Hartmann Number Research Articles

On the magnetohydrodynamic stability of channel flow of Navier–Stokes–Voigt fluid

The linear stability of a pressure-driven channel flow of an electrically conducting Navier–Stokes–Voigt type of the viscoelastic fluid subject to a transverse magnetic field is investigated. The validity of Squire's theorem is proved, and the generalized eigenvalue problem for two-dimensional modes is obtained by adopting the Galerkin method, which is subsequently solved using the QZ-algorithm. Although the base flow retains its Newtonian fluid characteristics, the noticeable influence of the Kelvin–Voigt parameter in conjunction with the Hartmann number on the stability of fluid flow is perceived. Instability is exclusively identified within a specific range of the Kelvin–Voigt parameter, markedly affected by the Hartmann number. Furthermore, closed neutral stability curves arise, indicating the requirement of two values of the Reynolds number to completely assess the linear stability criteria, in contrast to the typical single value observed in the case of Newtonian fluids.

Numerical study on magnetic control of boundary layers in non-Newtonian flows over stretching cylinders using Keller box analysis

This article presents an analysis of the magnetic field’s effects on two-dimensional, two-directional, incompressible, and steady third-grade fluid flow over a stretched circular cylinder. A mathematical model describing the behavior of third-grade fluid in the cylindrical coordinate system is developed, accounting for nonlinear differential conditions. To simplify the analysis, appropriate transformations are applied to convert the fractional differential conditions into ordinary differential conditions. The resulting nonlinear differential framework is solved using the Keller Box method. The influences of several novel parameters on the velocity are depicted and examined. Furthermore, the expression for the skin-friction coefficient is computed and provided. The comparison of the obtained results with existing literature is made and found in good accordance. Through comprehensive numerical simulations and analytical derivations, this study contributes to the understanding of magnetic field control in boundary layers of third-grade fluid over stretching cylinders, with implications for a wide range of practical applications in engineering and fluid dynamics. The stronger influence of the magnetic field, indicating an increase in the Hartmann number, corresponds to suppression of thermal and solutal transport, thereby leading to a decrease in the temperature and concentration gradients. Conversely, the velocity profile exhibits an increase, indicating enhanced fluid motion under the influence of the magnetic field. This behavior is consistent with the magnetohydrodynamic effects, where the Lorentz force induced by the magnetic field alters the fluid flow, resulting in changes in the velocity distribution while impacting temperature and concentration gradients.

Investigation of the spreading of a liquid metal droplet under a vertical magnetic field

In the liquid metal divertor of a magnetic confinement fusion device, the spreading characteristics of the liquid metal are crucial for ensuring the stable operation of the divertor. This study has experimentally investigated the spreading characteristics of a GaInSn alloy droplet on a solid substrate under a strong vertical magnetic field, with the magnetic field intensity ranging from 0 to 2.5 T. First, several parameters of the droplet, such as droplet shape, spreading factor, dynamic contact angle, spreading velocity, and rebound behavior after impacting, were studied without a magnetic field. The fitting relationship between maximum spreading factor βmax and Weber number We was obtained and has been compared with the scaling laws from the literature. Furthermore, the effect of the vertical magnetic field on those parameters has been investigated systematically. Quantitative results on βmax and the maximum spreading time tDmax, varied with the Hartmann number (Ha) and the We number, provide a comprehensive understanding of the spreading dynamics. The specific relationship between βmax and We number under different magnetic field intensities (B) shows that a vertical magnetic field has a great inhibiting effect on liquid metal droplet spreading. Finally, the influence of oxidation on droplet spreading characteristics also has been studied. These basic findings are important for the application of liquid metal on a divertor/limiter in a fusion reactor, offering a theoretical reference engineering design.

Dual solutions of magnetized radiative flow of Casson Nanofluid over a stretching/shrinking cylinder: Stability analysis

The enhanced thermal efficiency exhibited by Casson nanofluids offers significant practical applications across various industrial and engineering sectors. This study focuses on the mathematical investigation of the steady magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid through a stretched/shrinking cylinder, taking into account the effects of suction and thermal radiation. The governing partial differential equations (PDEs) have been subjected to a similarity transformation, resulting in a set of nonlinear ordinary differential equations (ODEs). These ODEs were solved numerically utilizing the code of bvp4c in the software of Matlab which offers high accuracy (4th order). The employed nanofluid model incorporates the effects of Brownian motion and thermophoresis. The present study illustrates the graphical depictions of the impacts of different governing parameters, namely Hartmann (M) number, curvature (γ) parameter, Brownian motion (Nb) parameter, mass suction (S) parameter, thermal radiation (Rd) parameter, and thermophoresis (Nt) parameter, on heat transfer, flow, and mass transfer characteristics. Comprehensive determination and visual presentation of the coefficient of skin friction, local Nusselt number, and local Sherwood number were conducted for a range of estimates of applied parameters. Based on our examination, it has been determined that dual similarity solutions are present within a specific range of mass suction parameters. The relationship between the Casson parameter and various fluid dynamic properties, such as skin friction coefficient, heat transfer rate, and mass transfer rates, has been found to exhibit a decreasing trend. Furthermore, the stability analysis discovered that the first solution exhibits linear stability, whereas the second solution displays linear instability. Additionally, the motivation behind this study is to enhance industrial performance through the optimization of thermal power generation systems, thereby increasing their overall efficiency.

Unsteady, two-dimensional magnetohydrodynamic (MHD) analysis of Casson fluid flow in a porous cavity with heated cylindrical obstacles

This research presents an analysis of entropy generation during natural convection in a porous medium using triangular heated cylindrical obstacles with equal spacing. The study consists of three cylindrical obstacles arranged in a triangular pattern. Each cylinder is uniformly spaced from its neighboring cylinders, creating equilateral triangles throughout the arrangement. All of these cylindrical obstacles are heated. The triangular arrangement guarantees an even distribution of obstacles across the experimental space. The governing equations, with entropy, are numerically solved using the finite element method. The study aims to investigate the interactions between several key elements in fluid dynamics: Casson fluid, magnetohydrodynamics, the Darcy–Forchheimer model, entropy, and natural convection. The goal is to gain insights into the individual behaviors of these elements and their interactions in combined systems. The results indicate that the Casson fluid parameter has an impact on the flow and heat transfer characteristics, while the Hartmann and Nusselt numbers exhibit control mechanisms for the intensity of natural convection and affect the patterns of isotherms, streamlines, and entropy.

MHD free convection with Joule heating and entropy generation inside an H-shaped hollow structure

In this research, a free convective flow of water inside an H-shaped hollow structure which is subjected to the existence of an exterior magnetic field and Joule heating is computationally investigated. The structure's right and left upright surfaces are maintained at invariant ambient thermal condition, while the top and bottom-most surfaces of the structure are in adiabatic condition. The rest of the inner walls are heated isothermally. Computational analysis is carried out for different configurations of the chamber by solving Navier-Stokes and heat energy equations via the finite element approach. Parametric computations are conducted by varying Hartmann numbers (0 ≤ Ha ≤ 20), Rayleigh numbers (103 ≤ Ra ≤ 106), width of the vertical sections (0.2 ≤ d/L ≤ 0.4, where L denotes the structure's reference dimension), and thickness of the horizontal middle section (0.2 ≤ t/L ≤ 0.4). To find out the impact of the governing parameters on thermal performance for different configurations, the mean Nusselt number along the hot walls, mean temperature of fluid, overall entropy generation, and thermal performance criterion are assessed. In addition, the variations in fluid motion and thermal patterns are reported in terms of streamlines, isotherms, and heatlines. With a larger mean Nusselt number and smaller thermal performance criterion, better heat transmission performance is found for thicker horizontal middle section and wider vertical sections. The maximum reduction in thermal performance criterion is found to be 87.8 % for increasing the width of the vertical sections. However, in the cases of Ha and d/L, there is an interesting transition in Nusselt number noticed for different Rayleigh numbers.

Thermal and solutal transport by Cattaneo-Christov model for the magnetohydrodynamic Williamson fluid with joule heating and heat source/sink

This article scrutinizes the 2-dimensional and boundary layer flow of magnetohydrodynamic Williamson fluid flowing on a stretchable surface with variable viscosity. The thermal and solutal rates are examined through the Cattaneo-Christov model with Joule heating, heat source/sink, and chemical reaction. The authors are motivated to conduct this study because of its practical and scientific significance in various processes, including polymer processing, textile industries, food industries, solar energy, biomedical science, wind turbine blades, oil spill clean-up, metal rolling, and forging. With the mentioned assumptions, the partial differential equations are achieved by using the basic governing laws, including momentum law, energy law, and concentration law. This non-linear system of equations is transmuted into ordinary differential equations by taking similarity transformations. The main novelty behind the conduction of this work is the numerical technique, namely the ‘Adams-Milne (Predictor-Corrector)’ method along with the Runge-Kutta technique on Matlab software, which has not previously been studied by any researcher in the literature. The analytical solution of the determined equations is not possible due to their highly non-linear nature; therefore the multistep numerical method namely the ‘Adams-Milne (Predictor-Corrector)’ method, along with the Runge-Kutta technique is used to determine the numerical results. The outcomes are noted due to numerous parameters for velocity, temperature, and concentration profiles. The explanation of graphical and numerical results is discussed here. The graphical impression of the Williamson parameter reveals that the velocity and temperature curves diminish for higher inputs of this parameter. The movement of fluid shows the declining behavior for the Hartmann number and viscosity parameter. The solutal and thermal findings due to Cattaneo-Christov heat and mass relaxation coefficients mark the reducing behaviour in respective field. The rise in reaction coefficient decreases the mass distribution. The analyses of comparison of results are also presented here.

Electrically conducting mixed convective nanofluid flow past a nonlinearly slender Riga plate subjected to viscous dissipation and activation energy

This paper reports the mass and energy transmission characteristics of an electrically conducting mixed convective nanofluid flow past a stretching Riga plate. An additional effect of viscous dissipation, Arrhenius activation energy and heat source is also studied. The energy and mass transmissions are evaluated by a zero-mass flux of nanoparticle and convective boundary conditions. Buongiorno’s relations are proposed for the Brownian motion and thermophoretic diffusion. The similarity substitutions are employed to derive the non-dimensional set of modeled equations. The obtained set of equations is numerically processed via parametric continuation method (PCM). Several flow factors affecting the velocity, energy, and mass distributions are graphically discussed. It has been perceived that the fluid velocity field declines with the influence of velocity power index (m), while improves with the upshot of modified Hartmann number (Q). The effect of Schmidt number and chemical reaction diminishes the concentration profile [Formula: see text]. Furthermore, the energy curve enhances with the effect of thermophoresis factor, Biot and Eckert number.

Effect of radiation and slip parameter on MHD mixed convective Casson fluid flow along a vertical stretching sheet

The flow behavior of Casson fluids along a vertical stretching sheet is important for a wide range of industrial processes where such fluids are encountered. For example, knowledge of this study might be used in the design of coating processes or in biomedical applications involving blood flow. Aims of this study are the optimization of engineering processes, ensuring efficiency and quality in various applications and analysis of boundary layer along stretching sheet. Mathematical formulation of the problem consists parial differential equations and later on converted to a set of ordinary differential equations (ODEs) with boundary conditions and solved using “Bvp4c solver” in MATLAB. The Bvp4c solver is a numerical technique used to solve boundary value problems (BVPs) for ODEs. For various values of physical parameters the velocity, temperature, and concentration distribution are presented through figures. Skin friction coefficient, Nusselt number, and Sherwood number are tabulated and analyzed through bar graphs. It is noted that for assisting flow [Formula: see text], velocity profile decreases near the sheet while it increases away from the sheet for growing inputs of Casson fluid parameter ([Formula: see text]), while opposite seniro has been observed for Hartmann number ([Formula: see text]). Coefficient of surface drag is lowered with growing inputs of Casson fluid parameter and heat transfer rate is enhanced with increased inputs of Hartmann number in both assisting and opposing flow. The temperature profile enhances for raising inputs of radiation parameter ([Formula: see text]) in both assisting and opposing flow. The concentration profiles also fall, when chemical reaction parameter ([Formula: see text]) and Schmidt number ([Formula: see text]) are enhanced.

Artificial neural network (ANN) analysis on thermophysical properties of magnetohydrodynamics flow with radiation in an arc-shaped enclosure with a rotating cylinder

The objective of this research is to examine the thermophysical features of magnetic parameter (Ha) and time step (τ) in a lid-driven cavity using a water-based Al2O3 nanofluid and the efficacy of ANN models in accurately predicting the average heat transfer rate. The Galerkin weighted residual approach is used to solve a set of dimensionless nonlinear governing equations. The Levenberg-Marquardt back propagation technique is used for training ANN using sparse simulated data. The findings of the investigation about the flow and thermal fields are shown. Furthermore, a comparative study and prediction have been conducted on the impact of manipulating factors on the average Nusselt number derived from the numerical heat transfer analysis. The findings of the research indicate that, in the absence of magnetohydrodynamics, a rise in the Hartmann number resulted in a drop in both the fluid velocity profile and magnitude. Conversely, it was observed that the temperature and Nusselt number exhibited an increase under these conditions. The mean temperature of the fluid rises as the Hartmann number drops, reaching a peak value of 0.114 when Ha = 0. The scenario where Ha = 0, representing the lack of magnetohydrodynamics, shows the highest average Nusselt number, whereas the instance with Ha = 45 presents the lowest Nusselt number. The ANN model has a high level of accuracy, as seen by an MSE value of 0.00069 and a MAE value of 0.0175, resulting in a 99% accuracy rate.

Numerical Simulation and Sensitivity Analysis Using RSM on Natural Convective Heat Exchanger Containing Hybrid Nanofluids

This work presents a numerical analysis for exploring heat transfer phenomena in an enclosed cavity using magnetohydrodynamics natural convection. Because of the numerous real-world applications of nanofluids and hybrid nanofluids in industrial and thermal engineering developments, hybrid nanofluids are used as fluid mediums in the fluid field. A hexagonal-shaped heat exchanger is taken with two circular surfaces along the middle part. The upright circular surface acts as a homogeneous heat source, while the lower circular surface functions as a heat sink. The remaining portions of the adjacent walls are thermally insulated. The copper (Cu) and titanium dioxide (TiO2) nanoparticles are suspended into water to make a hybrid nanofluid. For solving the corresponding governing equations, the weighted-residual finite element method is applied. To explain the major outcomes, isotherms, streamlines, and many others 2D and 3D contour plots are involved graphically with a physical explanation for different magnitudes of significant parameters: Rayleigh number 103≤Ra≤106, Hartmann number 0≤Ha≤100, and nanoparticle volume fraction 0≤ϕ≤0.06. The novelty of this work is to apply response surface methodology on the natural convective hybrid nanofluid model, to visualize 2D and 3D effects, and to study the sensitivity of independent parameters on response function. Due to the outstanding thermal properties of the hybrid nanofluid, the addition of Cu and TiO2 nanoparticles into H2O develops the heat transfer rate to 35.85% rather than base fluid. Moreover, a larger magnitude of Ra and the accumulation of mixture nanoparticles result in the thermal actuation of a hybrid nanofluid. With greater magnetic impact, an opposite response is exhibited.

Numerical investigations on the entropy generation and heat transfer of an unsteady micropolar hybrid nanofluid flow over an inclined stretching surface

Studies on stagnation point flow on inclined surfaces have gained momentum in recent times due to its application in a variety of fields. This study aims at the heat transfer properties of an incompressible unsteady stagnation point flow of a non-Newtonian micropolar hybrid nanofluid over an inclined stretching sheet with thermal radiation, viscous dissipation, and Joule heating. The governing equations of the problem are transformed into a system of ordinary differential equations by employing similarity variables. They are then solved numerically using the Runge-Kutta 4 th order method along with the shooting approach. Numerical solutions on velocity, microrotation, and temperature distribution along with entropy generation and Bejan number are consolidated graphically and those on heat transfer rate and skin friction coefficient are tabulated. The results indicate that the heat transfer rate is higher in hybrid nanofluid as compared to that of mononanofluid, the angle of inclination of the sheet is unfavorable for the velocity profile, and the temperature of the hybrid nanofluid escalates with a rise in viscous dissipation. Entropy generation rate is reduced when the Hartmann number is increased and the Bejan number diminishes with elevating viscous dissipation. The results were validated using existing studies and comparing heat transfer rate values between the present results and the results obtained from NDSolve.

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Scaling laws of the plasma velocity in visco-resistive magnetohydrodynamic systems

We consider a visco-resistive magnetohydrodynamic modelling of a steady-state incompressible tokamak plasma with a prescribed toroidal current drive, featuring constant resistivity η and viscosity ν. It is shown that the plasma velocity root-mean-square behaves as ηf(H) as long as the inertial term remains negligible, where H stands for the Hartmann number H≡(ην)−1/2, and that f(H) exhibits power-law behaviours in the limits H≪1 and H≫1. In the latter limit, we establish that f(H) scales as H1/4, which is consistent with numerical results.

Influence of a magnetic field on double‐diffusive convection in an inclined porous layer

AbstractThe present study investigates the impact of a magnetic field on double‐diffusive convection in an inclined porous layer, employing linear instability theory. The perturbed state is solved using the normal mode technique, and the stability eigenvalue problem is numerically analyzed for longitudinal and traveling rolls using the Runge‐Kutta method coupled with the shooting method. Various dimensionless physical parameters, including solutal and thermal Rayleigh numbers, inclination angle, Hartmann number, and Lewis number, are examined for their influence on system stability. The findings reveal that, for , the Hartmann number, solute Rayleigh number, and inclination angle act as stabilizing factors, with greater stability observed for traveling rolls compared to longitudinal rolls. In the case of , the critical Rayleigh number shows a monotonic relationship with the solute Rayleigh number and inclination angle, while its relationship with the Hartmann number is non‐monotonic for traveling rolls. Moreover, for , the Hartmann number stabilizes the system by raising the onset threshold value, favouring longitudinal modes. The solute Rayleigh number also contributes to system stability. The impact of the inclination angle on system stability is contingent upon its magnitude, with small angles favouring the stability of longitudinal rolls and larger angles leading to an initial transition from traveling to longitudinal rolls, indicating a complex non‐monotonic behavior.

Enhancing energy efficiency and heat transfer performance of engine oil flow through hybrid nanoparticles in convergent/divergent channel

Engine oil (EO) is employed as a lubricant in various machinery engines. Efficient heat transfers are a fundamental requirement for all processes. To improve heat transfer rates and reduce the energy loss caused by high temperatures, this study focuses on incorporating Iron Oxide (Fe3O4) and Cupper Oxide (CuO) into the engine oil as suspended particles. However, the focus of this research paper is to analyze entropy generation in a convergent/divergent channel that contains a hybrid nanofluid. Mathematical modeling is utilized to present the continuity, momentum, and energy equations. Using the resemblance transformation variables, the governing dimensional partial differential equations (PDEs) are transformed into a system of non-dimensional ordinary differential equations (ODEs), which are then resolved in ascending order through the BVP4c scheme. The graphical results illustrate the effects of various parameters on fluid velocity, temperature, entropy generation, and Bejan number. The study explores changes in velocity profiles under different Hartmann numbers, revealing opposing variations in divergent and convergent channels. Velocity profiles exhibit similar patterns when varying the porosity parameter. In the convergent passage, a higher porosity parameter results in a higher temperature field. Entropy rises against Eckert and Hartmann numbers in both Convergent and Divergent cases. These insights aid in designing and optimizing machinery engines.

Double-diffusive mixed convection in an inclined square cavity filled with nanofluid: A numerical study with external magnetic field and heated square blockage effects

This study explores the influence of Fe3O4 – water nanofluid, magnetic forces, and double-diffusive mixed convection characteristics on a steady-state, two-dimensional, laminar flow within an inclined square cavity containing four heated square blockages. The governing equations are solved using the Finite Volume Method (FVM). In this configuration, the temperature and concentration inside the square blockages are higher than those on the left and right walls, which are moving in opposite directions to each other. The remaining two are adiabatic and impermeable. A wide range of parameters is investigated, including cavity nanoparticle volume fractions (φ = 0.0, 0.02, 0.04, 0.06), inclination angle (γ = 0°, 30°, 60°), Richardson number (Ri = 0.1, 1.0, 10), Hartmann number (Ha = 0, 50, 100), heated block ratio (B = 1/8), Lewis number (Le = 5.0), Prandtl number (Pr = 0.71), and Buoyancy ratio (N = 2.0). The study extensively analyzes temperature, concentration, and streamline contours based on these parameters. Furthermore, the research examines the heat and mass transfer rates on the heated block surfaces by analyzing local and average Nusselt (Nuavg) and Sherwood numbers (Shavg). The results suggest that introducing nanofluid has a more pronounced influence on the flow fields than the temperature and concentration patterns. Both the inclination angle and the Hartmann number have a significant impact on both the flow and temperature patterns. At higher Ri, an increase in φ reduces the Nuavg and Shavg. However, the total Nuavg and Shavg decrease at any Ri and γ in a magnetic field.

A theoretical analysis of rotating electromagnetohydrodynamic and electroosmotic transport of couple stress fluid through a microchannel

AbstractThe main motivation behind this research work is the electroosmotic flow (EOF), which characterizes the movement of charged particles in a fluid when subjected to an external electric field, which offers precise control over fluid movement without mechanical components. The study of bio‐fluids in rotating microfluidic platforms is becoming much more significant. Hence, it is important to discuss the non‐Newtonian fluids in such environments. This paper analytically investigates the hydrodynamic characteristics of combined electromagnetohydrodynamic (EMHD) and EOF transport of non‐Newtonian fluid through a rotating microchannel with Navier‐slip boundary conditions at the walls. The couple stress fluid model is considered a non‐Newtonian fluid in the flow domain. The linearized Poisson‐Boltzmann equation is considered inside the electric double layer (EDL). The modified Stokes equation is governed by a combined imposed magnetic and EOF field. Closed form expressions are obtained for electrical potential, flow velocity, and volume flow rate in the channel using analytical methods. The dependence of rotating electromagnetic flow velocity and flow rates on appropriate parameters is explained. It is found that the rotational flow velocity displays an opposite pattern when the couple stress parameter and electric field intensity parameters are varied due to the influence of channel rotation. It is also found that the secondary flow rate ratio is amplified with the Hartmann number and slip length parameter, due to the stronger impact of the non‐Newtonian behaviour than the Newtonian situation on the volume flow rate at a relatively higher rotational value. The findings of this study may aid in the design and analysis of practical thermal micro/nano‐equipment for transporting biofluids.

Time dependent magnetic field effects on the MHD flow and heat transfer in a rectangular duct

AbstractWe consider the effect of time dependent magnetic field on the natural convection magnetohydrodynamic flow in a rectangular duct. The flow is two‐dimensional, unsteady, laminar and the fluid is electrically conducting and incompressible. The heat transfer is taken into account using the Boussinesq approximation and the buoyancy force is included in the momentum equations for the thermal coupling. The flow is considered at low magnetic Reynolds number setting and hence, the induced magnetic field is neglected. The proposed model in which the governing equations are given in terms of stream function, vorticity and temperature, is approximated by using a Chebyshev spectral collocation method for the spatial discretisation coupled with a backward difference scheme that is unconditionally stable for the temporal integration. The flow and heat transfer characteristic are analysed for several definitions of applied time varying magnetic field. Increase of the Hartmann number and the time variation of the applied magnetic field, changes the flow behaviour, especially at transient time levels and at the steady‐state.

Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method

Purpose—This study aims to perform an in-depth analysis of double-diffusive natural convection (DDNC) in an irregularly shaped porous cavity. We investigate the convective heat transfer process induced by the lower wall treated as a heat source while the side walls of the enclosure are maintained at a lower temperature and concentration, and the remaining wall is adiabatic. Various factors, such as the Rayleigh number, Darcy effects, Hartmann number, Lewis number and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. Design/methodology/approach—After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10−4 ≤ Da ≤ 10−1), Lewis number (0.1≤Le≤10), and Hartmann number 0≤Ha≤40 as the dimensionless operating parameters. Findings—The finding shows that the patterns of convection and the shape of the isotherms within porous enclosures are notably affected by the angle of the applied magnetic field. This study enhances our understanding of how double-diffusive natural convection (DDNC) operates in these enclosures, which helps improve heating and cooling technologies in various engineering fields. Research limitations/implications—Numerical and experimental extensions of the present study make it possible to investigate differences in thermal performance as a result of various curvatures, orientations, boundary conditions, and the use of three-dimensional analysis and other working fluids. Practical implications—The geometry configurations used in this study have wide-ranging applications in engineering fields, such as in heat exchangers, crystallization, microelectronics, energy storage, mixing, food processing, and biomedical systems. Originality/value—This study shows how an inclined magnetic field affects double-diffusive natural convection (DDNC) within a porous system featuring an irregularly shaped cavity, considering various multiphysical conditions.