z} $ are the Alfv\'{e}n sound speeds in three direction of cylindrical coordinate $ (r,\varphi,z) $. The dominant mechanism of energy dissipation is assumed to be the magnetic diffusivity due to turbulence and viscosity in the accretion flow. Also, we adopt a more realistic model for kinematic viscosity $ (\nu=\alpha c_{s} H) $, with both $ c_{s} $ and $ H $ as a function of magnetic field. As a result in our model, the kinematic viscosity and magnetic diffusivity $ (\eta=\eta_{0}c_{s} H) $ are not constant. In order to solve the integrated equations that govern the behavior of the accretion flow, a self-similar method is used. It is found that the existence of magnetic resistivity will increase the radial infall velocity as well as sound speed and vertical thickness of the disk. However the rotational velocity of the disk decreases by the increase of magnetic resistivity. Moreover, we study the effect of three components of global magnetic field on the structure of the disk. We found out that the radial velocity and sound speed are Sub-Keplerian for all values of magnetic field parameters, but the rotational velocity can be Super-Keplerian by the increase of toroidal magnetic field. Also, Our numerical results show that all components of magnetic field can be important and have a considerable effect on velocities and vertical thickness of the disk.

Laminar MHD Flow in the Entrance Region of a Plane Channel with Dissipation

In this paper Laminar MHD flow in the entrance region of a plane channel with dissipation under the influence of transverse magnetic field. The motion of laminar conducting fluid between two parallel plates is considered. The channel has height of 2a and a width of d. A rectangular coordinate system is placed on channel with the origin at the center of channel at the left hand edge. The flow problem is described by means of partial differential equations and solutions are obtained by the use of a finite difference technique. The velocity, temperature and pressure profiles are shown in graphs and their behaviour is discussed for the different values of magnetic field parameter M and Eckert Number Ek for fixed Prandtl Number Pr.

MHD stagnation‐point flow towards a shrinking sheet

PurposeThe purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied.Design/methodology/approachA similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.FindingsThe solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.Practical implicationsThe flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface.Originality/valueThe present results are original and new for the MHD flow near the stagnation‐point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.

Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation

Numerical solutions are obtained for the problem which involves both the heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation using Chebyshev finite difference method (ChFD). A similarity transformation was employed to change the governing momentum, angular momentum, energy, and concentration partial differential equations into ordinary ones. Numerical calculations have been carried out for various values of magnetic field parameter, material parameter, Prandtl number, Eckert number, Schmidt number, couple stress at the surface, local Nusselt number and Sherwood number. The numerical results indicate that the temperature and the concentration increase, while the velocities, the Nusselt number and the Sherwood number decrease with increasing magnetic field parameter. In all of the above results, the material parameter has the opposite effect of magnetic field parameter. The temperature increases with increasing Eckert number, and decreases with increasing Prandtl number. An increase in the Schmidt number gives an increase in the Sherwood number, or a decrease in the concentration.

Magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer

AbstractThis paper presents a numerical study of magnetic effect on the formation of longitudinal vortices in a rotating laminar boundary layer. The criterion for the position marking the onset of longitudinal vortices is defined in this paper. The onset position characterized by the rotational Goertler number Gδ,rot, depends on the local rotation number, Reynolds number, the magnetic field parameter, the Prandtl number and the wave number. The results show that positive rotation destabilizes the flow. The flow is found to become more unstable to the vortex mode of instability as the value of magnetic field parameter M increases. The numerical data shows good agreement with the experimental results. Copyright © 2005 John Wiley & Sons, Ltd.

MHD free convection flow of visco-elastic fluid past an infinite vertical porous plate

This work provides a comprehensive theoretical analysis of a two-dimensional unsteady free convection flow of an incompressible, visco-elastic fluid past an infinite vertical porous plate. Solutions for the zero order perturbation velocity profile, the first order perturbation velocity and temperature profiles in closed form are obtained with the help of Laplace transform technique. The numerical solutions are carried out for the Prandtl number 0.1, 0.72, 1.0, 1.5 and 2.0 which are appropriate for different types of liquid metals and for different values of magnetic field parameter, M.

Melvin solution in string theory

We identify string theory counterpart of the dilatonic Melvin D = 4 background describing a “magnetic flux tube” in low-energy field theory limit. The corresponding D = 5 bosonic string model containing extra compact Kaluza-Klein dimension is a direct product of the D = 2 Minkowski space and a D = 3 conformal σ-model. The latter is a singular limit of the [SL(2,R) × R] R gauged WZW theory. This implies, in particular, that the dilatonic Melvin background is an exact string solution to all orders in α 1. Moreover, the D = 3 model is formally related by an abelian duality to a flat space of non-trivial topology. The conformal field theory for the Melvin solution is exactly solvable (and for special values of magnetic field parameter is equivalent to CFT for a Zn orbifold of 2-plane times a circle) and should exhibit tachyonic instabilities.