Magnetohydrodynamic Natural Convection Research Articles

MHD natural convection of a micropolar nanofluid flowing inside a radiative porous medium under LTNE condition with an elliptical heat source

The present study deals with MHD (Magnetohydrodynamic) natural convection associated to a micropolar nanofluid flowing in a radiative porous medium. An elliptical heat source is placed in the porous medium. The Darcy model and local thermal non-equilibrium condition are acceptable to simulate the porous medium. KKL model is employed to simulate the nanofluid flow. This model associates the viscosity and thermal conductivity with the temperature and considers the effects of Brownian motions on these two thermos-physical properties. The Galerkin finite element approach is utilized to dissolve the equations. The impacts of governing key parameters are investigated on the streamlines, isotherms of fluid and solid phases, and isolines of micro-rotation as well as the rates of heat transfer. The range of these parameters are Darcy-Rayleigh number Ra = 10–1000, Hartman number Ha = 0–50, nanoparticles volume fraction φ = 0–0.04, interface heat transfer coefficient H = 1–1000, porosity ε = 0.1–0.9, modified thermal conductivity ratio Kr = 0.1–10, vortex viscosity parameter Δ = 0–2 and radiation parameter Rd = 0–2. The results illustrate that the strength of the particles' micro-rotations slightly increases when Rd grows. The increment of porosity increases and decreases the strength of the flow and micro-rotations of the particles, respectively. In addition, an increase in Δ, Ha and ε enhance the total Nusselt number, while a reverse trend can be observed for H, Rd, Kr and Ra.

Interplay of non-conducting and conducting walls on magnetohydrodynamic (MHD) natural convection flow in vertical micro-channel in the presence of induced magnetic field

In this research paper, exact solution for fully developed magnetohydrodynamic (MHD) natural convection flow of viscous, incompressible, electrically conducting fluid in vertical micro-channel formed by electrically non-conducting and conducting infinite vertical parallel walls in the presence of velocity slip and temperature jump at the micro-channel walls is investigated. The influence of induced magnetic field (I.M.F) arising due to the motion of an electrically conducting fluid in the presence of transverse magnetic field is taken into consideration. Due to the presence of induced magnetic field, the momentum and induction equations are coupled. The exact solutions in dimensionless form have been obtained under relevant boundary conditions. The expressions for velocity field, the induced magnetic field, temperature field, induced current density and skin friction have been obtained. The effects of the various physical parameters appearing into the model such as rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number are demonstrated through graphs and table. The results indicate that, increase in Hartmann number and magnetic Prandtl number causes a pronounced reduction in volume flow rate.

Optimization and sensitivity analysis of magneto-hydrodynamic natural convection nanofluid flow inside a square enclosure using response surface methodology

This article studies buoyancy-driven natural convection of a nanofluid affected by a magnetic field within a square enclosure with an individual conductive pin fin. The effects of electromagnetic forces, thermal conductivity, and inclination angle of pin fin were investigated using non-dimensional parameters. An extensive sensitivity analysis was conducted seeking an optimal heat transfer setting. The novelty of this work lies in including different contributing factors in heat transfer analysis, rigorous analysis of design parameters, and comprehensive mathematical analysis of solution domain for optimization. Results showed that magnetic strength diminished the heat transfer efficacy, while higher relative thermal conductivity of pin fin improved it. Based on the problem settings, we also obtained the relative conductivity value in which the heat transfer is optimal. Higher sensitivity of heat transfer was, though, noticed for both magnetic strength and fin thermal conductivity in comparison to fin inclination angle. Further studies, specifically with realistic geometrical configurations and heat transfer settings, are urged to translate current findings to industrial applications.

An Integral Vonkarman Treatment of Magnetohydrodynamic Natural Convection on Heat and Mass Transfer Along a Radiating Vertical Surface in a Saturated Porous

An Integral Vonkarman Treatment of Magnetohydrodynamic Natural Convection on Heat and Mass Transfer Along a Radiating Vertical Surface in a Saturated Porous

Impact of induced magnetic field on magnetohydrodynamic (MHD) natural convection flow in a vertical annular micro-channel in the presence of radial magnetic field

This study is devoted to investigate the effect of induced magnetic field on fully developed magnetohydrodynamic (MHD) natural convection flow of electrically conducting fluid in a vertical annular micro-channel formed by two concentric cylinders in the presence of imposed radial magnetic field. The velocity slip and temperature jump at the annular micro-channel surfaces are taken into account. The influence of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into consideration. The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained under relevant boundary conditions. The expressions for velocity field, the induced magnetic field, temperature field, induced current density and skin friction have been obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity field, the induced magnetic field, temperature, induced current density, volume flow rate and skin friction are illustrated graphically to show interesting features of the radius ratio, rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number. During the course of investigation, it is found that for fixed value of Hartmann number, the skin friction profiles in the presence of induced magnetic field are higher compared to the case when the induced magnetic field is neglected.

Double MRT Lattice Boltzmann simulation of 3-D MHD natural convection in a cubic cavity with sinusoidal temperature distribution utilizing nanofluid

In this work numerical simulation of magneto hydrodynamics (MHD) natural convection in a three-dimensional cubic cavity with sinusoidal temperature distribution on one side wall has been considered. New means of the Lattice Boltzmann method with double Multi-Relaxation-Time (MRT) model has been applied utilizing cu/water nanofluid. D3Q19 and D3Q7 models have been used to solve the momentum and energy equations, respectively. Different Rayleigh numbers (Ra = 103_105) and various Hartmann numbers (Ha = 0–100) for volumetric fraction of the nanoparticles (Ø) between Ø = 0 and 12% have been investigated. Also, phase deviation varied from θ = 0 to π with interval π/2. The magnetic field is considered horizontally and the results have been shown at different planes and lines of the 3-D enclosure. Based on the results, the double MRT-LBM method is a proper method for simulating the 3-D flows with complex boundary conditions. The results show that augmentation of the Hartmann number decreases the heat transfer rate whereas the increase of the Rayleigh number and nanoparticles’ volumetric fraction enhance the heat transfer rate. The highest effect of magnetic field is obtained at Ra = 104 and the lowest effect is seen at Ra = 103. Also, the greatest effect of Rayleigh number is captured at Ha = 0 for all volumetric fraction of the nanoparticles.

LBM simulation of free convection in a nanofluid filled incinerator containing a hot block

The present study explores nanofluid magnetohydrodynamics (MHD) natural convection in an incinerator shaped enclosure including a rectangular hot block situated on the bottom wall. A parametric investigation is conducted to explore the effect of different parameters such as nanoparticles volume fraction (ϕ = 0–4%), Rayleigh number (Ra = 103–105), external magnetic field intensity (Ha = 0–100), incinerator tilting angle (γ = 0–360°) and hot block's height (0.1–0.5), width (0.1–0.8) and position on heat transfer, nanofluid flow, and entropy generation inside the incinerator. The top and bottom horizontal walls of enclosure are adiabatic; the right, left vertical and inclined walls are supposed to have cold temperature whereas the hot block is maintained at a hot temperature. The Brownian motion was also considered in calculating the effective nanofluid thermal conductivity and viscosity using Koo–Kleinstreuer–Li (KKL) correlation. The lattice-Boltzmann method is used with a D2Q9-D2Q9 double population's model as utilized CFD approach. The mesh independency study and the validation of proposed model are accomplished in several cases and very good agreement is found between present results and former experimental and numerical findings. The results showed that entropy generation is augmented by increasing height and width of heater, nanoparticles volume fraction and Rayleigh number but it is reduced by enhacing Hartmann number. However, increasing the magnetic field does not have notable influence on heat transfer, compared to other parameters. The optimum incinerator inclination angles to maximize heat transfer and minimize entropy generation are 90° and 270°.

A numerical investigation of magneto-hydrodynamic natural convection of Cu–water nanofluid in a wavy cavity using CVFEM

In this work, magneto-hydrodynamic natural convection of a nanofluid in a wavy cavity considering Brownian motion is studied numerically using the control volume finite element method. The effective viscosity and thermal conductivity of the nanofluid are defined by the correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered wavy cavity is heated from the left side and it cooled from the right side. Also, the top and bottom walls of the considered wavy cavity are assumed adiabatic. The impacts of various controlling parameters such as the Rayleigh number, wavy contraction ratio, Hartmann number and undulation number are examined on the contour maps of the streamlines and the isotherms. Further, the average and local Nusselt numbers are calculated and presented graphically and discussed. The findings narrate that the strength of the convective flow has a direct relationship with the Rayleigh number and also it has a reverse relationship with the wavy contraction ratio.

Effects of Magnetohydrodynamics on Natural Convection and Entropy Generation with Nanofluids

The paper presents a numerical study of the magnetohydrodynamic natural convection heat transfer of a heated block situated on the bottom wall of an enclosure filled with nanofluids. The transport equations for a Newtonian fluid are solved numerically using the lattice-Boltzmann method. The effective thermal conductivity and viscosity of the nanofluid are calculated by the Koo–Kleinstreuer–Li correlation. The influence of pertinent parameters such as Rayleigh number, solid volume fraction, Hartmann number, magnetic field inclination angle, nanoparticle volume concentration and aspect ratio of the rectangular heated block on the flow, heat transfer characteristics, and entropy generation has been investigated. It is found that the total entropy generation is an increasing function of the Rayleigh number, whereas it is a decreasing function of the Hartmann number. Moreover, the numerical results demonstrate that the average Nusselt number increases steadily but nonlinearly by the augmentation of the nanoparticle volume fraction. Also, the results show that the magnetic field with an inclination angle of has the maximum heat transfer coefficient and total entropy generation.

Magnetohydrodynamic natural convection flow in a vertical micro-porous-channel in the presence of induced magnetic field

In this work, the exact solution for fully developed magnetohydrodynamic natural convection flow of viscous, incompressible, electrically conducting fluid in vertical micro-porous-channel formed by electrically non-conducting infinite vertical parallel porous plates in presence of induced magnetic field is investigated. Effects of velocity slip and temperature jump conditions are taken into account due to their counter effects both on the volume flow rate and the rate of heat transfer. The governing coupled equations responsible for present physical situation are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field subject to the relevant boundary conditions. The expressions for the induced current density and skin friction at the micro-porous-channel surfaces are also obtained. A parametric study of some physical parameters is conducted and a representative set of numerical results for the velocity field, the induced magnetic field, temperature, induced current density, volume flow rate and skin friction are illustrated graphically to show interesting features of the suction/injection, rarefaction, fluid wall interaction, Hartmann number and the magnetic Prandtl number. Result reveals that, for a fixed value of the Hartmann number, the skin frictions at micro-porous-channel surfaces in the presence of induced magnetic field are higher compared to the case when the induced magnetic field is neglected.

Magnetohydrodynamics Natural Convection in a Triangular Cavity Filled With a Cu-Al2O3/Water Hybrid Nanofluid With Localized Heating From Below and Internal Heat Generation

This study investigates the convective heat transfer of a hybrid nanofluid filled in a triangular cavity subjected to a constant magnetic field and heated by a constant heat flux element from below. The inclined side of the cavity is cooled isothermally while the remaining sides are thermally insulated. The finite difference method with the stream function-vorticity formulation of the governing equations has been utilized in the numerical solution. The problem is governed by several pertinent parameters namely, the size and position of the heater element, B = 0.2–0.8 and D = 0.3–0.7, respectively, the Rayleigh number, Ra = 102–106, the Hartmann number, Ha = 0–100, the volume fraction of the suspended nanoparticles, ϕ = 0–0.2, and the heat generation parameter Q = 0–6. The results show significant effect of increasing the volume fraction of the hybrid nanofluid when the natural convection is very small. Moreover, the hybrid nanofluid composed of equal quantities of Cu and Al2O3 nanoparticles dispersed in water base fluid has no significant enhancement on the mean Nusselt number compared with the regular nanofluid.

Entropy generation of MHD nanofluid inside an inclined wavy cavity by lattice Boltzmann method

In this study, lattice Boltzmann method is applied in order to simulate the magnetohydrodynamic (MHD) natural convection heat transfer and entropy generation of CuO–water nanofluid inside an inclined wavy cavity. The left wavy wall is heated sinusoidal, while the right flat wall is kept at a constant temperature. The top and the bottom horizontal walls are smooth and insulated against heat and mass. The effects of active parameters such as solid volume fraction of nanoparticles, Rayleigh number, Hartmann number and inclination angles are examined on flow, heat transfer and entropy generation. The results proved that the heat transfer and entropy generation decline significantly with increasing Hartmann numbers, while those rise with increasing Rayleigh numbers. The results show that the effect of nanoparticles volume fraction on dimensionless Nusselt number and entropy generation is more pronounced at high Rayleigh number than at low Rayleigh number. Also the results indicate that the mean Nusselt number and total entropy generation changes with inclination angle, while the minimum values of $$Nu_{\text{m}}$$ and S belong to $$\theta = \pi /3$$ and 0, respectively.

Computational analysis of magneto-hydrodynamic natural convection in partially differentially heated cavity: Effect of cooler size

This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (Lc = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (103 ≤ Ra ≤ 105; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, while it varied inversely with Hartmann number. Further, the functional dependence of average Nusselt number with cooler size, Rayleigh number, and Hartmann number is established for possible use in engineering design purpose.

Unsteady MHD natural convection flow of a rotating viscoelastic fluid over an infinite vertical porous plate due to oscillating free-stream

PurposeThe purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.Design/methodology/approachThe resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.FindingsAn interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.Originality/valueVery little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3-Cu/water hybrid nanofluid filled with square porous cavity

The present work is focused on the analysis of the entropy generation and magneto-hydrodynamics natural convection flow and heat transfer in a square porous cavity differentially heated and cooled by heat source and sink, respectively filled with the Cu-Al2O3-Water hybrid nanofluid. The effective segments of the left and right sides of the cavity are kept at cooled temperature and the effective segments of top and bottom sides are kept at hot temperature. The enclosure’s ineffective segments of its sides are kept adiabatic. The thermal conductivity and the dynamic viscosity of the nanofluid are represented by different experimental correlations which are suitable to each nanoparticles. The finite difference methodology is used to solve the dimensionless partial differential equations governing the problem. A comparison with previously published studies and the present results shows very good agreement. Results are presented for entropy production in terms of Hartmann number, nanoparticle volume fraction and geometric parameters of the cavity.

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.

Analysis of magnetohydrodynamic natural convection in closed cavities through integral transforms

A hybrid numerical-analytical solution is proposed to analyze MHD (magnetohydrodynamic) natural convection of an electrically-conducting fluid within a square cavity, differentially heated at the sidewalls and subjected to an inclined external magnetic field. The first goal is to expand the spectrum of application of the so called Generalized Integral Transform Technique (GITT), dealing with a multiphysics formulation, while further demonstrating the relative merits of the proposed eigenfunction expansion approach in handling highly nonlinear and coupled systems of partial differential equations. The second goal is to provide a set of benchmark results in this important application for quantities of practical interest in determining the heat transfer rates, such as the average Nusselt number. The two-dimensional steady state equations are written in dimensionless form using the streamfunction-only formulation and are subsequently solved with the GITT approach, under automatic relative error control. Critical comparisons are performed against previous work reported in the literature, both computational and experimental, together with the corresponding physical interpretations, for different values of the governing parameters, such as Grashof number, Hartmann number, Prandtl number, and magnetic field inclination angle.

Natural convection flow of heat generating hydromagnetic couple stress fluid with time periodic boundary conditions

In this paper, analysis has been conducted to investigate the effects of couple stresses and internal heat generation on the magnetohydrodynamic (MHD) natural convection channel flow with steady-periodic heat input. By applying the steady-periodic heating assumptions, the flow-governing equations driving the fluid system are reduced to boundary-value problems and solved by a convergent successive approximation. The result of the computation shows that the skin friction at the lower wall decreases with increasing values of the couple stress parameter while it enhances the heat transfer rate.

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.

Analysis of magnetohydrodynamics (MHD) natural convection in 2D cavity and 3D cavity with thermal radiation effects

In this work, the thermal radiation effects on magnetohydrodynamics (MHD) natural convection in 2D cavity and 3D cavity are investigated numerically with different Plank number Pl and Hartmann number Ha. The radiative flux is obtained by solving radiative transfer equation (RTE) instead of widely used approximation methods. A combined method SCM-ACM (spectral collocation method-artificial compressibility method) is developed to solve the N-S equations. Comparative analysis of thermal radiation effects on MHD flow and heat transfer in 2D cavity and 3D cavity is conducted with same parameters. The results show that the thermal radiation strengthens the flow and heat transfer on the spanwise direction in 3D cavity, while the magnetic field plays opposite effects. The differences on flow and temperature distribution between 2D cavity and 3D cavity (on the middle XY-plane in the spanwise direction) are remarkable for high level thermal radiation and weak magnetic flied, and become smaller for weaker thermal radiation and stronger magnetic flied.