MHD Natural Convection Flow Research Articles

Unsteady MHD natural convection flow of heat generating/absorbing fluid near a vertical plate with ramped temperature and motion

This work investigates the unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid near an infinite vertical plate with ramped temperature and ramped motion. A unified closed form solution is obtained for the velocity field and skin friction coefficient corresponding to the case when the magnetic field fixed relative to the fluid or the moving boundary. It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Graphical representations are attained for different values of the Prandtl number, magnetic field and heat sink parameter. Results show that wall ramped temperature and ramped motion tend to decrease fluid temperature, velocity, Nusselt number and skin friction.

MHD Convection Fluid and Heat Transfer in an Inclined Micro-Porous-Channel

Abstract This study is devoted to investigate the influence of transverse magnetic field as well as suction/injection on MHD natural convection flow of conducting fluid in an inclined micro-porous-channel. The analytical solutions for velocity profile and temperature profile have been obtained considering the velocity slip and temperature jump conditions at the micro-porous-channel walls. The solution obtained for the velocity has been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem are discussed with the aid of line graphs. Results reveal that the impact of inclination angle on fluid velocity is dependent on the value of the wall ambient temperature difference ratio, hence increase in inclination angle yields an enhancement in fluid velocity within the micro-porous-channel for some selected values of the wall ambient temperature difference ratio whereas it displays a dual character for other values. Also, injecting through the micro-porous channel thickens the thermal boundary layer, resulting to weakening the convective current and consequently decreasing the fluid velocity whereas suction weakens the thermal boundary layer yielding an increase in fluid velocity.

Optimal Homotopy Analysis of MHD Natural Convection Flow of Thixotropic Fluid under Subjection of Thermal Stratification: Boundary Layer Analysis

In this article, the model of a non-Newtonian fluid (Thixotropic) flow past a vertical surface in the presence of exponential space and temperature dependent heat source in a thermally stratified medium is studied. It is assumed that free convection is induced by buoyancy and exponentially decaying internal heat source across the space. The dynamic viscosity is taken to be constant and thermal conductivity of this particular fluid model is assumed to vary linearly with temperature. Thermal stratification has been properly incorporated into the governing equation so that its effect can be revealed and properly reported. The governing partial differential equations describing the model are transformed and parameterized to a system of non-linear ordinary differential equation using similarity transformations. Approximate analytic solutions were obtained by adopting Optimal Homotopy Analysis Method (OHAM). The results show that for both cases of non-Newtonian parameters (Thixotropic) (K1=K2=0 & K1=K2=1.0), increasing stratification parameters, relate to decreasing in the heat energy entering into the fluid region and thus reducing the temperature of the Thixotropic fluid as it flows.

Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

Thermal radiation and inclined magnetic field effects on MHD flow past a linearly accelerated inclined plate in a porous medium with variable temperature

AbstractAn analysis of unsteady MHD natural convective flow, transfer of mass, and radiation past linearly accelerated slanted plate inserted in an immersed permeable medium with uniform permeability, variable temperature, and concentration within the sight of a slanted magnetic field has been done. The novelty of the current examination is to analyze the effect of a slanted magnetic field on the flow phenomena with heat source/sink and destructive reaction for linearly accelerated slanted plate. The governing equations have been solved by using Laplace transform strategy. The estimations of flow velocity, concentration, and temperature are exhibited graphically, while local skin friction, mass, and heat transfer rates are put on view in tabular form for different values of relevant stream parameters. It is fascinating to observe that the raise of inclination angle of an applied magnetic field diminishes both velocity profiles and local skin friction.

Numerical analysis of three-dimensional MHD natural convection flow in a short horizontal cylindrical annulus

A numerical study of three-dimensional (3D) MHD laminar flow in a short horizontal cylindrical annulus has been performed to characterize the impacts of a uniform axial magnetic field on both hydrodynamic and thermal behaviors. This configuration corresponds to a horizontal annular mold containing molten iron or low carbon steel in electromagnetic casting (EMC). Complex nonlinear governing equations are solved numerically by means of the finite volume method based on artificial compressibility algorithm. The induced electric potential caused by the magnetic field is considered. Results show that a typical 3D steady spiral flow arises and the symmetry breaking occurs under a weak magnetic field of Ha < 10. As the Hartmann number increases, the spiral flow is distinctly suppressed, and then it changes to a helical flow with two transverse cells adjacent to each of the end walls. Correspondingly, the flow patterns and isotherms of fluid become symmetric with respect to the mid-axial plane of the annulus. Further increasing the Hartmann number, the fluid particle trajectories essentially lie in the cross-section of the annulus, as for two-dimensional solutions, with an extremely small axial dependency. In addition, both the values of local Nusselt number at the isothermal walls and its axial dependency, mainly in the upper region (−38π≤φ≤38π), are significantly affected by the magnetic field. The results of the present work can be useful in producing high-quality products by magnetic control.

Transient MHD Natural Convective Flow Past a Heated Vertical Non-porous Surface with Thermal Radiation and Double-Diffusion Effects

&#x0D; &#x0D; &#x0D; &#x0D; The problem of transient MHD natural convective flow past a vertical plate with thermal radiation, cross-diffusion and zero suction effects is investigated. The governing one-dimensional spatial and non-linear partial differential equations of the Boussineq form are non-dimensionalized to, among others, bring out the necessary parameters. The evolving dimensionless equations are transformed into ordinary differential equations using the similarity transformation, and linearized using the regular perturbation expansion series solutions. The linearization leads to the zeroth and first order equations, and are solved semi-analytically using the Mathematica 11.0 computational software. Expressions for the temperature, concentration, velocity, Nusselt number, Sherwood number and Skin friction are obtained, computed and presented graphically. The analysis of results, amidst others, shows that the increase in the Dufour number increases the temperature, but decreases the Nusselt number; the increase in the Soret number decreases the concentration, but increases the Sherwood number; the increase in the Prandtl number decreases the temperature and concentration, but increases the Nusselt number and Sherwood number; the increase in the Hartmann number decreases the velocity and skin friction. These results are benchmarked with the existing reports in literatures, and are in good agreement.&#x0D; &#x0D; &#x0D; &#x0D; &#x0D;

A steady MHD natural convection and heat transfer fluid flow through a vertical surface in the existence of hall current and radiation

A steady MHD natural convection and heat transfer fluid flow through a vertical surface in the existence of hall current and radiation

MHD Slips Flow of a Micro-polar Fluid Due to Moving Plate in Porous Medium with Chemical Reaction and Thermal Radiation: A Lie Group Analysis

An attempt is made to investigation of MHD natural convection flow of a micropolar fluid due to a permeable moving plate in porous medium in the presence of chemical reaction and radiation. The Lie group analysis used to create similarity transformations and by using those transformations, the system of governing highly non-linear partial differential equations is converted into a set of non-linear coupled ordinary differential equations. The ordinary differential equations thus obtained have been solved by utilizing Keller box method. Numerical solutions for the skin-friction coefficient, Nusselt and Sherwood numbers as well as the velocity, micro-rotation, temperature and concentration are presented graphically for different parametric conditions and discussed in detail. The results show that the skin-friction coefficient reduces with greater values of micro-polar or material parameter and the heat transfer rate advances with reduction in micropolar and radiation parameters. The mass transfer rate accelerates with higher values of chemical reaction parameter.

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.

MHD natural convection flow enclosure in a corrugated cavity filled with a porous medium

In this article, a complete structure of corrugated surface is established for heat transfer effects in the presence of uniform magnetic field. A natural convection phenomenon is presented for MHD flow filled in a porous corrugated cavity at various wavelengths and partially heated domain. The governing partial differential equations consist of continuity, momentum and energy equations along with the corrugated conditions at the surface. This system is properly nondimensionalized and then solved via finite element method (FEM). In order to obtain the high resolution near the surface of corrugation, mesh generation is improved at the various portions of the cavity. The flow patterns and temperature distribution within the entire domain of the cavity can be visualized through streamlines and isotherms, respectively. Computational experiment is performed for various values of wavelength number (0⩽n⩽15), Rayleigh number (104⩽Ra⩽106), Darcy number (10-5⩽Da⩽10-3), and Hartmann number (10⩽Ha⩽103) to illustrate the effects on streamlines, isotherms, velocities and heat transfer rate. Heat transfer rate is increased due to increase in Rayleigh number and wavelength parameter. Darcy and Hartmann number does not have significant effects on the temperature distribution.

Soret Effect on Mhd Natural Convection Flow With Radiative Heat Transfer Past An Impulsively Moving Plate With Ramped Wall Temperature Through Porous Medium

Soret Effect on Mhd Natural Convection Flow With Radiative Heat Transfer Past An Impulsively Moving Plate With Ramped Wall Temperature Through Porous Medium

Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: Effects of a heat sink and source size and location

The effects of a heat sink and the source size and location on the entropy generation, MHD natural convection flow and heat transfer in an inclined porous enclosure filled with a Cu-water nanofluid are investigated numerically. A uniform heat source is located in a part of the bottom wall, and a part of the upper wall of the enclosure is maintained at a cooled temperature, while the remaining parts of these two walls are thermally insulated. Both the left and right walls of the enclosure are considered to be adiabatic. The thermal conductivity and the dynamic viscosity of the nanofluid are represented by different verified experimental correlations that are suitable for each type of nanoparticle. The finite difference methodology is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published works is performed, and the results show a very good agreement. The results indicate that the Nusselt number decreases via increasing the nanofluid volume fraction as well as the Hartmann number. The best location and size of the heat sink and the heat source considering the thermal performance criteria and magnetic effects are found to be D = 0.7 and B = 0.2. The entropy generation, thermal performance criteria and the natural heat transfer of the nanofluid for different sizes and locations of the heat sink and source and for various volume fractions of nanoparticles are also investigated and discussed.

MHD Natural Convection Flow of CuO/Water Nanofluid in a Differentially Heated Hexagonal Enclosure with a Tilted Square Block

A numerical investigation has been performed to analyze the effect of magnetohydrodynamic natural convection flow in a differentially heated hexagonal enclosure having a tilted square block filled with CuO/water nanofluid. The horizontal walls of the cavity and tilted walls of the obstacle are uniformly heated of temperature $$\hbox {T}_\mathrm{h}$$ while the inclined walls are kept at constant temperature $$\hbox {T}_\mathrm{c}$$ . The governing conservation equations of the physical problem have been solved using finite element method based on Galerkin weighted residual technique and obtained numerical results are presented graphically in terms of streamlines, isotherms, average Nusselt numbers, mid height horizontal and vertical velocities, average temperature and average velocity of nanofluid for a range of Rayleigh number ( $$10^{3} \le { Ra} \le 10^{6}$$ ), Hartmann number ( $$0 \le { Ha} \le 70$$ ) and solid volume fraction ( $$0.1\% \le \phi \le 5\%$$ ) to show the flow structures and temperature characteristics. It is found that the flow fields and temperature distributions are influenced significantly for the effect of pertinent parameters. In addition, overall heat transfer rate enhanced due to higher values of Ra and $$\phi $$ along with lower value of Ha. Comparisons of the present results with the previously published results on the basis of special cases are performed and found to be in good agreement.

MHD natural convective flow of nanofluids past stationary and moving inclined porous plate considering temperature and concentration gradients with suction

PurposeThis paper aims to focus on the mathematical modeling of magnetohydrodynamic natural convective boundary layer flow of nanofluids past a stationary and moving inclined porous plate considering temperature and concentration gradients with suction effects.Design/methodology/approachThe transformed non-dimensional and coupled governing partial differential equations are solved numerically using the finite element method.FindingsThe obtained numerical results for physical governing parameters on the velocity, temperature and concentration distributions are exemplified graphically and presented quantitatively. The boundary layer thickness increased with the increasing values of Soret, Dufour and Grashof numbers, while the thickness of boundary layer decreased with increasing values of suction for both stationary and moving plate cases. The primary and secondary velocity profiles are decreasing with an angle of inclination for moving plate and inclination has no significant effect for the stationary plate. An increase of the Soret number and Dufour number tend to increase the heat and mass transfer, while an increase of suction reduces the heat and mass transfer.Originality/valueThe problem is an important contribution to the field of nanofluid science and technology and is relevant to high temperature rotating chemical engineering systems exploiting magnetized nanofluids. This study is relatively original in nanofluids.

Unsteady MHD Natural Convective Flow of a Rotating Fluid over an Infinite Vertical Plate due to Oscillatory Movement of the Free-Stream with Hall and Ion-Slip Currents

In the present research study a mathematical analysis has been presented for unsteady MHD natural convective flow of a rotating fluid over an infinite vertical plate immersed in a fluid saturated porous medium with oscillating free-stream. The effects of Hall and ion-slip currents also considered on the fluid flow. The unsteady MHD flow over the vertical plate is induced due to thermal and concentration buoyancy forces and oscillatory movement of the free-stream. The partial differential equations governing the motion for the fluid flow are solved analytically. The effects of various pertinent flow parameters on the fluid velocity, fluid temperature and species concentration are presented in graphical form whereas that on skin friction and rate of heat and mass transfer at the plate are presented in tabular form. An interesting observation recorded from the present analysis that there appears reversal flow in the secondary flow direction due to presence of thermal and/or concentration buoyancy forces. However, in the absence of both reversals flow does not exist in the secondary flow direction. It is also noted that the thickness of momentum boundary layer decreases with rise in frequency of oscillations of the free-stream.

Unsteady general solution for MHD natural convection flow with radiative effects, heat source and shear stress on the boundary

PurposeThe purpose of this note is to provide general solutions for radiative magnetohydrodynamic natural convection flow.Design/methodology/approachTo obtain exact solutions for such motions of Newtonian fluids, as seen in the existing literature, the Laplace transform technique is used.FindingsGeneral solutions are obtained for temperature, velocity and Nusselt number in the presence of heat source and shear stress on the boundary. They can generate exact solutions for any motion with technical relevance of this type. Fluid velocity is presented as the sum of mechanical and thermal components. Influence of physical parameters on temperature and velocity is graphically underlined for ramp-type heating plate that applies a constantly accelerating shear stress to the fluid. Thermal and mechanical effects are significant and must be taken into consideration.Practical implicationsFor illustration, as well as for a check of results, three special cases with applications in engineering are considered and some known results are recovered.Originality/valueObtained solutions are presented in the simplest forms. In addition, the solutions corresponding to cosine oscillatory heating and oscillating shear are presented so that they can be immediately reduced to those corresponding to constant heating and uniform shear if the oscillations’ frequency becomes zero. Heat transfer characteristics with thermal radiation are graphically illustrated using one parameter only for such motions.

Unsteady MHD Natural Convective Flow of a Rotating Walters’-B Fluid Over an Oscillating Plate with Fluctuating Wall Temperature and Concentration

AbstractIn the present study, unsteady MHD boundary layer flow of a rotating Walters’-B fluid (viscoelastic fluid) over an infinite vertical porous plate embedded in a uniform porous medium with fluctuating wall temperature and concentration taking Hall and ion-slip effects into consideration is discussed. The MHD flow in the rotating fluid system is induced due to the non-torsional oscillations of the plate in its own plane and the buoyancy forces arises from temperature and concentration differences in field of gravity. The partial differential equations governing the fluid motion are solved analytically by using regular perturbation and variable separable methods by assuming very small viscoelastic parameter. Solution for velocity field in the case when natural frequency due to rotation and Hall current is equals to the frequency of oscillations i.e. in the case of resonance is also obtained. In order to note the influences of various system parameters and to discuss the important flow characteristics, the numerical results for fluid velocity in the non-resonance case, temperature and species concentration are computed and depicted graphically versus boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form. An interesting observation recorded that there arises flow reversal in the primary flow direction due to high rotation. When natural frequency is greater than the frequency of oscillations the fluid velocity in the primary flow direction is maximum at the plate whereas incase when natural frequency is smaller than the frequency of oscillations, it is maximum in the neighborhood of the plate.

Influence of viscous dissipation on unsteady MHD natural convective flow of Casson fluid over an oscillating vertical plate via FEM

Abstract In this paper, an unsteady magnetohydrodynamic natural convection, heat transfer, electrically conductive non-Newtonian Casson fluid over an oscillating vertical porous plate taken in to the account with an influence of viscous dissipation. An efficient computational Finite Element Method (FEM) employed to solve non-dimensional boundary layer partial differential equations for velocity and temperature distribution with the influence of emerging dimensionless parameters. Also, the local Skin-friction and local Nusselt number coefficients are obtained and analyzed through graphical and tabular forms. The results shows that increasing of Eckert number leads to increase in the velocity and temperature distribution while decrease in the local Skin-friction and Nusselt number coefficients. An increasing of Casson parameter leads to decrease in the velocity distribution and the local Skin-friction coefficient. Compared the present results with earlier reported studies of analytical solutions of Newtonian and non-Newtonian fluid flow problems. The current results are in excellent agreement with earlier existed results. The velocity and temperature distributions are closure for various mesh (grid) size. Therefore, these computational results are stable and converge. FEM is flexible and simplest method to solve this type of problems in various cases like Newtonian and non-Newtonian fluid flow problems.

Hall effects on MHD natural convection flow in a vertical microchannel

In this work, the steady fully developed magnetohydrodynamic natural convection flow in a vertical microchannel formed by two infinite vertical parallel plates due to asymmetric heating of parallel plates in the presence of Hall current is studied. Effects of velocity slip and temperature jump have been considered on the microchannel surfaces and exact solutions have been obtained for momentum and energy equations under relevant boundary conditions. The influence of each governing parameter such as Hall current parameter, Hartmann number, rarefaction parameter, fluid wall interaction parameter and wall-ambient temperature ratio on flow formation is discussed with the aid of graphs. The significant result from the study is that, increase in the value of rarefaction parameter leads to enhancement in volume flow rate. Furthermore, it is evident that volume flow rate is found to be increasing function of Hall current parameter.