Horizontal Magnetic Field Research Articles

Stability for the 2D magnetic Bénard system with partial dissipation and thermal damping near an equilibrium

In this paper, we focus on the Boussinesq equations with magnetohydrodynamics convection, in which the temperature obeys degenerate damped wave equations. Under the influence of an equilibrium, we prove that the 2D magnetic Bénard system remains stable in the whole space . In particular, we obtain the decay rate and large‐time behavior. Without the coupling, the 2D MHD system with only vertical dissipation is not known to be stable. It is revealed that both the thermal damping and the horizontal background magnetic field are indispensable.

Structure, morphology and crystallization behavior of PVDF/Co nanowire nanocomposites under horizontal and vertical magnetic fields

So far, very limited research has been carried out on the fabrication of polyvinylidene fluoride (PVDF) composited with anisotropic magnetic nanostructures such as nanowires or nanorods, which can potentially provide specific reactions to magnetic fields. Here, single crystal Co nanowires (CNWs) with an average length and diameter of about 220 and 12nm, respectively, are synthesized using a solvothermal method, followed by adding them to PVDF matrix in order to prepare flexible PVDF/CNW nanocomposites by solvent casting and solution crystallization processes at room temperature. The nucleation and growth of PCNW nanocomposites are investigated in the absence and presence of horizontal and vertical magnetic fields. According to FESEM images, in addition to the direction of the applied magnetic field, the presence or absence of CNWs induces different effects on the size of spherulites and the configuration of polymer chains. By adding CNW to the PVDF matrix in the absence of a magnetic field and under a horizontal magnetic field, the size of the spherulites in the pure PVDF film increases about 67% (from 3 to 5 μm) and 300% (from 3 to 12 μm), respectively. Under a vertical magnetic field, the addition of CNW reduces the size of the spherulites to 1 μm, thereby forming a film with a combination of spherulites and filamentary structure likely due to the nanowire-nanowire, nanowire-chain and chain-chain interactions. Also non-contact flexible triboelectric nanogenerators of magnetic force are fabricated.

Solar active region evolution and imminent flaring activity through color-coded visualization of photospheric vector magnetograms

Context. The emergence of magnetic flux, its transition to complex configurations, and the pre-eruptive state of active regions are probed using photospheric magnetograms. Aims. Our aim is to pinpoint different evolutionary stages in emerging active regions, explore their differences, and produce parameters that could advance flare prediction using color-coded maps of the photospheric magnetic field. Methods. The three components of the photospheric magnetic field vector are combined to create color-combined magnetograms (COCOMAGs). From these, the areas occupied by different color hues are extracted, creating appropriate time series (color curves). These COCOMAGs and color curves are used as proxies of the active region evolution and its complexity. Results. The morphology of COCOMAGs showcases typical features of active regions, such as sunspots, plages, and sheared polarity inversion lines. The color curves represent the area occupied by photospheric magnetic field of different orientation and contain information pertaining to the evolutionary stages of active regions. During emergence, most of the region area is dominated by horizontal or highly inclined magnetic field, which is gradually replaced by more vertical magnetic field. In complex regions, large parts are covered by highly inclined magnetic fields, appearing as abrupt color changes in COCOMAGs. The decay of a region is signified by a domination of vertical magnetic field, indicating a gradual relaxation of the magnetic field configuration. The color curves exhibit a varying degree of correlation with active region complexity. Particularly the red and magenta color curves, which represent strong, purely horizontal magnetic field, are good indicators of future flaring activity. Conclusions. Color-combined magnetograms facilitate a comprehensive view of the evolution of active regions and their complexity. They offer a framework for the treatment of complex observations and can be used in pattern recognition, feature extraction, and flare-prediction schemes.

Comparison of natural convection in liquid gallium under horizontal and vertical magnetic fields

The dynamics of two-dimensional natural convection in liquid metal under the influence of magnetic fields within a confined square enclosure are numerically investigated using a high-accuracy method. The study focuses on the flow transition process influenced by both horizontal and vertical magnetic fields, examining the impacts of temperature difference, magnetic field strength, and orientation on flow characteristics and heat transfer. The range of Rayleigh numbers (Ra) explored is from 104 to 106, while Hartmann numbers (Ha) vary from 0 to 100. Liquid gallium is used as the working fluid with a Prandtl number (Pr) of 0.025. Our investigation reveals rich variations in flow patterns, categorized into unsteady periodic, steady “two-in-one” vortex, and steady single vortex states. As Rayleigh numbers increase, a complex series of flow transitions is observed, leading to enhanced flow dynamics. The transition from a steady state to periodic motion is accompanied by a notable increase in heat transfer efficiency. However, increasing the strength of the magnetic field suppresses the flow. A sufficiently strong suppression transitions the flow from periodic motion back to a steady state, resulting in a gradual decrease in heat transfer efficiency. For the parameters considered, the suppression efficiency of horizontal magnetic fields is stronger than that of vertical ones, especially when Ra>6×105 and Ha=100, with a 14% greater suppression efficiency. A scaling law for heat transfer is also identified: Nu:Ra/Ha2γ, where 14≤γ≤12, independent of the magnetic field orientation.

Statistical and Numerical Investigations of Convective Heat Transfer Enhancement of Nanofluids Inside a Rectotrapezoidal Enclosure in the Presence of Horizontal Periodic Magnetic Field

Statistical and Numerical Investigations of Convective Heat Transfer Enhancement of Nanofluids Inside a Rectotrapezoidal Enclosure in the Presence of Horizontal Periodic Magnetic Field

Modelling and Analysis of Evacuated Tube Solar Collector Working with Hybrid Nanofluid

This research study is concerned with developing a mathematical model for an Evacuated Tube Solar Collector (ETSC) that utilizes a Hybrid Nanofluid flow in a manifold. The model consists of a set of the partial differential equations that, using the dimensional analysis approach, are reduced to a dimensionless system. The exact solution method, assisted by the Mathematica program, is used to solve the system. The study examines the impact of certain factors on flow and heat transmission, including horizontal velocity, temperature variation, heat source, magnetic field, Prandtl Number, and Eckert Number, and provides a detailed analysis of the results. The key findings of the analysis revealed that an increase in hybrid nanoparticle volume effects in a reduce in velocity and heat transfer coefficient. Additionally, elevated heat source and Prandtl number correspond to an increased heat transfer coefficient.

Effects of horizontal magnetic field position on oxygen control in 12-inch Czochralski silicon

The application of a horizontal magnetic field is an important method for controlling point defects and impurity distribution in 12-inch Czochralski silicon used in integrated circuits. This work introduces the effects and mechanisms of horizontal magnetic field positioning on oxygen concentration in 12-inch single crystal silicon used for commercial integrated circuits. Effect of melt convection, and temperature distribution on oxygen concentration at the bodying length of 500 mm was presented and analyzed by combining growth experiments and numerical simulations (using CGSim_23_2 from STR) with different horizontal magnetic field positioning. This study found that the mechanism of magnetic field control of oxygen is not directly correlated with the convection suppression effect. It is important to avoid the overlap of strong magnetic regions with high-temperature areas, as this can lead to additional oxygen dissolution.

Effect of static magnetic field on corrosion of X70 pipeline steel in dilute sodium bicarbonate solutions

This paper focuses on the effect of a 0.1 T static horizontal magnetic field on the corrosion of X70 pipeline steel in 0–0.05 mol/L sodium bicarbonate solutions. The weight loss data indicate that the magnetic field reduces the average corrosion rate during immersion within 48 h in all the test solutions. The magnetic field tends to increase the average corrosion rates for the immersion time of 72 h and 96 h. The magnetic field increases the proportion of magnetite in corrosion products formed on the specimen of immersion in 0.05 mol/L sodium bicarbonate solution for 168 h. The open-circuit potentials (OCP) are in the active zone of the E-pH diagram within 48 h immersion with 0 T and 0.1 T magnetic field. A 0.1 T magnetic field delays the process for the electrode to enter the passive zone of the E-pH diagram. The linear polarisation resistance (LPR) data shows that the resistance of the active zone with 0.1 T magnetic field is larger than that with 0 T. The electrochemical impedance results also indicate that the electrode is in an active state when the potential is below −700 mVSCE and in a passive state when the potential is above −200 mVSCE.

Mass Cycle and Dynamics of a Virtual Quiescent Prominence

The mass cycle of solar prominences or filaments is still not completely understood. Researchers agree that these dense structures form by coronal in situ condensations and plasma siphoning from the underlying chromosphere. In the evaporation–condensation model siphoning arises due to evaporation of chromospheric plasma from localized footpoint heating, but this is challenging to justify observationally. Here, we simulate the reconnection–condensation model at extreme resolutions down to 20.8 km within a three-dimensional (3D) magnetohydrodynamic coronal volume. We form a draining, quiescent prominence and associated coronal rain simultaneously. We show that thermal instability—acting as a trigger for local condensation formation—by itself drives siphoning flows from the low corona without the need of any localized heating. In addition, for the first time, we demonstrate through a statistical analysis along more than 1000 magnetic field lines that cold condensations give rise to siphoning flows within magnetic threads. This siphoning arises from the strong pressure gradient along field lines induced by thermal instability. No correlation is found between siphoning flows and the prominence mass, making thermal instability the main in situ mass-collection mechanism. Our simulated prominence drains by gliding along strongly sheared, asymmetric, dipped magnetic arcades, and develops natural vertical fine structure in an otherwise horizontal magnetic field due to the magnetic Rayleigh–Taylor instability. By synthesising our data, our model shows remarkable agreement with observations of quiescent prominences such as its dark coronal cavity in extreme-ultraviolet emission channels, fine-scale vertical structure, and reconnection outflows, which, for the first time, have been self-consistently obtained as the prominence evolves.

Design of a combined X–Y scanning magnet with high field uniformity for pencil beam scanning proton therapy

In proton therapy, scanning magnets play a crucial role in the treatment equipment. Specifically, in pencil beam scanning, these magnets are responsible for deflecting the proton beam, thereby enabling the illumination of the tumor’s precise location. To reduce the size of the scanning system, a combined X–Y scanning magnet is used instead of separate scanning magnets, which can reduce the overall size of the gantry. The design in this paper combines a window-shaped yoke and three sets of elephant-ear-shaped coils, and one of the coils generates a horizontal magnetic field while the other two coils generate a vertical magnetic field. By adjusting the distance between the coils and the shape of the coils at both ends, the magnetic integral field exhibits higher uniformity compared to other combined scanning magnets. The simulation results show that the integrated field achieves a uniformity of 0.84% in the horizontal direction and 0.60% in the vertical direction. Particle tracking simulation and steady-state thermal analysis were also conducted. After cutting a certain number of slits with the same size at the ends of the magnetic yoke, the magnet can meet the requirements of a suitable working temperature. This magnet design has the capability to effectively decrease the space utilized by the scanning system, consequently reducing the rotational radius of the frame and minimizing the equipment required.

Report on the effects of the May 2024 Mother's day geomagnetic storm observed from Chile

This study investigates the extreme geomagnetic storm of May 10–15, 2024, utilizing data from the SER ground-based station in Chile and the DSCOVR satellite. The methodology involves calculating the horizontal magnetic field (H), filtering geomagnetic data using a Butterworth filter, and conducting cross-correlation analysis between solar wind parameters and Pc5 pulsations. The storm, starting with a sudden storm commencement triggered by a coronal mass ejection around 18:00 UT on May 10, exhibited a main phase lasting about 8 h, followed by a recovery phase starting on May 11. The extreme storm exhibited abrupt fluctuations in the interplanetary magnetic field data and solar wind parameters, inducing a depression in the geomagnetic field H-component reaching ΔH ∼ −551 nT at the SER station. Throughout the storm, solar wind parameters such as density, speed, and temperature exhibited varied ranges, with significant changes observed in all storm phases. Notably, during the initial and main phases, cross-correlation analysis unveiled robust associations between Pc5 pulsations and solar wind parameters such as density and speed, with maximum R values reaching 0.98 for both phases.

Scaling of the geomagnetic secular variation timescale

SUMMARY The ratio of the magnetic power spectrum and the secular variation spectrum measured at the Earth’s surface provides a timescale $\tau _{\rm sv}(l)$ as a function of spherical harmonic degree l. $\tau _{\rm sv}$ is often assumed to be representative of timescales related to the dynamo inside the outer core and its scaling with l is debated. To assess the validity of this surmise and to study the time variation of the geomagnetic field $\dot{\boldsymbol {B}}$ inside the outer core, we introduce a magnetic timescale spectrum $\tau (l,r)$ that is valid for all radius r above the inner core and reduces to the usual $\tau _{\rm sv}$ at and above the core–mantle boundary (CMB). We study $\tau$ in a numerical geodynamo model. At the CMB, we find that $\tau \sim l^{-1}$ is valid at both the large and small scales, in agreement with previous numerical studies on $\tau _{\rm sv}$. Just below the CMB, the scaling undergoes a sharp transition at small l. Consequently, in the interior of the outer core, $\tau$ exhibits different scaling at the large and small scales, specifically, the scaling of $\tau$ becomes shallower than $l^{-1}$ at small l. We find that this transition at the large scales stems from the fact that the horizontal components of the magnetic field evolve faster than the radial component in the interior. In contrast, the magnetic field at the CMB must match onto a potential field, hence the dynamics of the radial and horizontal magnetic fields are tied together. The upshot is $\tau _{\rm sv}$ becomes unreliable in estimating timescales inside the outer core. Another question concerning $\tau$ is whether an argument based on the frozen-flux hypothesis can be used to explain its scaling. To investigate this, we analyse the induction equation in the spectral space. We find that away from both boundaries, the magnetic diffusion term is negligible in the power spectrum of $\dot{\boldsymbol {B}}$. However, $\dot{\boldsymbol {B}}$ is controlled by the radial derivative in the induction term, thus invalidating the frozen-flux argument. Near the CMB, magnetic diffusion starts to affect $\dot{\boldsymbol {B}}$ rendering the frozen-flux hypothesis inapplicable. We also examine the effects of different velocity boundary conditions and find that the above results apply for both no-slip and stress-free conditions at the CMB.

Weakly nonlinear analysis of rotating magnetoconvection with anisotropic thermal diffusivity effect

The influence of anisotropic thermal diffusive coefficient on the stability of the horizontal fluid planar layer rotating about its vertical axis and permeated by the horizontal homogeneous magnetic field is studied. The linear stability analysis is carried out using the normal mode method. The stationary cross/oblique and parallel modes are calculated for different ranges of control parameters arising in the system. The SA (Stratification Anisotropy) parameter, α (the ratio of horizontal and vertical thermal diffusivities), plays a key role in deciding the boundaries between these modes and their instability regions when there is a combination of high and low rotation with weak and strong magnetic fields. The obtained isotropic results coincide with those obtained by pioneers in the literature. The weakly nonlinear behavior of the stationary convective motion in the vicinity of primary instability threshold is studied using the two-dimensional Landau–Ginzburg (LG) equation with cubic nonlinearity. This equation derived using the multiple scale analysis is similar to the one obtained in the literature having different relaxation time, nonlinear coefficient, and coherence lengths. These coefficients are used to study the heat transfer rate. In the case of high rotation, Nusselt number gets decreased from atmospheric (α < 1) to oceanic (α > 1) SA types. The domain for secondary instability of Eckhaus is obtained using the spatiotemporal LG equation and it is observed that the Eckhaus instability region decreases with increasing α.

Searching for Evidence of Subchromospheric Magnetic Reconnection on the Sun

Within the coronae of stars, abundances of those elements with low first ionization potential (FIP) often differ from their photospheric values. The coronae of the Sun and solar-type stars mostly show enhancements of low-FIP elements (the FIP effect) while more active stars such as M dwarfs have coronae generally characterized by the inverse-FIP (I-FIP) effect. Highly localized regions of I-FIP effect solar plasma have been observed by Hinode's EUV Imaging Spectrometer in a number of highly complex active regions (ARs), usually around strong light bridges of the umbrae of coalescing/merging sunspots. These observations can be interpreted in the context of the ponderomotive force fractionation model, which predicts that plasma with I-FIP effect composition is created by the refraction of waves coming from below the plasma fractionation region in the chromosphere. A plausible source of these waves is thought to be reconnection in the (high-plasma-β) subchromospheric magnetic field. In this study, we use the 3D visualization technique of Chintzoglou & Zhang combined with observations of localized I-FIP effect in the corona of AR 11504 to identify potential sites of such reconnection and its possible consequences in the solar atmosphere. We found subtle signatures of episodic heating and reconnection outflows in the expected places, in between magnetic flux tubes forming a light bridge, within the photosphere of the AR. Furthermore, on either side of the light bridge, we observed small antiparallel horizontal magnetic field components, supporting the possibility of reconnection occurring where we observe I-FIP plasma. When taken together with the I-FIP effect observations, these subtle signatures provide a compelling case for indirect observational evidence of reconnection below the fractionation layer of the chromosphere, however direct evidence remains elusive.

Martian Crustal Magnetic Field Effects on the Ionospheric Main Peak

Planetary magnetic fields can affect ionospheric plasma transport and coupling with the solar wind. In contrast to the terrestrial global magnetic field, there are only weaker and sporadic crustal magnetic fields on Mars. Many studies have indicated that Martian crustal fields can still modulate the topside ionosphere and its coupling with the solar wind. Nevertheless, it is unclear whether the crustal fields can affect the ionospheric main peak, which does not directly interact with the solar wind and is dominated by photochemical processes. In this study, the crustal field effect was identified from ionospheric measurements over unevenly distributed crustal fields. Both the intensity and configuration of the crustal fields were found to be capable of affecting the ionospheric main peak. The ionospheric peak electron density tends to decrease in the strong horizontal crustal field region. The results suggest that the crustal fields may affect the ionospheric main peak through modulating solar wind energetic particle precipitation; strong horizontal magnetic fields can partially prevent energetic particle precipitation and thus weaken impact ionization.

Control of Three-Dimensional Natural Convection of Graphene–Water Nanofluids Using Symmetrical Tree-Shaped Obstacle and External Magnetic Field

This numerical investigation explores the enhanced control of the 3D natural convection (NC) within a cubic cavity filled with graphene–water nanofluids, utilizing a bottom-center-located tree-shaped obstacle and a horizontal magnetic field (MF). The analysis includes the effects of the Rayleigh number (Ra), the solid volume fraction of graphene (φ), the Hartmann number (Ha), and the fins’ length (W). The results show complex flow patterns and thermal behavior within the cavity, indicating the interactive effects of nanofluid properties, the tree-shaped obstacle, and magnetic field effects. The MHD effects reduce the convection, while the addition of graphene improves the thermal conductivity of the fluid, which enhances the heat transfer observed with increasing Rayleigh numbers. The increase in the fins’ length on the heat transfer efficiency is found to be slightly negative, which is attributed to the complex interplay between the enhanced heat transfer surface area and fluid flow disruption. This study presents an original combination of non-destructive methods (magnetic field) and a destructive method (tree-shaped obstacle) for the control of the fluid flow and heat transfer characteristics in a 3D cavity filled with graphene–water nanofluids. In addition, it provides valuable information for optimizing heat transfer control strategies, with applications in electronic cooling, renewable energy systems, and advanced thermal management solutions. The application of a magnetic field was found to reduce the maximum velocity and total entropy generation by about 82% and 76%, respectively. The addition of graphene nanoparticles was found to reduce the maximum velocity by about 5.5% without the magnetic field and to increase it by 1.12% for Ha = 100. Varying the obstacles’ length from W = 0.2 to W = 0.8 led to a reduction in velocity by about 23.6%.

Hydromagnetic Thermosolutal Instability of an Oldroyd Nanofluid in a Porous Medium

The onset of double-diffusive convection of an Oldroyd nanofluid fluid saturated in a porous medium, heated and soluted from below, is examined both analytically and numerically under the linear stability analysis in the presence of a horizontal magnetic field and physically realistic boundary condition on the volume fraction of nanoparticles. The resulting eigenvalue problem is solved numerically by employing Galerkin method. We recover the important works of Umavathi and Prathap Kumar (J. C. Umavathi and J. Prathap Kumar, J. Heat Transfer 139, 012401 (2017)), Jaimala et al. (R. Jaimala, Singh, and V. K. Tyagi, Int. J. Heat Mass Transfer 111, 451 (2017); Jaimala, R. Singh, and V. K. Tyagi, Int. J. Heat Mass Transfer 125, 290 (2018)) and Kuznetsov and Nield (A. V. Kuznetsov and D. A. Nield, International Journal of Thermal Sciences 77, 126 (2014)) as special cases. The important findings include: (i) the independence of thermal Rayleigh-Darcy number for stationary convection upon relaxation and retardation parameters, (ii) the parameters Rn, Rs, Le, NA and λ1 (absent in case of stationary convection) enhance both the stationary and oscillatory convections and the parameter Q, ε and λ2 (absent in case of stationary convection) delay the occurrence of both convections, (iii) instability first sets in as oscillatory convection and (iv) a number of sufficient conditions for the existence and also for the non-existence of oscillatory convection are obtained analytically but only stated (without proof).

Experimental study of a single bubble's motion in a liquid metal under a horizontal magnetic field

An ultrasonic phased array system is introduced to study the three-dimensional (3-D) movement of a single bubble in a GaInSn alloy under a transverse magnetic field (MF), which is verified by bubble experiments in water. The 3-D motion trajectories of individual bubbles in the GaInSn are obtained under a horizontal MF. As the MF becomes stronger, the bubble successively oscillates in random directions (R mode), a direction perpendicular to the MF (V mode), a direction parallel to the MF (P mode) and finally it rises straight (S mode). The significant anisotropy of the oscillation directions at a moderate MF intensity may be due to the anisotropy of the vortex structure around the bubble. Furthermore, the oscillation amplitude gradually declines with increasing MF intensity until the bubble trajectory finally becomes a straight line. Our measurements allow us to specify the characteristic regions for the observed bubble modes in the $N-Eo-Re$ parameter space (N is the magnetic interaction parameter, Eo is the Eötvös number and Re is the Reynolds number). In addition, more detailed characteristics of bubble terminal velocity are revealed, showing that the bubble velocities are closely related to the motion modes. The increase in bubble velocity at a moderate MF intensity is caused by the weakening oscillation. At a high strength, the MF monotonically suppresses the rise velocity of the bubble with a fixed scaling law.

The impact of the Hunga Tonga–Hunga Ha’apai volcanic eruption on the Peruvian atmosphere: from the sea surface to the ionosphere

The eruption of the Hunga Tonga Hunga Ha’apai volcano on 15 January 2022 significantly impacted the lower and upper atmosphere globally. Using multi-instrument observations, we described disturbances from the sea surface to the ionosphere associated with atmospheric waves generated by the volcanic eruption. Perturbations were detected in atmospheric pressure, horizontal magnetic field, equatorial electrojet (EEJ), ionospheric plasma drifts, total electron content (TEC), mesospheric and lower thermospheric (MLT) neutral winds, and ionospheric virtual height measured at low magnetic latitudes in the western South American sector (mainly in Peru). The eastward Lamb wave propagation was observed at the Jicamarca Radio Observatory on the day of the eruption at 13:50 UT and on its way back from the antipodal point (westward) on the next day at 07:05 UT. Perturbations in the horizontal component of the magnetic field (indicative of EEJ variations) were detected between 12:00 and 22:00 UT. During the same period, GNSS-TEC measurements of traveling ionospheric disturbances (TIDs) coincided approximately with the arrival time of Lamb and tsunami waves. On the other hand, a large westward variation of MLT winds occurred near 18:00 UT over Peru. However, MLT perturbations due to possible westward waves from the antipode have not been identified. In addition, daytime vertical plasma drifts showed an unusual downward behavior between 12:00 and 16:00 UT, followed by an upward enhancement between 16:00 and 19:00 UT. Untypical daytime eastward zonal plasma drifts were observed when westward drifts were expected. Variations in the EEJ are highly correlated with perturbations in the vertical plasma drift exhibiting a counter-equatorial electrojet (CEEJ) between 12:00 and 16:00 UT. These observations of plasma drifts and EEJ are, so far, the only ground-based radar measurements of these parameters in the western South American region after the eruption. We attributed the ion drift and EEJ perturbations to large-scale thermospheric wind variations produced by the eruption, which altered the dynamo electric field in the Hall and Pedersen regions. These types of multiple and simultaneous observations can contribute to advancing our understanding of the ionospheric processes associated with natural hazard events and the interaction with lower atmospheric layers.Graphical

Modeling of magnetohydrodynamic free convection in an enclosure having elliptical sinks using lattice Boltzmann method

AbstractThis paper adopted the Lattice Boltzmann Method (LBM) to compute a two‐dimensional incompressible convective flow field with two isothermal elliptical sinks attached vertically to the horizontal bottom north side of the enclosure, which is subjected to a horizontal magnetic field. The attained results show that LBM can effectively capture vortex shedding structures and other features inside such complex flow. Also, the Hartmann numbers with a panoply of heated sinks location were studied, and the results showed that fluid flow and heat transfer rate depend on the Hartmann number and are greatly influenced by the heated sinks positions. The effect of the Prandtl number on the average Nusselt number is also highlighted.