Hydromagnetic Free Convection Research Articles

Dual Stratification on the Double Diffusive Magnetohydrodynamics Flow of Nanofluids with Dissipation Effects-Revised Buongiorno Model

We analyze the effects of double stratification and dissipation on the hydro magnetic free convection flow of nanofluids over a vertical plate in this work. Considered two different kinds of nanofluids, such as copper and alumina–water nanofluids. By employing the similarity transformation, partial differential equations are converted into non-linear ordinary differential equations, which can be numerically computed with MATLAB. In practical situations where the heat and mass transfer mechanisms run simultaneously, the analysis of natural convection in the influence of double stratification is a fundamentally interesting and important problem, because of its broad range of engineering applications. These applications include the rejection of heat into the environment, such as lakes, rivers, and seas; the storage of thermal energy, such as solar ponds; and the transmission of heat from thermal sources, such as the condensers of power plants. To highlight the impact of double stratification and dissipation on the hydromagnetic free convective flow of nanofluid over a vertical plate, a wide variety of parameter values are used. The numerical outcomes for the different parameters of velocity, temperature, volume fraction, and concentration are obtained and displayed graphically. The skin friction coefficient and reduced Nusselt number are also determined numerically and tabulated.

EXPLORING THE DYNAMICS OF AN EXOTHERMIC CHEMICAL REACTION CONTROLLED BY ARRHENIUS KINETICS WITH HALL EFFECT IN A MICROCHANNEL

The consequences of chemically reactive fluids have provoked many researchers due to their potential to enhance the behavior of heat. Hence, this article discussed a theoretical investigation to explore the actions of Arrhenius chemical reaction and Hall current on hydro-magnetic free convection of a viscous fluid flowing along an upstanding micro-channel. Subject to the required boundary conditions, the governing coupled equations representing the flow pattern in non-dimensional form were solved using the homotopy perturbation method (HPM). Line graphs are also used to generate expressions for energy, momentum, volume flow rate, drag force, and Nusselt number in both primary and secondary flow directions as a function of regulating parameters like chemical reaction, Hall current, rarefaction, and wall ambient temperature difference ratio. It is worthy of note that the fluid temperature and the fluid flow are substantially propelled by the viscous heating term in the Arrhenius chemical reaction of the system for growing values of the wall ambient temperature difference ratio parameter. Additionally, it is noticeable that volume flow rate performance is seen as a growing influence of viscous heating and rarefaction parameters. The findings of this study can be applied to a wide range of electrically controlled devices, thermal and petro chemical engineering, and the serviceability of industrial products.

Hydromagnetic free convection flow in a vertical microporous channel with Hall current and ion-slip effect

AbstractIn the present work, steady-state hydromagnetic analysis and flow formation of Newtonian viscous fluid through a vertical microporous channel is studied theoretically. The transport governing equations include the effect of Hall current and ion-slip effects in the microchannel slip regime. Unlike the usual employed thermal properties of constant heat flux/temperature at the boundary, the current work assumes that the microporous walls are influenced by different surrounding wall temperatures. Solution to the governing equations depending on Prandtl number, rarefaction parameter, Hall current parameter, ion-slip parameter, Hartmann number and suction/injection parameter are obtained by utilizing the method of undetermined coefficient. Results demonstrating the effect of these parameters on different flow features are presented graphically in MATLAB. The results reveal that in the simultaneous occurrence of Hall and ion-slip currents, higher values of rarefaction parameter enhance the momentum boundary layer in both primary and secondary flow directions. In addition, results from this analysis also reveal that the main component of fluid velocity remains unaffected to higher values of Hall current, whereas it decreases along the induced flow directions. Furthermore, for a specific value of Hall parameter and ion-slip current, injection weakens the buoyancy drive resulting in a reduction in volume flow rate. The contrast is true with suction.

Hydromagnetic free convection in a vertical channel with induced magnetic field: Open and short circuits

Hydromagnetic free convection in a vertical channel with induced magnetic field: Open and short circuits

Hall current and thermo-diffusion effects on magnetohydrodynamic convective flow near an oscillatory plate with ramped type thermal and solutal boundary conditions

The present discussion deals with the study of time-dependent hydromagnetic free convection fluid flow with heat and mass transfer over an oscillating vertical plate which is placed in a porous medium with ramped wall temperature and wall concentration in the presence of Hall current, rotation, chemical reaction, thermal radiation, thermo-diffusion (Soret effect). The governing system of equations is non-dimensionalized by using suitable dimensionless variables and parameters. The non-dimensional equations are solved analytically using the Laplace transform technique. The influence of various pertinent flow parameters on velocity, temperature and concentration fields are analyzed and portrayed through figures, whereas the skin friction, Nusselt number and Sherwood number are described and shown in tabular form.

Effect of a Point/Line Heat Source on Hydromagnetic Free Convection between Vertical Walls due to Induced Magnetic Field

The hydromagnetic natural convective flow of an incompressible electrically conducting and viscous liquid amid non-conducting vertical walls with a constant point heat source/sink under the impact of the induced magnetic field has been studied. A wavelet function is used to formulate the point heat source. The considered problem is described by a group of simultaneous ODEs with significant boundary conditions, and their solutions have been acquired for the induced magnetic field, the velocity field and the temperature field by applying the Laplace technique. The skin friction, induced current density and mass flux have also been discussed. The influences of controlling parameters on the fluid flow are discussed with the tables and graphs. The valuable consequence of this investigation is that an enhancement in the length of point heat source enhances the induced magnetic field, velocity, induced current density and temperature field.

Application of statistical method on thermal resistance and conductance during magnetization of fractionalized free convection flow

Thermally induced damages such as hypolimnion, metalimnion and epilimnion are usually caused by thermal stratification; due to this fact, fluid flows at a low velocity with large temperature variances. In this manuscript, thermal stratification phenomenon is discussed on the basis of fractionalized hydromagnetic free convection flow over the boundary of inclined plate. For the first time in literature, accelerated exponentially plate within generalized velocity R0Eα−atα has been considered as the boundary condition at the inclined plate. The analytical solutions have been invoked for knowing the thermal resistance and conductance of heat and mass transfer. For the sake of satisfaction of boundary condition as a Mittage-Leffler function, the combined techniques of Laplace and Fourier sine transforms are treated. The fractional approach of non-singular and non-local kernel along with concept of infinite series has been utilized for knowing the optimal profiles of concentration, temperature and velocity. Our results are elucidated by means of graphical illustrations on the basis of statistical data and analytical method for the enhancement of thermal stratification.

Effects of Thermal Radiation, Heat Generation, and Induced Magnetic Field on Hydromagnetic Free Convection Flow of Couple Stress Fluid in an Isoflux-Isothermal Vertical Channel

The study scrutinizes the effects of thermal radiation, heat generation, and induced magnetic field on steady, fully developed hydromagnetic free convection flow of an incompressible viscous and electrically conducting couple stress fluid in a vertical channel. The channel walls are maintained at an isoflux-isothermal condition, such that the left channel wall is maintained at a constant heat flux. In contrast, the right channel wall is maintained at a constant temperature. The governing simultaneous equations are solved analytically utilizing the method of undetermined coefficient, and closed form solutions in dimensionless form have been acquired for the velocity field, the induced magnetic field, and the temperature field. The expression for the induced current density has been also obtained. A parametric study for the velocity, temperature, and induced magnetic field profiles, as well as for the skin-friction coefficient, Nusselt number, and induced current density, is conducted and discussed graphically.

Magnetohydrodynamics free convection flow of Carbon nanotubes viscous nanofluids over an infinite plate with Newtonian heating and fractional derivative

The problem of hydromagnetic (MHD) free convection flow of viscous nanofluids over a moving infinite vertical plate with carbon nanotubes (CNTs) and Newtonian heating on the boundary is considered. The Caputo time‐fractional derivative is introduced to classical constitutive equations by using the generalized constitutive shear stress equation and generalized Fourier law. Analytical solution for the temperature distribution and semi‐analytical solution for the velocity profile are found by means of Laplace transform. The solution of temperature distribution is presented in terms of Wright and Gauss complementary error functions. The inverse Laplace transform of velocity profile is approximated by Stehfest algorithm, and for validation, Tzou algorithm is used. Finally, for illustration, three special cases are considered, and the influence of physical parameters on some fundamental motions are graphically underlined and discussed. The fractional derivative and volume faction parameter has a good influence on temperature distribution and velocity field.

Hydromagnetic free convection flow of viscous fluid between vertical parallel plates with damped thermal and mass fluxes

In this article, hydromagnetic free convection flow of viscous fluid between two vertical plates is considered. The Caputo time-fractional derivative is used and the governing equations are fractionalized by means of generalized Fourier’s and Fick’s laws. Laplace transform coupled with the finite sine-Fourier transform which is suitable to problems with boundary conditions. Closed form general solutions are expressed in terms of Mittag-Leffler function. The effects of fractional parameters as well as physical parameters are plotted graphically.

Magnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in Porous Medium

The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. The exact solutions for the fractional governing differential equations for fluid temperature, Nusselt number, velocity field, and skin friction are obtained by using the Laplace transform method. The numerical calculations are carried out and the results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with the thermal memory and the ordinary fluid is made. It was observed that due to evolution in the time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time t. Moreover, it is found that the fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction.

Unsteady hydromagnetic-free convection flow with suction/injection

This article analyses the unsteady hydromagnetic free convection flow near impulsive as well as accelerated motion of the infinite vertical porous plate. The governing momentum and energy partial differential equations exhibiting the physics of the flow formation are presented. Using suitable dimensionless parameters, the equations are transformed to their corresponding dimensionless form and solved exactly in the Laplace domain using the well-known Laplace transform technique. However, the Riemann-sum approximation method is used to invert the solution from the Laplace domain to time domain due of the complexity of the solutions obtained in the Laplace domain. The effect of various pertinent parameters such as suction/injection, Hartmann number, Grashof number, and Prandtl number is discussed with the aid of line graphs.

MHD free convection flow of a viscous fluid in a rotating system with damped thermal transport, Hall current and slip effects

Unsteady hydromagnetic free convection flows of a rotating incompressible viscous fluid over an infinite moving plate with fractional thermal transport are studied in the presence of heat source, Hall current and slip velocity effects. The modern definition of the fractional integral Caputo-Fabrizio operator with non-singular kernel is used in the constitutive equation for the thermal flux and closed form solutions for the dimensionless temperature and velocity components are established by using the Laplace transform technique. For comparison, the solutions for the ordinary fluid as well as those corresponding to the no-slip condition on the boundary are also determined. The influence of fractional, magnetic, Hall and rotation parameters as well as that of heat generation/absorption coefficient on the fluid motion and the heat transfer is graphically underlined and discussed. It is found that the damping of the thermal transport has significant influence on the fluid temperature and motion. The Hall current mainly affects the secondary flow.

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

English

English

Heat and Mass Transfer of Unsteady Hydromagnetic Free Convection Flow Through Porous Medium Past a Vertical Plate with Uniform Surface Heat Flux

AbstractSimultaneous effects of thermal and concentration diffusions in unsteady magnetohydrodynamic free convection flow past a moving plate maintained at constant heat flux and embedded in a viscous fluid saturated porous medium is presented. The transport model employed includes the effects of thermal radiation, heat sink, Soret and chemical reaction. The fluid is considered as a gray absorbing-emitting but non-scattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. The dimensionless coupled linear partial differential equations are solved by using Laplace transform technique. Numerical results for the velocity, temperature, concentration as well as the skin friction coefficient and the rates of heat and mass transfer are shown graphically for different values of physical parameters involved.

English

English

Unsteady MHD Free Convective Flow Past an Inclined Parabolic Accelerated Plate with Hall Current, Radiation Effects and Variable Temperature in a Porous Medium

We analyze the effects of hall current and radiation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an inclined parabolic accelerated plate in a porous medium by applying a transverse magnetic field which makes an angle α to the inclined plate.The fluid is assumed to be viscous, incompressible and electrically conducting with a strong magnetic field. Using the modified Ohm’s law and the Bossinesq approximation the governing equations of the problem are reduced to local non-similarity boundary layer equations using suitable transformation.The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference method for different values of governing flow parameters. The velocity and temperature profiles are shown through graphs.

Time-dependent hydromagnetic free convection nanofluid flows within a wavy trapezoidal enclosure

This paper considers unsteady MHD free convection flows of alumina (Al2O3)-water and single-walled carbon nanotube (SWCNT)-water nanofluids within a symmetrical wavy trapezoidal enclosure. Initially, the fluid within the enclosure has a constant cold temperature and is at rest. The temperature of the wavy bottom wall is suddenly raised to a constant hot temperature, while the top wall is thermally insulated. The temperature of the side walls is maintained at the initial cold temperature. The dimensionless governing equations with the corresponding initial and boundary conditions are solved using the mixed finite element method with polynomial pressure projection stabilization. The effects of Rayleigh number Ra and Hartmann number Ha on the nanofluid flow and heat transfer are investigated.

Computer Simulation of a Radiative MHD flow in a Rotating Fluid

A hydromagnetic free convection flow has been modeled and simulated. The flow is considered unsteady, near a moving infinite flat plate in a rotating fluid. For the radiative heat transfer to be significant, very high temperatures are involved rendering the problem highly non-linear. The simulation is based on a generic finite element scheme coupled with a stepwise Lagrange polynomial. The equations and other parameters entering into the description of the flow are transformed into interpretable postfix codes. Numerical values are computed for the temperature and velocity distributions. The results obtained are depicted graphically and discussed.