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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]

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]

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]

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]

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]

• 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, 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 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]

Buoyancy assisted and buoyancy opposed mixed convection of a third‐grade fluid, which flows through vertically oriented parallel plates, subjected to uniform and constant wall heat fluxes, under the effect of an externally applied magnetic field, are investigated. The coupled, nonlinear conservation equations of momentum and energy are solved employing the collocation method (CM) and velocity and temperature distributions are solved semianalytically. The results produced by the CM and the results of exact solution are compared for the buoyancy assisted and buoyancy opposed flow of a Newtonian fluid through the vertically oriented parallel plates arrangement without the effect of the externally applied magnetic field. An excellent agreement is exhibited by demonstrating the efficacy of the CM. The effects of the third‐grade fluid parameter, Hartmann number, and mixed convection parameter on the dimensionless velocity, temperature, and Nusselt number are studied. The results imply that in the case of buoyancy assisted flow, an increment in the non‐Newtonian third‐grade fluid parameter causes a decrease in the fluid velocity near the plate walls, which finally causes an increase in the velocity in the central core of the plates. In buoyancy opposed flow, the effect of the same parameter is to oppose the flow reversal near the walls and with higher values of this parameter, it can totally prevent the flow reversal near the walls. The results of the present study can be useful in the fields of flow and heat transfer of various grades of polymers, paints, and food processing. [ABSTRACT FROM AUTHOR]

The problem of cooling two hot blocks in a novel geometry using magnetohydrodynamic flow of Al2O3–water nanofluid has been studied utilizing a D2Q9 Lattice Boltzmann Model. While the Hartmann number (Ha) takes 0, 50, or 100 values, the Richardson number (Ri) varies between 0.02 and 20. Four variations of the geometry are selected. The gravity angle is set to be either 0∘, 30∘, or −30∘. Results reveal that the Nusselt number (Nu) increases as Ri increases for all cases. Furthermore, the Hartmann number has a deteriorating effect on the Nusselt number except for low Ri numbers. In addition, the results indicate that while the geometrical configuration is having a considerable impact on the average Nusselt number at low and high Richardson numbers, it has a negligible effect at the mixed convection flow. The best angle for the gravitational force is also between 0 and −30∘. A new correlation for the Nu number based on all parameters is also presented. [ABSTRACT FROM AUTHOR]

This research aims to utilize the local thermal non-equilibrium (LTNE) model to discuss the heat transfer within a thermally developing region. This study delves into the effects of magnetohydrodynamics couple-stress fluid flow in a channel filled with porous medium within the framework of the LTNE model with consideration for axial conduction. The flow within this system is unidirectional, and the walls of the channel sustain a constant heat flux. Numerical solutions are obtained using the finite difference method. The computational and numerical findings are visually depicted through graphical representations. Our analysis concludes that as the couple stress parameter increases, the local Nusselt number decreases. Conversely, the Nusselt number rises with the Hartmann and Peclet numbers increase. Thermally fully developed condition is satisfied under the LTNE mode. Applications like heat exchangers or pipelines carrying heated fluids require careful consideration of thermal expansion and material stress due to their significant impact. Comprehending the impacts of non-equilibrium heat transfer can enhance the efficiency and effectiveness of heat exchanger designs. The present findings are validated by the existing literature's computational and experimental investigations. • Examine the effect of MHD couple-stress fluid in the thermal field forming under local thermal non-equilibrium (LTNE) with consideration for axial conduction. • A finite difference approach has been implemented to solve the coupled differential equation. • Hydrodynamics and convective heat transfer analysis have been discussed in this study. • Dimensionless temperature based on bulk mean temperature is discussed. • Fully developed conditions for the thermal field are satisfied under the LTNE model. • 3D visualization of temperature profiles is shown for the axial conduction effects. • As the couple stress parameter rises, the local Nusselt number decreases, while the Nusselt number increases with the Hartmann and Peclet numbers. • The present findings are validated by the existing literature's computational and experimental investigations. [ABSTRACT FROM AUTHOR]

In this paper, the steady fully developed MHD flow of a viscous incompressible electrically conducting fluid through a channel filled with a porous medium and bounded by two infinite walls is investigated numerically for the cases (i) Poiseuille flow and (ii) Couette--Poiseuille flow; with uniform suction and injection at the walls in the presence of an inclined magnetic field. The Brinkman equation is used for the flow in the porous channel and solved numerically using the finite difference method. Numerical results are obtained for velocity. The effects of various dimensionless parameters such as Hartmann number (M), suction//injection parameter (S), permeability parameter (α) and angle of inclination (θ) on the flow are discussed and presented graphically. [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. [ABSTRACT FROM AUTHOR]

The current paper studied the behavior of a triangular cavity occupied with Ag-MgO/water nanofluid under MHD natural convection and provided with a rotating circular barrier, while the right-angled corner is equipped with quarter-circle porous medium and maintained at a fixed hot temperature Th. Several parameters are tested such as Rayleigh number (103 ≤ Ra ≤ 106), Hartmann number (0 ≤ Ha ≤ 80) and Darcy number (10−5 ≤ Da ≤ 0.15). The obtained results depict the enhancing effect of Ra and the controlling role of the magnetic parameter on heat transport. Increasing the characteristics of the porous media such as the porosity and the permeability showed a substantial impact on the heat transport efficiency within the enclosure. Moreover, the novelty findings in this paper are principally illustrated in the boosting impact of raising the porous medium thickness when it is associated with the growing up of the heated parts of the geometry by increasing the dimension of the radius (rp). Also, the rotational velocity (ω) and the radius (rob) of the circular obstacle are tested and showed an important influence on the energy transport within the cavity. Moreover, the obtained results by modifying the length (a) prove its pertinent influence on the heat transfer performance. [ABSTRACT FROM AUTHOR]

This article deals, the pulsating flow of blood carrying Au/CuO Oldroyd‐B nanofluid through a porous channel with the effects of viscous dissipation, thermal radiation, and Joule (Ohmic) heating, and applied magnetic field. The perturbation technique is employed to get analytic solutions for flow variables. A comparison between analytical and numerical results shows a good agreement. The effect of various parameters is addressed extensively aided by pictorial results. The obtained results present that the velocity is reduced with the higher values of Hartmann number and volume fraction of nanoparticles. The temperature of nanofluid is enhanced with an enhancement of Eckert number and radiation parameter while it reduces with a rise in Hartmann number. Furthermore, the rise of the volume fraction of nanoparticles boosts up the rate of heat transfer. [ABSTRACT FROM AUTHOR]

The laminar, viscous and incompressible flow of an electrically conducting fluid across an unconfined wedge structure in the presence of a transverse magnetic field has been studied. Two-dimensional numerical simulations have been performed for Reynolds number (Re) = 1-150 and Hartmann number (Ha) = 0-10 for a fixed blockage ratio (ß) = d/W = 1/30. The magnetic induction method in magnetohydrodynamics module built in ANSYS FLUENT solver has been employed to compute the flow fields. Results show that the vortex shedding can be completely eliminated if the applied magnetic field is strong enough. In the steady flow regime, it has been found that the recirculation length reduces with the increase in Ha. A minimal reduction in the drag coefficient is observed with the increase in Ha as long as unsteady flow is maintained (Ha < 7.3). However, the drag coefficient has a tendency to significantly increase with the increase in Ha for steady flow. Similarly, the lift amplitude decreases with the increase in Ha indicating a diminishing effect on the strength of vortices. A critical Hartmann number (Hacr) of 7.3 has been found for Re = 100 at which complete suppression of vortex shedding is observed. [ABSTRACT FROM AUTHOR]

A numerical investigation is conducted to review the entropy study of magnetohydrodynamic (MHD) convection nanofluid flow from an inclined surface. In evaluating the thermophoresis and Brownian motion impacts, Buongiorno's model is applied to nanofluid transfer. Using Keller's implicit box technique, the governing partial differential conservation equations and wall and free stream boundary conditions are made into the dimensionless form and solved computationally. For different thermos physical parameter values, the numerical results are discussed both graphically and numerically. Verification of the present code with previous Newtonian responses is also included. To analyze the variability in fluid velocity, temperature, nanoparticle volume fraction, entropy, Bejan number, shear stress rate, wall heat, and mass transfer rates, graphical and tabulated results are reported. The study suggests applications in the manufacturing of nanomaterial fabrication, and so on. [ABSTRACT FROM AUTHOR]

The current work pertains to the peristaltic motion of a Casson fluid through a non-uniform channel with exposure to a radial magnetic field. The wall properties of the channel are taken into consideration. Moreover, the fluid is considered to possess variable viscosity which shows exponential variation across the width of the channel. The investigations also consider the mass and heat transfer properties of the Casson fluid, where convective boundary conditions are used and the thermal conductivity is taken be varying with fluid temperature. The model is built to give insight into blood flow through small vessels. Solution to the problem is obtained by the method of perturbation. The graphical analysis reveals an increase in the effect of variable viscosity on the fluid velocity close to the walls of the channel and also on the size of the bolus formed during trapping. Furthermore, an increase in fluid temperature was observed due to variable thermal conductivity. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann method is used to investigate the Rayleigh–Bénard convection of magnetohydrodynamic fluid flow inside a rectangular cavity filled by porous media. The Brinkman–Forchheimer model is considered in the simulation to formulate a porous medium mathematically, and the multi-distribution function model is considered to include the magnetic field effect with different inclination angles. The water is considered as the working fluid, which is electrically conducting. A comprehensive analysis of the impact of governing dimensionless parameters is performed by varying Rayleigh (Ra), Hartmann (Ha), and Darcy (Da) numbers, porosity (ϵ ), and inclination angles (ϕ ) of the applied magnetic field. Numerical results are evaluated in the form of streamlines, isotherms, and the rate of heat transfer in terms of the local and average Nusselt number as well as the entropy generation due to the irreversibility of the fluid friction, temperature gradient, and magnetic field effects. The results imply that increasing Ha and decreasing Da reduce the rate of heat transfer. The average Bejan number Be avg increases for increasing the Hartmann number. On the other hand, augmenting Ra and ϵ improves the heat transfer rate. It is also found that the change of the magnetic field inclination angle ϕ changes the rate of heat transfer and entropy generation. [ABSTRACT FROM AUTHOR]

Alfred studied on the steady Magneto hydrodynamic (MHD) Poiseuille flow between two infinite parallel porous plates in an inclined magnetic field. The case of steady Poiseuille flow without oscillatory to extend the existing work. The study examines the unsteady MHD Poiseuille oscillatory flow between the two infinite parallel porous plates in a magnetic field. The motion of two dimensional unsteady oscillatory flow of viscous, electrically, conducting, incompressible fluid flowing between two infinite parallel plates at constant pressure gradient was examined. The analytical expression for the fluid velocity obtained was expressed in terms of Hartmann number. The effects of the magnetic inclinations, Hartmann number, suction/injection and pressure gradient to the velocity are presented graphically. It was discovered that the increase in the Hartmann number and suction/injection leads to the increase in the velocity. [ABSTRACT FROM AUTHOR]

Two-dimensional magnetohydrodynamic (MHD) electroosmotic flow (EOF) in zeta potential patterned micro-parallel channels was studied. The flow was driven by the combination of the Lorentz force and the electric field force produced due to an externally imposed vertical magnetic field and two horizontal electric fields. The analytical solutions of stream function and velocity distribution were obtained under the condition of hydrodynamic slippage. The variations of velocities with related non-dimensional parameters, such as Hartmann number Ha,slip length B and electrokinetic width K were addressed in detail. Results show that, the patterned charged surfaces induce a vertical velocity component leading to the formation of the vortexes. Also, the magnitudes of velocities increase with slip length B and electrokinetic width K.Moreover, it is interesting to note that the magnitudes of velocities become small with the increasing value of Ha, unlike the situation where there exists a critical value of Ha in one-dimensional flow. The present theoretical results can be utilized to design efficient microfluidic devices. [ABSTRACT FROM AUTHOR]

In the present work, the magnetohydrodynamic flow of a micropolar fluid through the membrane composed of impermeable cylindrical particles coated by porous layer is considered. The flow of a fluid is taken parallel to an axis of cylinder and a uniform magnetic field is applied in transverse direction of the flow. The problem is solved by using the cell model technique for the flow through assemblage of cylindrical particles. The solution of the problem has been obtained by using no‐slip condition, continuity of velocity and stresses at interfaces along with Happle's no‐couple stress condition as the boundary conditions. The expressions for the linear velocity, micro‐rotational velocity, flow rate and hydrodynamic permeability of the membrane are achieved in this work. The obtained solution for velocities is used to plot the graph against various transport parameters such as, Hartmann number, coupling parameter, porosity, scaling parameter etc. The effect of these transport parameters on the flow velocity, micro‐rotational velocity, and the hydrodynamic permeability of the membrane have been presented and discussed in this work. [ABSTRACT FROM AUTHOR]

The present paper studies the impact of applied uniform transverse magnetic field on the flow of incompressible conducting fluid around a weakly permeable spherical particle bounded by a spherical container. Analytical solution of the problem is obtained using Happel and Kuwabara cell models. The concerned flow is parted in two regions, bounded fluid region and internal porous region, to be governed by Stokes and Darcy's law respectively. At the interface between the fluid and the permeable region, the boundary conditions used are continuity of normal component of velocity, Saffman's boundary condition and continuity of pressure. For the cell surface, Happel and Kuwabara models together with continuity in radial component of the velocity has been used. Expressions for drag force, hydrodynamic permeability and Kozeny constant acting on the spherical particle under magnetic effect are presented. Representation of hydrodynamic permeability for varying permeability parameters, particle volume fraction, slip parameter and Hartmann numbers are represented graphically. Also, the magnitude of Kozeny constant for weakly permeable and semipermeable sphere under a magnetic effect has been presented. In limiting cases many important results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, an exponential high-order compact alternating direction implicit (EHOC-ADI) difference method is developed for solving the coupled equations representing the unsteady incompressible, viscous magnetohydrodynamic (MHD) flow through a straight pipe of rectangular section. The method, in which the Crank-Nicolson scheme is used for the time discretization and an original EHOC difference scheme established for the steady 1D coupled system of convection-diffusion equations is used for the spatial discretization, is second order accurate in time and fourth-order accurate in space and requires only a regular five-point 2D stencil similar to that in the standard second-order methods and the three-point stencil for each 1D operator. A distinguishing desirable property of the proposed method is combining the computational efficiency of the lower order methods with superior accuracy inherent in high order approximations. The unconditional stable character of the method is verified by means of the discrete Fourier (or von Neumann) analysis. Numerical examples are carried out to illustrate and assess the performance and the accuracy of the method proposed currently. Computational results of the MHD flow in the 2D square-channel problems are presented for Hartmann numbers ranging from 0 to 106 and compared with the exact solutions and those obtained using other available methods in the literatures. [ABSTRACT FROM AUTHOR]

This study investigates steady two-dimensional laminar confined jet flow in the presence of an applied magnetic field. The magnetohydrodynamic equations with the format of the stream function and vorticity formulation of the fluid flow are solved numerically. A numerical method was developed by using a first-order upwind scheme at the boundaries and a second-order finite control volume scheme in the flow field. The results show that the expansion region of the jet is moving downstream while the channel width and the Reynolds number are increasing. The vortex and the recirculation zone are stretched with increased Hartmann number, and the jet expansion region is moving upstream while the vortex and the recirculation zone are reduced. The channel width and the Reynolds number for the jet development are positive efforts and the Hartmann number has a suppressed effect in the present confined jet flow field. [ABSTRACT FROM AUTHOR]

The transient Hartmann magnetohydrodynamic flow of two immiscible fluids flowing through a horizontal channel containing two porous media with oscillating lateral wall mass flux is studied. A two‐dimensional spatial model is developed for two fluids, one of which is electrically conducting and the other is electrically insulating. Both the fluid regimes are driven by a common pressure gradient. A Darcy‐Forchheimer drag force model is used to simulate the porous media effects on the flow in both the fluid regimes. Special boundary conditions are imposed at the interface. The governing second‐order nonlinear partial differential dimensionless equations are obtained for each region using a set of transformations. The resulting transport equations are controlled by the Hartmann hydromagnetic parameter (Ha), viscosity ratio parameter (α), two Darcy numbers (Da 1 and Da 2), two Forchheimer numbers (Fs 1 and Fs 2), two Reynolds numbers (Re 1 and Re 2), frequency parameter (εA) associated with the transpiration (lateral wall flux) velocity and a periodic frequency parameter (ω*t*). Numerical forward time/central space finite‐difference solutions are obtained for a wide range of the governing parameters. Bench marking is performed with a Galerkin finite‐element method (MAGNETO‐FEM), and the results are found to be in excellent agreement. Applications of the model include magnetic cleanup operations in coastal/ocean seabed oil spills and electromagnetic purification of petroleum reservoir fluids. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we develop a meshless collocation scheme for the numerical solution of magnetohydrodynamics (MHD) flow equations. We consider the transient laminar flow of an incompressible, viscous and electrically conducting fluid in a rectangular duct. The flow is driven by the current produced by electrodes placed on the walls of the duct. The method combines a meshless collocation scheme with the newly developed Discretization Corrected Particle Strength Exchange (DC PSE) interpolation method. To highlight the applicability of the method, we discretize the spatial domain by using uniformly (Cartesian) and irregularly distributed nodes. The proposed solution method can handle high Hartmann (Ha) numbers and captures the boundary layers formed in such cases, without the presence of unwanted oscillations, by employing a local mesh refinement procedure close to the boundaries. The use of local refinement reduces the computational cost. We apply an explicit time integration scheme and we compute the critical time step that ensures stability through the Gershgorin theorem. Finally, we present numerical results obtained using different orientation of the applied magnetic field. [ABSTRACT FROM AUTHOR]

In thermosfluid dynamics, free convection flows external to different geometries, such as cylinders, ellipses, spheres, curved walls, wavy plates, cones, etc., play major role in various industrial and process engineering systems. The thermal buoyancy force associated with natural convection flows can play a critical role in determining skin friction and heat transfer rates at the boundary. In thermal engineering, natural convection flows from cylindrical bodies has gained exceptional interest. In this article, we mathematically evaluate an entropy analysis of magnetohydrodynamic third-grade convection flows from permeable cylinder considering velocity and thermal slip effects. The resulting non-linear coupled partial differential conservation equations with associated boundary conditions are solved with an efficient unconditionally stable implicit finite difference Keller-Box technique. The impacts of momentum and heat transport coefficients, entropy generation and Bejan number are computed for several values of non-dimensional parameters arising in the flow equations. Streamlines are plotted to analyze the heat transport process in a two-dimensional domain. Furthermore, the deviations of the flow variables are compared with those computed for a Newtonian fluid and this has important implications in industrial thermal material processing operations, aviation technology, different enterprises, energy systems and thermal enhancement of industrial flow processes. [ABSTRACT FROM AUTHOR]

In the present paper, the effect of magnetic field on an incompressible viscous fluid flow past and through a porous sphere embedded in another porous medium at low Reynolds number is studied. The Brinkman equations for the flow inside and outside the porous sphere in their stream function formulations are used. Explicit expressions for the stream function are investigated for both the inside and outside flow regions. A new result for the drag on a porous sphere embedded in another porous medium has been reported. As a particular case, slow viscous flow through a porous sphere embedded in another porous medium is considered and the drag experienced by it is evaluated. An expression for the shearing stress has also been reported. The effect of magnetic field on the drag, shear stress, and stream lines has been presented graphically for different values of parameters and discussed. [ABSTRACT FROM AUTHOR]

Applicability of COMSOL multiphysics software for analyzing liquid metal MagnetoHydroDynamic (MHD) effect under fusion relevant parameters has been verified. For this purpose, few benchmark problems recommended by fusion MHD community have been simulated. The selected benchmark problems are steady state fully developed MHD duct flow, duct flow under transverse fringed magnetic field and transient phenomenon of natural convection in presence of magnetic field. Apart, from the recommended benchmark problems, an experimental scenario has been simulated having flow geometry with multiple 90° bends. For these simulations, two to three available independent physics modules have been suitably coupled under the single platform of COMSOL. The computed numerical results show good agreement with the available analytical or experimental or reported numerical data in the range of MHD parameters Hartmann number ∼10 4 , Interaction parameter ∼10 4 , wall conductance ratio ∼10 −2 & Grasshof number ∼10 6 . [ABSTRACT FROM AUTHOR]

Self-cooled liquid metal blanket of a thermonuclear fusion reactor has the most critical issue of strong MHD effects which influence the thermal efficiency of the reactor. Special attention needs to be paid to the MHD friction factors for flow in rectangular channels at low as well as at high Hartmann numbers. The effect on MHD friction factors of a magnetic field oblique to the channel walls for various channel wall conductivities and aspect ratios at different Hartmann numbers is investigated numerically. Even for relatively small channel wall conductivity at high Hartmann numbers, velocity jets are developed near the channel walls. Due to these jets, MHD friction factors increase by the orders of magnitude which can be observed in the numerical results. The finite-difference method has been used to discretize the coupled second-order linear partial differential equations of MHD by using both uniform and nonuniform grids. Nonuniform discretization of the mesh is more efficient than the uniform mesh due to steep velocity gradients near the walls. For parallel plates, an analytical solution for MHD friction factor has been developed, and then compared with the numerical solutions. It is found that an oblique magnetic field has a significant effect on MHD friction factors for different channel wall conductivities and aspect ratios at various Hartmann numbers. [ABSTRACT FROM AUTHOR]

In this study, the electrically conducting fluid flow inside a channel with local symmetric constrictions, in the presence of a uniform transverse magnetic field is investigated using Lattice Boltzmann Method (LBM). To simulate Magnetohydrodynamics (MHD) flow, the extended model of D2Q9 for MHD has been used. In this model, the magnetic induction equation is solved in a similar manner to hydrodynamic flow field which is easy for programming. This extended model has a capability of simultaneously solving both magnetic and hydrodynamic fields; so that, it is possible to simulate MHD flow for various magnetic Reynolds number (Rem). Moreover, the effects of Rem on the flow characteristics are investigated. It is observed that, an increase in Rem, while keeping the Hartman number (Ha) constant, can control the separation zone; furthermore, comparing to increasing Ha, it doesn't result in a significant pressure drop along the channel. [ABSTRACT FROM AUTHOR]