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An analytical investigation is conducted to analyze the impact of magnetic field and hydrodynamic slippage on two-dimensional electro-osmotic Brinkman flow in a microchannel with cosine surface zeta potential. The Brinkman equation is utilized to govern the fluid flow within a fully saturated, homogeneous, and isotropic porous medium. We consider a very small magnetic Reynolds number to eliminate the induced magnetic field equation. The Navier slip boundary condition is applied to assess the impact of hydrodynamic slippage. We utilize the Debye–Huckel length approximation to linearize the Poisson–Boltzmann equation, which governs the potential of the electrical double layer. The stream function is obtained analytically, and contour plots, velocity fields, shear stresses, and pressure gradients are assessed to gain a proper understanding of flow physics. We utilize the stream function to plot the streamline plots for distinct assumed flow parameters. We observed that for a fixed Darcy number, the intensity of flow vortices decreases with increasing Hartman number while increasing with increasing slip length. Further, altering the wave number in the assumed cosine-waved zeta potential causes asymmetrical recirculations in the flow, which helps in increasing the scalar mixing process in microdevices. Further, the proposed investigation has various crucial applications, such as microfluidic cooling systems, drug delivery systems, and so on. [ABSTRACT FROM AUTHOR]

This article thoroughly examined the impact of Lorentz and buoyancy forces on the movement of nanomaterials within a sealed container. The magnetic field was aligned with the x-axis, while gravity acted along the y-axis. The container featured a heated inner surface and a curved outer surface kept at a lower temperature, with a permeable domain allowing fluid flow. Using nanomaterials of various shapes was found to enhance heat transfer effectively. The investigation provides valuable insights into optimizing heat transfer in practical applications by utilizing the interaction between magnetic and buoyancy forces. The analysis applied Darcy’s formulation to account for permeable media and simplified the equations using a stream function concept. The numerical code underwent rigorous verification to ensure its accuracy and reliability. Introducing nanoparticles significantly increased the Nusselt number (Nu), indicating an approximate 41.42 % improvement in heat transfer efficiency. Additionally, raising the parameter “m” resulted in an 11.76 % increase in Nu. However, increasing Ha led to a 46.72 % reduce in Nu, reflecting reduced heat transfer efficiency. In contrast, boosting the Rayleigh number (Ra) substantially increased Nu, enhancing heat transfer efficiency by about 59.78 %.

This paper harnesses the spectral approach to study electromagnetohydrodynamics (EMHD) flow through an undulating 2D microchannel for a Newtonian fluid. The present study aims to investigate EMHD flow through a periodically patterned channel for large values of corrugation amplitude (surface roughness) relative to the channel height, Hartmann number and a wide range of wavelengths. A mathematical model is developed for the hydraulic permeability and the velocity field using the Fourier approach. By imposing a small pattern amplitude constraint, asymptotic analysis was employed to investigate the model presented in the literature. In the present study, hydraulic permeability is shown to strongly depend on the Hartmann number, pattern amplitude and wavelength. The spectral method predicts a monotonic decrease in hydraulic permeability irrespective of pattern amplitude at a small dimensionless wavelength (λ = 1) and Hartmann number (Ha < 1). At large wavelengths (λ > 3), the hydraulic permeability demonstrates an augmentation corresponding to the pattern amplitude. At intermediate wavelength ( 2.5 < λ < 3 ), the permeability of the channel firstly decreases and then increases with pattern amplitude. For large Hartmann numbers (H a ≫ 1) , the prediction from the spectral model exhibits a similar trend as a function of wavelength. Across a range of wavelengths, the spectral model captured the permeability minima for various large Hartmann number values. The spectral model is significantly faster than the finite-element-based numerical simulation, with computational efficiency ranging from 150 to 250 times higher. The existence of a limited pattern amplitude and Hartmann number for small-large wavelength patterns, at which the permeability of the channel is minimized, is one example of a prediction from the spectral model that is beyond the resolution of currently accessible asymptotic theories. [ABSTRACT FROM AUTHOR]

Two layered immiscible time-dependent flow in the presence of a magnetic field through a curved corrugated channel has been numerically studied. The flow is driven through a pulsatile pressure gradient and is mathematically formulated using a curvilinear coordinate system. The channel is characterized by sinusoidal corrugations that exhibit periodic behavior. The channel is divided into two regions: Region-I and Region-II. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using perturbation analysis and then solved using R-K $${4^{th}}$$4th-order method in conjunction with the shooting technique. The effects of various arising parameters on the flow variables have been investigated. A substantial effect of the magnetic field on flow has been observed when compared to the hydrodynamic case of liquid flow in a curved corrugated channel. Flow enhancement is observed for small corrugation wavenumbers, with maximum augmentation occurring for totally out-of-phase alignment. Notably, stress decreases as the value of the frequency parameter increases, whereas it increases with an elevation in Hartmann number at the outer wall of the channel. Interestingly, the opposite trend is observed for these parameters in relation to shear stress on the lower wall of the channel. [ABSTRACT FROM AUTHOR]

This investigation aims to examine the hydromagnetic flow of two liquid flows of fully developed incompressible Newtonian fluid in an inclined channel through the porous medium accounting for radiative heat flux, Joule heating, and viscous dissipation. The walls of the channel are maintained at different temperatures. A double perturbation method is employed to derive analytical results for velocity and temperature. Graphical results are presented for various arising parameters such as Hartmann number, Grashoff number, ratio of viscosity parameter, thermal conductivity ratio, and porous parameter. Further, the results for mass flux are presented in a tabular form and discussed. Reduction in the velocity and temperature distribution is observed by enhancing Darcy dissipation and frequency parameter. As the angle of inclination increases, there is a rise in flow and heat distribution. With the strength of the magnetic field and the rise in the Reynolds number, the mass flux decreases. A comparative study is carried out with the previously published work and the results are found to be in good agreement. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of magnetic field on two-dimensional flow of a viscous, incompressible fluid through composite porous channel using non-primitive boundary element method (BEM). We consider a rectangular channel consisting of two packings that are filled with fully saturated porous medium. It is assumed that both the porous regions are homogenous and isotropic with different permeabilities. Brinkman equation governs the fluid flow through porous media. We analyze the effect of Hartman number, stress-jump coefficient, Darcy number, thickness parameter, electrical conductivity ratio, and viscosity ratio on fluid mechanics. We present the effect of stress-jump coefficients on the interfacial velocity of the fluid against the thickness parameter and observe that the interfacial velocity increases with increasing stress-jump coefficients. We notice that for a fixed value of thickness parameter, the magnitude of vorticity (at lower and upper walls) increases with increasing Darcy number. Moreover, we observe that the magnitude of vorticity at the lower wall decreases and increases at the upper wall with increasing thickness parameter. We compute the Brinkman layer thickness near the interface of the composite porous channel in terms of several flow parameters and observe that the Brinkman layer thickness is strongly depend on the Hartman number, Darcy number, viscosity ratios, and stress-jump coefficient, respectively.

An analysis of the influence of inertia forces and ponderomotive forces on the destabilization of the flow of viscous fluids in the hydrodynamic initial section is given. Cases of flow of viscous, anomalously viscous and electrically conductive liquids are considered; the degree of influence of mass forces on the destabilization of the flow is estimated. As applied to the flow in the hydrodynamic initial section, the degree of influence of inertia forces from convective acceleration and forces with a magnetic nature can be different. Inertia forces stimulate the accelerated movement of the fluid, and in the case of forces with a magnetic nature, ponderomotive forces contribute to deceleration, which is confirmed by the results of studies of the velocity field. Recommendations are given for calculating the length of the hydrodynamic initial section in the presence of mass forces with different nature.

The creeping rotational motion of a magnetohydrodynamic couple stress fluid between two concentric spheres under the impact of slippages. The slippage conditions are applied on the surface of the inside sphere. In addition, the couple stresses on the boundary are assumed to vanish. The analytical solution to the problem is used to obtain the field functions of velocity, tangential stress, and couple stresses. The wall correction factor experienced by the fluid on the inner solid sphere is evaluated and plotted. However, in the presence of a magnetic field, the eddy current caused by rotating particles produces a torque that tends to rise because the assumption of the torque direction is the opposite direction of magnetic induction. Also, the first couple stress parameter, the angular velocity ratio, and slip condition did an improvement in the torque. On the other side, the wall correction factor slows down with slippage on the inner sphere and the size parameter. All results give limiting cases with no slippage and viscous fluid.

Numerical investigations are conducted to investigate the impact of the magnetic field on the molten phase formation and thermal performance of phase change material (PCM) incorporated with hybrid nanoparticles within a three-dimensional vertical channel subjected to differential heating. The PCM, lauric acid, is dispersed using nanoparticle pairings consisting of iron oxide combined with aluminum oxide, titanium dioxide, and single-wall carbon nanotubes. This study focuses on examining the melting characteristics under turbulent conditions, specifically at high Rayleigh (Ra) and Hartmann number (Ha) within the specified range of 106≤Ra≤1010 and 0≤Ha≤1500. The enthalpy-porosity method is being considered for evaluating the phase change characteristics with an in-house code. For Ha of 1500, the melting process influenced by thermal convection was effectively suppressed, leading to significant delays in the melting rates. The melting time and molten fraction of the PCM exhibit a decreasing trend in response to the applied magnetic field, which results in an 82.14% reduction in the heat transfer rate. The SWCNT-Fe3O4 nanoparticle pairs demonstrated superior thermal performance, as the melting fraction and convective heat transfer were increased by 84.03% and 43.83%, respectively. The thermal performance exhibits a decreasing relationship with the Hartmann number, resulting in a 23.87% reduction in the heat transfer of nanoenhanced lauric acid. The accuracy of the present mathematical model is confirmed through validation against experimental benchmark data.

Heat transfer and entropy generation are crucial considerations in the nuclear industry, where the safe and efficient transfer of heat is essential for the operation of nuclear reactors and other nuclear systems. Casson fluid is a useful tool in the nuclear industry for simulating the flow behavior of nuclear fuels and coolants, and for optimizing the design and operation of nuclear reactors. In view of this, the current investigation deals with the heat and fluid flow of unsteady Casson fluid in a circular pipe under the influence of magnetic field, internal heat generation, entropy generation and porous media. The governing equations have been simplified under suitable assumptions and nondimensional quantities. The simplified dimensionless governing equations have been solved using the method of separation of variables along with Bessel functions. It is concluded from the investigation that the temperature increases with time. The Casson fluid parameter raises the temperature and entropy generation. The temperature, entropy generation and Bejan number are the decreasing functions of the Prandtl number. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of magnetic field on two-dimensional flow of a viscous, incompressible fluid through composite porous channel using non-primitive boundary element method (BEM). We consider a rectangular channel consisting of two packings that are filled with fully saturated porous medium. It is assumed that both the porous regions are homogenous and isotropic with different permeabilities. Brinkman equation governs the fluid flow through porous media. We analyze the effect of Hartman number, stress-jump coefficient, Darcy number, thickness parameter, electrical conductivity ratio, and viscosity ratio on fluid mechanics. We present the effect of stress-jump coefficients on the interfacial velocity of the fluid against the thickness parameter and observe that the interfacial velocity increases with increasing stress-jump coefficients. We notice that for a fixed value of thickness parameter, the magnitude of vorticity (at lower and upper walls) increases with increasing Darcy number. Moreover, we observe that the magnitude of vorticity at the lower wall decreases and increases at the upper wall with increasing thickness parameter. We compute the Brinkman layer thickness near the interface of the composite porous channel in terms of several flow parameters and observe that the Brinkman layer thickness is strongly depend on the Hartman number, Darcy number, viscosity ratios, and stress-jump coefficient, respectively. [ABSTRACT FROM AUTHOR]

The aim of the present work is to examine the flow of electrically conducting immiscible Newtonian fluids with variable viscosity through an inclined channel under the influence of a magnetic field. The flow is generated because of a constant pressure gradient. The flow in an inclined channel is governed by the Navier–Stokes equations. Analytical expressions for the velocity, flow rate, and stress are derived. The influence of various parameters of the problem on the flow characteristics is analyzed. [ABSTRACT FROM AUTHOR]

This study examines the conjugate MHD free convection in an L-shaped chamber with a thick fin attached to one of its cold walls. The chamber's left and bottom parts have hot walls, whereas the ambient condition is maintained at the upper-right sides of the L-shaped chamber. A heat-conducting solid rectangular fin is vertically attached to the top of the mid-section of the chamber. The heat and fluid flow governed by heat energy and Navier-Stokes equations are numerically simulated with the help of finite element analysis. The influences of different governing and geometrical parameters such as Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (103 ≤ Ra ≤ 106), fin thickness (0.100 ≤ t/L ≤ 0.175, where L is the reference length of the chamber) and fin height (0.1 ≤ d/L ≤ 0.3) on the overall thermal characteristics of the system have been observed. The qualitative outcomes of this research are exhibited in the forms of streamline, isotherm, and heatline plots. The quantitative findings are presented utilizing the mean Nusselt number, the overall thermal performance ratio, and the average fluid temperature. These results confirm that the overall thermal improvement of the chamber due to the conjugate effects of heat transfer increases with increasing Hartmann number for a fin with the highest thickness and the shortest length. The overall thermal performance ratio increases by a maximum of 39.59% for an increase in Hartmann number from 0 to 30. Similarly, higher thickness and shorter length improve the overall thermal performance ratio by 45.18% and 415.06%, respectively.

This investigation aims to explain the study of heat transfer and entropy generation of Magnetohydrodynamics (MHD) viscous fluid flowing through a ciliated tube. Heat transfer study has massive importance in various biomedical and biological industry problems. The metachronal wave propagation is the leading cause behind this viscous creeping flow. A low Reynolds number is used as the inertial forces are weaker than viscous forces, and also, creeping flow limitations are fulfilled. For the cilia movement, a very large wavelength of a metachronal wave is taken into account. Entropy generation is used to examine the heat transfer through the flow. Numerical solutions are calculated by using MATHEMATICA. Exact mathematical solutions are calculated and analyzed with the help of graphs. Streamlines are also plotted. An axially symmetric flow as well as temperature profile is revealed through the graphical solutions. Both velocity and temperature profiles attain maximum value in the center of this ciliated tube that eventually declines toward the boundaries. [ABSTRACT FROM AUTHOR]

An analysis of the influence of inertia forces and ponderomotive forces on the destabilization of the flow of viscous fluids in the hydrodynamic initial section is given. Cases of flow of viscous, anomalously viscous and electrically conductive liquids are considered; the degree of influence of mass forces on the destabilization of the flow is estimated. As applied to the flow in the hydrodynamic initial section, the degree of influence of inertia forces from convective acceleration and forces with a magnetic nature can be different. Inertia forces stimulate the accelerated movement of the fluid, and in the case of forces with a magnetic nature, ponderomotive forces contribute to deceleration, which is confirmed by the results of studies of the velocity field. Recommendations are given for calculating the length of the hydrodynamic initial section in the presence of mass forces with different nature. [ABSTRACT FROM AUTHOR]

This paper presents a study on the influence of Magnetic Force impressed upon MHD fluid contained in a square cavity with a heated cone. The novelty of this work includes a heated cone whose orientation is varied at different angles. Calculations are performed for Prandtl number Pr = 0.71; Rayleigh number Ra = 10, 1000, and 100000; and Hartmann number Ha = 0, 50, and 100. The results are illustrated with streamlines, isotherms, and other relevant plots. It is observed that the influence of Ha becomes more noticeable with increasing Ra. Ha affects the flow by retarding the fluid movement and thus affects convective heat transfer. It is also observed that the cone orientation influences both fluid circulation and heat transfer. At high Ra, the vertical orientation of the cone resulted in lower heat flux than the left/right orientations. Also, under the same condition, the system remains cooler with the vertical cone at lower Ha, but becomes hotter after a certain value of Ha. These findings have practical design implications. [ABSTRACT FROM AUTHOR]

This paper investigated the run‐up flow of magnetohydrodynamics (MHD) incompressible, viscous, Newtonian fluid bounded by two parallel horizontal porous plates in the presence of transverse magnetic field. The fluid flow is initially due to constant pressure gradient, placed parallel to the plates. On attaining steady state, the pressure gradient is suddenly withdrawn and the lower porous plate is set into motion in its own plane, this phenomenon is termed as run‐up flow. The transfer of momentum is as a result of the disturbances emanating from the boundary into the fluid. The initial value problem is solved using Laplace transform technique to obtain the closed‐form solution for the velocity in the Laplace domain. Semi‐analytical result is obtained by an inversion technique based on Riemann‐sum approximation to invert the solution for velocity into its corresponding time domain. The mathematical simulation conducted shows that increasing the Hartmann number is observed to decrease the fluid velocity while increasing the pressure gradient is found to enhance the fluid velocity. Furthermore, the opposing effects of suction/injection parameter on the fluid velocity have been established in the research. [ABSTRACT FROM AUTHOR]

The MHD oscillatory flow of two immiscible, viscous liquids in a porous channel with heat transfer is the subject of this investigation. The two liquid layers with different viscosities flow in both regions. The analytical expressions for velocity and temperature distribution have been derived by solving the governing flow equations using the regular perturbation method. The effects of various parameters on the velocity, temperature, and Nusselt number have been shown graphically, and numerical values of skin friction and flow rate are presented in tabular form and discussed. According to our analysis, the mass flux reduces as the magnetic field strength rises. While the temperature of the liquid enhances with an increase in the Eckert number and the Prandtl number, the temperature distribution rises with a decrease in the thermal conductivity ratio. To validate the results, the analytical solutions are compared with the fourth-order numerical Runge-Kutta method coupled with the shooting approach, and the results are found to be in excellent agreement. [ABSTRACT FROM AUTHOR]

An investigative approach on study of a laminar natural heat convection on different geometric annuluses under impact of a constant magnetic field, using Ferro-Nano has been carried out. The three different cases of vertical cylindrical, cubic, and twisted cubic geometries, each are presented by a 3D model. These geometries are affected by a magnetic field which affects the variables such as heat transfer, natural heat convection, and entropy generation will be investigated. The chosen approach for this article is a numerical calculation, including Energy equations, Electrical potential equation, Hartmann number, Rayleigh, and Nusselt number. Results gathered by current study indicate that magnetic field is the primary reason of natural convection reduction phenomenon on each of the presented geometries. In the end it was illustrated that the average heat transfer has been reduced to 0.6% when the magnetic field is applied. Moreover, on the subject of the geometry amends, the twisted cubic had the highest amount or reduction of all the considered cases. [ABSTRACT FROM AUTHOR]

In this study, heat transfer due to forced convection of Al2O3-H2O nanofluid flow over an isothermal cylinder has been numerically investigated. Governing equations containing continuity, N-S equation and energy under steady state have been solved using finite volume method. Here, the Reynolds number (Re) are within the range of 10 to 40. Furthermore, volume fraction of nanoparticles (f) varies within the range of 0% to 5%. The effect of volume fraction of nanoparticles on fluid flow and heat transfer were investigated numerically. It was found that at a given Nusselt number, drag coefficient, re-circulation length, and pressure coefficient increases by increasing the volume fraction of nanoparticles. Transition from laminar flow with separation to creeping laminar flow is determined as a function of Hartmann number and the volume fraction of nanoparticle. The successive changes in the flow pattern are studied as a function of the Hartmann number. Suppression of vortex shedding occurs as the Hartmann number increases. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to investigate the flow and heat transfer of thermal radiation on the Jeffery fluid flow within a microchannel for the effects of the superhydrophobic surface (SHS) within suction/injection. The governing differential equations of motion and heat transfer are transformed into nonlinear coupled ordinary differential equations (ODEs) using appropriate similarity transformations. The ODEs are solved along with boundary conditions by adopting Runge–Kutta with shooting technique. Symbolic computational software such as MATLAB, the solver bvp4c syntax examines the behavior of the relevant physical parameters. However, some effective emerging parameters on the flow problem reveal that the microchannel walls within the suction/injection parameter increase the temperature, and the SHS is heated. In contrast, without slip, the opposite behavior is rendered. It is clearly shown that the velocity profile diminishes with increasing the Prandtl number. Furthermore, it is noticed that velocity decreases for increasing values of Hartmann number. Comparison with available results for particular cases is an excellent agreement. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to develop a mathematical foundation for exploring the complex interaction of Coriolis and Lorentz forces with the electromagnetohydrodynamic (EMHD) flow of a power-law fluid inside a microchannel with wall slip condition. Both the Lorentz and Coriolis forces act orthogonally to each other. Mathematical modeling of the problem is based on a set of classical Maxwell and Navier–Stokes equations, which are subsequently solved numerically by employing an implicit finite difference methodology. The numerical solution thus obtained has been found to be in an excellent agreement correlation with the ones reported in the scientific literature, for some limiting cases. A rigorous effort has been made to understand how the governing parameters (e.g., the Hartmann number, the fluid behavior index, the rotating Reynolds number, and the slip parameter) affect the flow under electromagnetohydrodynamic environment. The numerical results exhibit the strong dependence of the power-law flow velocity on the Reynolds number and the Hartman number. We have also noted that the shear-thinning flow accelerates rapidly, as compared to the Newtonian fluid, when the Hartmann number is greater than a particular value (which we call the critical value). Further, the existence of a cross-over point (the value of the governing parameter at which the way the parameter affects the centerline velocity is changed) has also been predicted. The outcome of the work may be helpful to meet the upcoming challenges in future technologies related to mechanical and electrical mechanisms where the non-Newtonian flows are encountered in rotating systems under intense magnetic forces. [ABSTRACT FROM AUTHOR]

This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the top wall is kept cold. Rayleigh–Bénard (RB) convection was considered a heat-transfer phenomenon within the cavity. The Hartmann ( H a ) number, by varying the inclination angle (θ), was considered in developing the equations by considering the input parameters, namely, the Rayleigh ( R a ) numbers, Darcy ( D a ) numbers, and porosity (ϵ) of the cavity in different segments. Each segment considers a data-driven approach to calibrate the Levenberg–Marquardt (LM) algorithm, which is highly linked with the artificial neural network (ANN) machine learning method. Separate validations have been conducted in corresponding sections to showcase the accuracy of the equations. Overall, coefficients of determination ( R 2 ) were found to be within 0.85 to 0.99. The significant findings of this study present mathematical equations to predict the average Nusselt number ( N u ¯ ). The equations can be used to quantitatively predict the heat transfer without directly simulating LBM. In other words, the equations can be considered validations methods for any LBM-MHD model, which considers RB convection within the range of the parameters in each equation. [ABSTRACT FROM AUTHOR]

In this article, we investigate the stability of flowing fluid in a horizontal cavity. The walls of which consists of a porous material under the influence of a magnetic field (MF) perpendicular to the cavity plane. We find that the real part of the wave velocity (α) is negative for any value of the Hartmann number (Ha) and the Ghratshof number (Gr) is greater than zero. In addition, we convert the governing equations to non-dimensional formulas. So, we obtain that Reynolds number (Re), wave number (k), Hartmann number (Ha), Ghratshof number (Gr), and Darcy number (Da) affect on the stability of the model through the graphs of these numbers. [ABSTRACT FROM AUTHOR]

The MHD oscillatory flow of two immiscible, viscous liquids in a porous channel with heat transfer is the subject of this investigation. The two liquid layers with different viscosities flow in both regions. The analytical expressions for velocity and temperature distribution have been derived by solving the governing flow equations using the regular perturbation method. The effects of various parameters on the velocity, temperature, and Nusselt number have been shown graphically, and numerical values of skin friction and flow rate are presented in tabular form and discussed. According to our analysis, the mass flux reduces as the magnetic field strength rises. While the temperature of the liquid enhances with an increase in the Eckert number and the Prandtl number, the temperature distribution rises with a decrease in the thermal conductivity ratio. To validate the results, the analytical solutions are compared with the fourth-order numerical Runge–Kutta method coupled with the shooting approach, and the results are found to be in excellent agreement.

The present work proposes a new, highly accurate and efficient computational technique for numerical solution of a strongly nonlinear singular two-point boundary value problem which governs electrohydrodynamic flow (EHF) of a fluid in an ion drag configuration in a circular cylindrical conduit. The nonlinearity confronted in the underlying problem is in the form of rational function and the governing equation has a singularity at the point z = 0. The proposed method tackles the singularity behavior at the origin. Analysis of the proposed method is carried out. Numerical experiments were performed to demonstrate the applicability and robustness of the new method. The velocity field of EHF of a fluid in radial direction is computed. In order to justify the advantage of the method, the computed results are compared with the results obtained from some recently developed computational techniques in the literature. The effects of two relevant parameters, namely the strength of nonlinearity (σ) and the Hartmann electric number (H) on the velocity profile are investigated. [ABSTRACT FROM AUTHOR]

Physical quantities such as skin friction coefficient, local Nusselt number, and local Sherwood number for Casson fluid flow in an irregular channel are determined in this article. Casson fluid properties are primarily enhanced in this flow due to the effects of magnetohydrodynamic (MHD), porous medium, thermal radiation, viscous dissipation, and chemical reaction. Because of the pressure gradient, oscillatory waves formed at the ends of the walls, which are also kept at constant temperatures and concentrations. The Lie group method is used to convert partial differential equations (PDEs) to ordinary differential equations (ODEs). Analytical solutions are provided for the momentum, energy, and concentration equations with benchmark solutions. Dimensionless numbers are computed to interpret physical quantities for this type of flow via graphs and tables. According to the variations of the emerging parameters, physical quantities exhibited reverse behaviour between the upper and lower walls. The velocity profile has an increasing attitude toward the Casson fluid parameter, the Darcy parameter, the wavelength, and the Reynolds number, but a decreasing attitude toward the Hartmann number. The concentration profile is decreasing due to the oscillation effect, but the Schmidt number has a growing influence.

• MHD conjugate mixed convection with internal heat generation and Joule heating is studied. • Heat transfer augments with increasing Grashof and Reynolds numbers and decreasing Stuart number. • Internal heat generation diminishes heat transfer and rises overall entropy generation. • Performance of aiding flow outperforms opposing flow configuration. The current investigation explores MHD combined free-forced convection and entropy generation within a square enclosure (e.g., a nuclear reactor heat removal system) incorporating resistive heating and interior heat production. The cavity features a centrally positioned rotating cylinder, with the leftmost edge kept at a greater temperature than the rightmost boundary. The upper and lower boundaries of the enclosure are thermally insulated throughout the analysis. The solid cylinder rotates clockwise or counterclockwise, generating an aiding or opposing flow configuration. The Galerkin finite element approach solves the two-dimensional Navier-Strokes and thermal energy equations. Four different cases are analyzed through numerical simulations within predetermined ranges of Grashof (103 ≤ Gr ≤ 105), Reynolds (31.623 ≤ Re ≤ 316.23), and Richardson (0.1 ≤ Ri ≤ 10) numbers to analyze conjugate laminar mixed convective flow. Besides, Hartmann (0 ≤ Ha ≤ 17.783) and Stuart (0 ≤ N ≤ 3.162) numbers are varied to address the change in the magnetic field's intensity considering resistive heating. Finally, the volumetric internal heat production factor (0 ≤ Δ ≤ 3) is considered to account for internal heat generation. This study's comprehensive quantitative findings encompass the system's thermal performance, leading to significant conclusions in their respective cases. It is observed that elevating Ri while decreasing Ha or increasing both Ri and N leads to enhanced heat transfer and a reduced average fluid temperature. In contrast, during pure mixed convective flow, Nu rises with simultaneous increments in Gr and Re and decreases in N. Conversely, internal heat production results in lower heat transfer and notable increases in entropy generation and thermal performance criterion. Significantly, during pure mixed convection (Ri = 1) with an aiding flow configuration, the introduction of internal heat generation results in a 36.47 % degradation in heat transport at constant Gr , Re, and N. However, under identical conditions (fixed Gr , Re , and N) and Δ = 0, the aiding flow exhibits 26.91 % better thermal performance than the opposing flow. [ABSTRACT FROM AUTHOR]

In this study, the steady state behavior of natural convection transport on a nanofluid in square enclosure was studied. The model equations were solved using Comsol Multiphysics; a solver for partial differential Navier–Stokes equations based on a two-dimensional Finite Element Method (FEM) over a range of Rayleigh numbers (103-106). Impact of the Rayleigh Number, the Darcy Number, the porosity, the solid fraction volume of porous medium and the nanoparticle concentration on natural convection are depicted. Obtained Results reveal that convection mode increases with rise of Rayleigh number. The simulated results were compared with other numerical data from the literature, which indicate that good agreement is founded.

The current study addresses the features of entropy generation and thermal flows regarding magnetized hybrid nanofluid in the presence of a cylinder in a closed hexagonal domain. The hexagonal cavity comprises two heated horizontal walls, and two are insulated while the other walls are cold. The whole system has been modeled as coupled non-linear partial differential equations. Also, normalized the governing coupled equation by utilizing a proper pair of variables and are computed with a finite element approach. For the approximation of velocity profiles, a finite element space involving the quadratic polynomial (P2) is selected whereas the pressure and temperature estimation is accomplished through a space of linear polynomial (P1). An analogy is handed with published findings at confining instance. The degree of freedom and grid convergence test is considered for the kinetic energy (KE) and Bejan number (Be). The study reveals a major role in enhancing the heat transfer rate due to hybrid nano-particles. The results show that the increase of magnetic field effect considers the reduction of the heat transfer because the conduction motion occupies the motion of the fluid flow. When the Hartmann number is increased, the magnetic entropy is raised, too. For intensified the Hartmann numbers, the highest ratio of heat transfer occurs for the case of the hybrid nanoparticles, and then MgO-water, followed by the Ag-water. The nature of thermal flow parameters has been scrutinized.

The impacts of MHD and heat generation/absorption on lid‐driven convective fluid flow occasioned by a lid‐driven square enclosure housing an elliptic cylinder have been investigated numerically. The elliptic cylinder and the horizontal enclosure boundaries were insulated and the left vertical lid‐driven wall was experienced at a fixed hot temperature, and the right wall was exposed to a fixed cold temperature. COMSOL Multiphysics 5.6 software was used to resolve the nondimensional equations governing flow physics. A set of parameters, such as Hartmann number (0≤Ha≤50 $0\le {Ha}\le 50$), Reynolds number (102≤Re≤103 $1{0}^{2}\le {Re}\le 1{0}^{3}$), Grashof number (102≤Gr≤105 $1{0}^{2}\le {Gr}\le 1{0}^{5}$), heat generation‐absorption parameter (−3≤J≤3 $-3\le J\le 3$), and elliptical cylinder aspect ratio (AR) (1.0≤AR≤3.0 $1.0\le {AR}\le 3.0$) have been investigated. The current study discovered that for low Reynolds number, the adiabatic cylinder AR of 2.0 provided the optimum heat transfer enhancement for the model investigated, also the impact of cylinder size diminishes beyond Gr = 104. But for high Reynolds (Re = 1000), the size of the cylinder with AR = 3.0 offered the highest heat transfer augmentation. The clockwise flow circulation reduces because of an increase in AR, which hinders the flow circulation. In addition, heat absorption supports heat transfer augmentation while heat generation can suppress heat transfer improvement. [ABSTRACT FROM AUTHOR]

The present study reveals the analysis of steady mixed convection MHD stagnation point flow of Casson fluid of non-Newtonian nature and Heat transfer over an exponentially stretching surface where the consequence of uniform heat source and sink are taken in to consideration. The presiding Non-linear Partial differential equations and the corresponding boundary conditions are formulated and thus transformed into pair of nonlinear ordinary differential equations. The equations thus obtained are deciphered using Runge-Kutta fourth - order method with the help of MATLAB software. The results obtained for Skin friction coefficient and heat transfer rate for the case of Newtonian fluid are determined, which are in good harmony with the previously proclaimed results of other researchers. The impact of physical quantities such as Casson parameter, buoyancy parameter, Hartmann number, Prandtl number, heat source and sink, Suction parameter, on the fluid velocity and temperature are discussed through graphs for both assisting and opposing flow. The variation in Skin friction coefficient and Nusselt number are tabulated for various values of Hartmann number. Divergence in the velocity profile is observed for increase in Suction for two different values of Velocity ratio parameter. As Skin friction coefficient escalates with suction parameter indicating the exertion of drag force by the surface on the fluid flow. Also, the study reveals that the impact of Hartmann number is to minimize the boundary layer separation. [ABSTRACT FROM AUTHOR]

In this study, two-dimensional incompressible steady and time-dependent magnetohydrodynamic (MHD) flows around a cylinder were simulated by applying a finite volume method. The method was first validated through fair agreement of its results with the analytical solution for MHD flows inside the channels. It was then applied to simulate the MHD flows around a cylinder at Reynolds (Re) numbers varying from 100 to 1000 and Hartmann (Ha) numbers varying from 10 to 100. According to the results, although the increase in Re number strengthens the flow instability, the magnetic field suppresses this effect. The evidence for this claim is that the increase in Ha number leads to reduce in the separation angle for each Re number. This was in such a way that no flow separation was observed at Ha number equal to 50 and above for any considered Re number. Instability and therefore unsteady flows were seen only for the cases where Ha number was equal to 10 (the minimum considered value) and Re number was 500 or above. The drag coefficient (as a constant value for steady flows) or its average value (for unsteady flows) was enhanced by increasing the Ha number. The amplitude of the drag and lift coefficient fluctuations for unsteady cases were grown up by increasing the Re number. The Strouhal number was also found as a parameter that is dependent on both Re and Ha numbers. [ABSTRACT FROM AUTHOR]

The present study investigates the influence of uniform magnetic field on the flow of a Newtonian fluid sandwiched between two micropolar fluid layers through a rectangular (horizontal) porous channel. Fluid flow in the every region is steady, incompressible and the fluids are immiscible. Uniform magnetic field is applied in a direction perpendicular to the direction of fluid motion. The governing equations of micropolar fluid are expressed in Eringen's approach and further modified by Nowacki's approach. For respective porous channels, expressions for linear velocity, microrotations, stresses (shear and couple) are obtained analytically. Continuity of velocities, continuity of microrotations and continuity of stresses are employed at the porous interfaces; conditions of no slip and no spin are applied at the impervious boundaries of the composite channel. Numerical values of flow rate, wall shear stresses and couple stresses at the porous interfaces are evaluated by MATHEMATICA and listed in tables. Graphs of flow rate and fluid velocity are plotted and their behaviors discussed. [ABSTRACT FROM AUTHOR]

The current exploration deals with the third grade hydromagnetic pulsating flow of blood-gold nanofluid in a channel with the presence of Ohmic heating, viscous dissipation and radiative heat. In the present analysis, blood (base fluid) is considered as third-grade fluid and gold (Au) as nanoparticle. This investigation is useful in the fields of food processing system, pressure surges (pulsatile flow application), biomedical engineering, nano drug delivery, radiotherapy, and cancer therapeutic (nanofluid application). Perturbation method is employed to transform the set of governing partial differential equations (PDEs) into the ordinary differential equations (ODEs) and then solved by employing the fourth order Runge-Kutta method with the aid of the shooting technique. The impacts of emerging dimensionless parameters of velocity, temperature, and heat transfer rate of blood-Au nanofluid are analysed via pictorial outcomes in detail. The obtained results depict that the improvement in viscous dissipation and heat source enhanced the temperature of third grade nanofluid. The velocity and temperature of the nanofluid are declining functions with the enhancement of frequency parameter, material parameter, and non-Newtonian parameter respectively. Intensifying the volume fraction of nanoparticle dwindles the velocity and temperature of nanofluid. Enhancing volume fraction and viscous dissipation accelerates the heat transfer rate of nanofluid. The velocity, temperature, and heat transfer rates are decreased by an escalation of the Hartmann number. Further, enhancing the radiation parameter reduces the heat transfer rate and temperature of nanofluid. [ABSTRACT FROM AUTHOR]

An externally imposed transverse magnetic field, due to its damping nature, can control the flow separation around an object. Consequently, an inherently unsteady (or steady separated) flow around a bluff body may be transformed into a steady separated (or attached) flow pattern when an externally imposed magnetic field acts throughout the fluid domain transversely. When a pair of cylinders is arranged in tandem in an unconfined medium, the interference effect may contribute further instability to the resulting flow in comparison to a single cylinder case. This work reports how a transverse magnetic field influences the flow around a pair of tandem circular cylinders placed with varying gap spacing within an unconfined and electrically conducting fluid medium. A finite volume based numerical computation technique is adopted to study the magneto-fluidic phenomena. The flow Reynolds number lies in the range 10 ≤ Re ≤ 40 . Additionally, computations are also performed at a relatively higher Reynolds number, Re = 100. The non-dimensional gap between the cylinders is varied as 0.7–5.0 and the magnetic field strength (Hartmann number) is kept in the range 0–5. The flow patterns are steady separated at 10 ≤ Re ≤ 40 and unsteady with vortex shedding at Re = 100. The critical magnetic field strength at which the steady separated (and the unsteady) flow around the cylinders transformed into an attached (and steady separated) flow is obtained for the range of Reynolds number and gap spacing. With increasing Reynolds number, the critical magnetic field strength increases, while it decreases with increasing gap spacing. The observations are substantiated through visual inspection of the streamline profiles around the cylinders for varying Reynolds number and gap spacing. [ABSTRACT FROM AUTHOR]

The fluid flow and heat transfer of a nanofluid past a circular cylinder in a rectangular duct under a strong transverse magnetic field is studied numerically using a quasitwo-dimensional model. Transition from laminar flow with separation to creeping laminar flow is determined as a function of Hartmann number and the volume fraction of nanoparticle, as are critical Hartmann number, and the heat transfer from the heated wall to the fluid. Downstream cross-stream mixing induced by the cylinder wake was found to increase heat transfer. The successive changes in the flow pattern are studied as a function of the Hartmann number. Suppression of vortex shedding occurs as the Hartmann number increases.

Magnetohydrodynamics (MHD) flow in cavities subjected to both the magnetisation and the Lorentz forces due to a point magnetic source is studied. The governing PDEs are derived and iteratively solved by the dual reciprocity boundary elements method (DRBEM) with linear elements. It is shown that the magnetic field decelerates the axial flow around the point magnetic source, and a further increase in Ha causes a reverse flow in the pipe axis direction. An increase in Re, Ha, or Mn reduces the electric potential in magnitude. The planar velocity values decrease at the same rate as the Re increment. The influence of the magnetisation force lessens in high Re cases without alternating the axial velocity and the electric potential within the pipe. This study is the first to give the effects of both the magnetisation and the Lorentz forces on the fluid behaviour in terms of velocity, pressure, and electric potential. [ABSTRACT FROM AUTHOR]