Magnetohydrodynamic Mixed Convection Flow Research Articles

Numerical computations of MHD mixed convection flow of Bingham fluid in a porous square chamber with a wavy cylinder

This work examines the behavior of Bingham fluids in porous media under magnetohydrodynamic (MHD) conditions, addressing a significant issue in fluid dynamics and heat transport. The authors study mixed convection in a porous square chamber with twisted cylinders using COMSOL Multiphysics and finite element techniques. Compared to other research, this one offers a more complicated and realistic model since it integrates Bingham fluid flow and MHD effects in a porous chamber with wavy cylinders. Plotting of streamlines, isotherms, and Nusselt numbers is done for several parameters: Numbers Reynolds (1, 5, 10, 50), Hartmann (0, 25, 50, 100), Bingham (0, 1, 5, 10), Darcy (10−4, 10−3, 10−2, 10−1), and Grashof (102,103,104,105) are among those assigned numbers. According to findings, larger Bn values promote thermal stratification and decrease flow mobility, which results in dominating conductive heat transmission. The nusselt number falls with Ha and Bn but rises with Re, Da, and Gr. The study aims to provide useful insights into several industrial disciplines, such as nuclear power plant architecture and petroleum engineering, by enhancing heat transfer in non-Newtonian fluids under magnetic fields. It also boosts the efficiency of chemical reactors and filters. Based on our findings, for lower Re = 1, the lowest value of Numean is 2.602, while at Re = 50, its values rise to 6.425.

Identifying the mixed and forced convection flow with transverse magnetic field

AbstractOptimal control of the steady, laminar, magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid is considered under the effect of the transverse magnetic field in a square duct. The viscous and Joule dissipations are included and the flow is driven by a constant pressure gradient. The triple nonlinear set of momentum, induction, and energy equations are solved in dimensionless form by using the mixed finite element method (FEM) with the implementation of Newton's method for nonlinearity with the discretize‐then‐linearize approach. Accordingly, FEM solutions are obtained for various values of the problem parameters to ensure the efficiency of the underlying scheme. This study aims to investigate the problem of controlling the steady flow by using the physically significant parameters of the problem as control variables in the case of a mixed convection flow. In this respect, classification of the type of convection, forced or free, is achieved by controlling the Grashof number (Gr). Besides, single and pairwise controls with Hartmann number (M), Prandtl number (Pr), and magnetic Reynolds number (Rm) are also used to regain the prescribed fluid behaviors and required magnetic field. Control simulations are conducted with the sequential‐least‐squares‐programming (SLSQP) algorithm in the optimization.

A comparative analysis on the magnetohydrodynamic mixed convective flow of a hybrid nanofluid with radiative heat transfer using bagging regression

Hybrid nanofluids exhibit enhanced attributes such as increased mechanical strength, chemical inertness, thermal diffusivity, and structural robustness compared to traditional nanofluids. In connection with this, the current study explores a comparative analysis of the mixed convection phenomenon in a magnetohydrodynamic flow of a hybrid nanofluid with radiative heat transfer. The originality of the current illustration is to scrutinise the hybrid nanofluids with combinations of Copper–sliver (Cu–Ag), Aluminium oxide–Titanium dioxide (Al2O3–TiO2 ), and Copper–Aluminium oxide (Cu–Al2O3 ) on flow and heat transfer. Here, the basis fluids are assumed to be kerosene and water. The perturbation approach is used to solve the governing equations, and bagging regression is used to show the velocity characteristics of the hybrid nanofluid magnetohydrodynamic flow. The outcomes are scrutinised using tables and figures. The results reveal that the shear stress on a surface rises as the radiation parameter increases. The shear stress on a surface typically decreases as the magnetic field strength rises. However, shear stress escalates with the increase in radiation parameter due to heat absorption.

Computational study of magnetohydrodynamic mixed convective flow in a nanofluid-filled cavity with diagonally moving lid

This study examines the phenomenon of uniform magnetohydrodynamic mixed convective flow in a cavity filled with nanofluid. The research focuses on analyzing the mixed convection induced by a uniformly heated lid-driven cavity with diagonal motion. The fluid and heat transport equations are solved using the finite volume method. Numerical simulations are conducted for various parameters including Richardson number (Ri) ranging as 0.1, 1 & 10, Hartmann number (Ha) 0, 10, 25 & 50, angle of inclination (γ) 0°, 30°, 45°, 60° & 90°, and solid volume fraction from 0.0 to 0.05. The results are presented in terms of flow and thermal fields. It is observed that higher Hartmann numbers and inclination angles of the magnetic field lead to a suppression of convection, favoring a dominant conduction mode and reducing the overall heat transfer rate. Specifically, the study highlights a significant enhancement in the heat transfer rate in a nanofluid-filled cavity with a diagonally moving wall. The movement’s of diagonal wall has significant power consumption, the tool may be used in an industrial process that improves heat transfer, offers flexibility, and raises the quality of the finished product. Additionally, the correlations that were found are a useful tool for heat exchanger design.

Mathematical modeling of entropy generation in MHD mixed convective Cu–Ag-Al2O3/H2O tri-hybrid nanofluid over an exponential permeable shrinking surface with radiation and slip impacts: Multiple solutions with stability analysis

The present investigation aims to determine the existence of a dual solution in magnetohydrodynamic (MHD) mixed convective radiative flow of Cu-Ag- A l 2 O 3 / H 2 O tri-hybrid nanofluid in a permeable Darcy–Forchheimer porous medium over an exponentially shrinking surface by considering velocity, thermal slips, and suction effects at the surface. This study focuses on assessing entropy production in novel coolant applications. To streamline the analysis, the complex nonlinear partial differential equations (PDEs) are simplified by converting them into a set of ordinary differential equations (ODEs) through the utilization of the similarity transformation technique. These ODEs are then solved utilizing the bvp4c numerical MATLAB function. Graphical and tabular analyses are conducted to investigate the impact of emerging variables on entropy generation, as well as velocity, temperature, skin friction coefficient, and Nusselt number. Due to the contraction of the surface, dual solutions are found, but dual solutions cannot be found beyond the critical values. The critical values of S C are 1.58928, 1.48700, and 1.66058, but ξ C are − 1.239499 , − 1.416999 , and − 1.130030 for Cu / H 2 O nanofluid, Cu − Ag / H 2 O hybrid nanofluid, and Cu − Ag − A l 2 O 3 / H 2 O tri-hybrid nanofluid, respectively. A positive minimum eigenvalue γ 1 signifies the existence of the upper stable solution branch, while a negative minimal eigenvalue indicates the presence of the lower unstable solution branch. The tri-hybrid nanofluid exhibits superior thermal properties compared to nanofluid and hybrid fluids. Adding nanoparticles to traditional fluids is perceived as improving their ability to transmit heat. The analysis has demonstrated that the thermal radiation and temperature slip parameters significantly influence the heat transfer rate. Thermal radiation is found to speed up the creation of entropy. Additionally, in the case of a stable solution, an increase in the Forchheimer number results in a deceleration of the liquid flow, an effect which is further amplified by the presence of the magnetic field and velocity slip parameter.

Linear stability analysis of MHD mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation

PurposeThis paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.Design/methodology/approachThe treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.FindingsAnalysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.Originality/valueLinear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

Mechanisms of Diffusion thermo and Thermal diffusion on MHD Mixed Convection Flow of Casson fluid over a vertical cone with porous material in the presence of thermophoresis and a Brownian motion

In this present article, we analyzed the Effects of Diffusion thermo and Thermal Diffusion on magnetohydrodynamic (MHD) mixed convection flow for Casson nanofluid is deliberated a vertical cone with porous material. The modeled equations are transformed into a set of non-linear ODEs by employing similar transformable variables. These equations are then solved numerically using the shooting method, through the fourth-order Runge–Kutta integration procedure. Effects of some prominent physical parameters, such as diffusion thermo, Prandtl number, thermophoresis parameter, and magnetic parameter on the velocity, temperature, and concentration profiles are discussed graphically and numerically. Numerical calculations and graphs are used to illustrate the important features of the solution on fluid flow velocity, heat, and mass transfer characteristics under different quantities of parametric circumstances entering into the problem. Moreover, we computed the physical variables such as the coefficient of shear stress, rate of heat, and mass transfer. To establish the veracity of our present results, we compared them to previously published research and found substantial concordance.

Dual solutions of Darcy-Forchheimer radiative-convective magneto-nanofluid flow over an exponentially stretching/shrinking surface: Stability and entropy generation analysis

A numerical investigation was conducted to examine the existence of dual solutions over exponentially stretching or shrinking permeable surfaces. The study aimed to analyze the impact of thermal and second-order velocity slip on magnetohydrodynamic (MHD) mixed convective radiative nanofluid flow within a Darcy-Forchheimer porous medium while considering heat generation. Two distinct types of nanofluids, namely Cu-water and TiO 2/water, were employed in the investigation. To address the nonlinear partial differential equations (PDEs), similarity transformations were utilized to transform them into a system of ordinary differential equations (ODEs). The resulting coupled higher-order nonlinear ODEs were then solved using a MATLAB-based boundary value algorithm known as bvp4c. Two distinct solutions are observed within a restricted range of the stretching/shrinking parameter ξ ( ξ > ξ c ) and suction parameter S ( S > S c ), terminating respectively at ξ = ξ c or S = S c . The critical values are identified as ξ c = − 1.1952 ( Cu − water ) , − 0.9304 ( Ti O 2 − water ) and S c = 1.6437 ( Cu − water ) , 1.8900 ( Ti O 2 − water ) , maintaining the fixed values of the remaining physical parameters. Notably, the critical value for Cu-water is lower than that of TiO 2-water. Moreover, in both solution branches, the range of skin-friction coefficient and local Nusselt number for Cu-water surpasses that of TiO 2-water. An evaluation of the temporal stability of these solutions reveals that only the first solution remains stable. This is supported by the positivity of the smallest eigenvalues ( γ 1 > 0 ), indicating stability. Conversely, for the second solution, the smallest eigenvalues ( γ 1 < 0 ) are negative, signifying its instability. Also, Cu-water nanofluid exhibits higher fluid velocity and lower fluid temperature than TiO 2-water nanofluid for stable solutions and the opposite behavior for unstable solution branches. Significantly, within the initial solution branch, there is an escalation in velocity profiles attributed to the magnetic parameter, Grashof number, porous parameter, and first- and second-order velocity slip parameter. Conversely, a decrease is observed for the Forchheimer number, while the opposite holds true for the second solution branch. For both solution branches, the temperature profiles experience a reduction due to thermal slip and stretching/shrinking parameters, whereas enhancements are noted for thermal radiation and heat generation parameters. Furthermore, an increase in the suction parameter leads to elevated skin friction coefficient and local Nusselt number in the first stable solution, thereby promptly improving heat transfer efficiency. Moreover, improvements in entropy generation arise from factors such as thermal radiation, magnetic field, and nanoparticle solid volume fraction, presenting opportunities to optimize heat transmission in cooling and heating systems.

Heat and mass transfer under MHD mixed convection in a four‐sided lid‐driven square cavity

AbstractThis paper investigates the heat and mass transfer under magnetohydrodynamic mixed convection flow of a binary gas mixture in a four‐sided lid‐driven square cavity. The enclosure's left wall is sinusoidally heated and acts as a source term, while the right wall functions as a sink. The cavity's horizontal walls are adiabatic and impermeable to mass transfer. The governing equations under Boussinesq approximation and stream function‐vorticity formulation are solved using the alternating‐direction‐implicit scheme, a finite‐difference method. The numerical scheme's consistency and stability are demonstrated using the matrix method. The MATLAB code is written, validated against some existing studies, and used to perform numerical simulations. The numerical solutions are graphically examined by visualizing the streamline, isotherm, and concentration contours for nondimensional parameters, such as Hartmann number , heat absorption or generation coefficient , Richardson number , and buoyancy ratio . The magnetic field modifies the temperature and concentration distribution in the cavity, depending on the convection mode. The magnetic field forces the fluid to stagnate in different regions of the cavity, depending on the mode of convection. It was found that the difference between the maximum and minimum temperature and concentration at the cavity's midpoint increases up to 13 and 10 times, respectively, in the natural convection compared with the forced convection. The average Nusselt number on the vertical walls of the cavity is maximum in natural convection in the absence of a magnetic field but reaches a minimum value at in forced and mixed convection. The average Sherwood number on the cavity's vertical walls decreases with the magnetic field in mixed and natural convection.

Nanoparticle Shape Effects of Aligned Magnetohydrodynamics Mixed Convection Flow of Jeffrey Hybrid Nanofluid over a Stretching Vertical Plate

This study investigates the nanoparticle shape effects of aligned magnetohydrodynamics (MHD) mixed convection flow of Cu-Al2O3/water-EG Jeffrey hybrid nanofluid over a stretching vertical plate. Five different shapes of nanoparticles which are spherical, cylindrical, blades, bricks, and platelets are considered in this study. The governing equations in the form of Partial Differential Equations (PDEs) had been reduced to nonlinear Ordinary Differential Equations (ODEs) by using similarity transformation. The solver bvp4c in MATLAB software was applied to numerically solve the dimensionless governing equations towards the physical parameters which are aligned angle of magnetic field, interaction of magnetic field, mixed convection, Deborah number, volume fraction of nanoparticles, and nanoparticle shape factor. The effects of nanoparticle shapes and other relevant thermophysical parameters on fluid velocity, temperature, skin friction coefficient and Nusselt number are discussed in tables and figures. In comparison of all shapes, this study found that blade shaped nanoparticles have the highest values of skin friction coefficient and Nusselt number. The parameters blobid0.pngblobid1.pngblobid2.png and blobid3.png decrease the velocity profiles but increase the temperature profiles.

Significance of dust particles volume fraction to optimization of entropy in magnetohydrodynamic mixed convection flow via inclined surface

The main purpose of this study is to assessment the rate of entropy generation in magneto-hydrodynamic free convection with flow through the boundary layers of a fluid that is viscous and dusty fluid flow subject to dispersed dust particles across the stretching surface. Dusty fluids are utilized in a wide range of construction and manufacturing sectors, included the transportation of petroleum, gas purification, auto exhaust fumes, power station piping, sedimentation process, and many more. The primary objective of this elaborated fluid problem is to observe the influence of dust particles volume fraction on the heat transfer rate and entropy generation. By using appropriate similarity transformation, for first fluid phase and second dust phase simulations, the governing partial differential equations are transfigured into nonlinear non-dimensional ordinary differential equations. The final forms of obtained equations are solved numerically via MATLAB built-in bvp4c solver scheme. When the scientific validity of the findings is analyzed, it is found that there is substantial agreement among the latest results and the existing research. The entropy generation and thermal performance in fluid is influenced by the growing volume fraction of dust particles and significance variation is noted. As volume fraction of dust particles increased, causes a decrease in fluid flow, and reduced the velocity of both fluid and dusty fluid phases. But, it plays remarkable improvement in fluid temperature and entropy generation, and cause a decline in Bejan number. In fluid phase and dust fluid phase, temperatures are increased while inclined angle fluid parameter strength increases while the fluid velocity is decreased. Additionally, dimensionless variable expressions for Bejan number (Be) and entropy generation (Ns) are produced. It is noticed how several physical attributes influence entropy generation values.

Irreversibility analysis of Magnetohydrodynamic (MHD) mixed convection flow of viscoelastic hybrid nanofluid flow in a channel

This manuscript delves into the analysis of irreversibility in Magnetohydrodynamic (MHD) mixed convection flow of a viscoelastic hybrid nanofluid within a vertical channel. The study adopts a parallel plate configuration and employs Aluminum oxide (Al2O3) and Titanium oxide (TiO2) nanoparticles dispersed in a Carboxymethyl cellulose (CMC)-water base fluid. Utilizing similarity transformations, the governing partial differential equations (PDEs) are converted into a set of ordinary differential equations (ODEs), streamlining the mathematical model. These ODEs are then solved using the homotopy analysis method via Mathematica software for various governing parameter values. Key parameters including the Brinkman number, volume fractions of nanoparticles, magnetic effects, and wall temperature parameter are systematically investigated. Noteworthy insights include that volume fraction and magnetic parameter augments velocity at the left wall and slows down it toward the right wall; Brinkman number and wall temperature parameters significant in elevating temperature; Entropy and Bejan number respond differently to variations in the Brinkman number. Entropy escalates with increasing magnetic parameter, while the Bejan number declines. Illustrated through graphs, these findings enrich the comprehension of MHD mixed convection flow and heat transfer in viscoelastic hybrid nanofluids, elucidating irreversibility aspects tied to such systems.

Analysis of entropy generation in the flow of MHD water–ethylene glycol nanofluid over a spinning down pointing vertical cone

ObjectivesEntropy generation is investigated by considering the consequence of Magnetic field in H2O − C2H6O2 (50:50) mixture based Al2O3 and Fe3O4 nanoparticles. The 2D magnetohydrodynamic mixed convective boundary layer fluid flow characteristics are assumed to be independent of time at every point. The boundary conditions are mathematically formulated with the slip conditions (velocity and thermal). Significant outcomesThe investigation discloses that the F′(η) (tangential and swirl) drops for the increasing effects of the M. Fe3O4 shows a rise in velocity compared to Al2O3. In case of Magnetic parameter Fe3O4 shows 0.71% and 0.89% of Cf and Nu respectively compared to Al2O3. For changed estimation of the Brinkman number, both the Entropy generation and Bejan number shows opposite behavior. To verify the exactness of the numerical method, a comparison is made between the obtained outcomes and previously published results, corresponding to the skin friction and Nusselt number and the results are reliable. Practical implicationsThis work is developed to multiply the rate of energy transference and increasing the execution as well as effectiveness of energy delivering in industrial field. This model considers the effect of magnetic field, since it helps in achieving energy circulation in numerous devices like refrigerators and in other heating applications. Especially using the magnetized nanofluid helps in improved energy transmission in biomedical imaging. Additionally, the entropy generation model is verified using the thermodynamics second law.

Analytical Study of MHD Mixed Convection Flow for Maxwell Nanofluid Through a Vertical Cone with Porous Material in the Presence of Variable Thermal Conductivity and Soret, Dufour Effects

The key purpose of the existing article is to discuss the magnetohydrodynamic (MHD) mixed convection flow for Maxwell nanofluid is deliberated a vertical cone with porous material. A variable thermal conductivity and Dufour, Soret effects are also taken into consideration. The modeled equations are transformed into a set of non-linear ODEs by employing similar transformable variables. These equations are then solved numerically using the shooting method, through the fourth-order Runge–Kutta integration procedure. Effects of some prominent physical parameters, such as diffusion thermo, Prandtl number, thermophoresis parameter, and magnetic parameter on the velocity, temperature, and concentration profiles are discussed graphically and numerically. The main outcomes of this investigation are that Velocity slows down with augmentation in Maxwell and magnetic parameters. Temperature increases with radiation and thermophoresis parameters and reduces with growing values of Prandtl number and Brownian motion parameters. The values of skin-friction coefficient, Nusselt number coefficient and Sherwood number coefficient are presented in table. A comparison with previously reported data is made and an excellent agreement is noted.

Numerical study of MHD mixed convection flow in the EU DEMO WCLL breeding blanket

The Water-Cooled Lithium Lead (WCLL) breeding blanket is a proposed candidate option for European DEMO nuclear fusion reactor. The utilization of PbLi as the predominant material occupying the bulk region of the breeding blanket has received significant attention. The interaction between Lorentz forces (Ha≈9800), intense buoyancy forces (Gr≈1.77×1010), and pressure-driven flow (Re≈236.77), plays a crucial role in the magnetohydrodynamics(MHD) and heat transfer phenomena of the region. To replicate the dynamics of PbLi, taking into account the impact of the strong magnetic field used for plasma confinement and the non-uniform heat source generated by nuclear heating, a 3-D DNS numerical simulation has been employed. Owing to the influence of buoyancy forces, several medium-sized circulations that are elongated in the direction of the magnetic field occupy the plenum region which is situated between the cooling pipes. Moreover, the electrical interaction between the liquid metal and the conducting wall gives rise to high-velocity flow jets, which exhibits peak velocities that are increased with the magnitude of the magnetic field. To characterize the heat transfer occurring in different regions of the system, local Nusselt and Grashof numbers have been determined. Optimization strategies for the BZ cooling system geometrical configurations are proposed based on the estimation of heat transfer and prediction of tritium permeation.

Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating

Abstract Nanofluids have many applications in industries as well as engineering such as biomedicine, manufacturing, and electronics. Nanofluid is used for improvement of thermal and mass transmission. Based on the aforementioned applications, in the present study, a two-dimensional Maxwell nanofluid with thermal radiation effect on the existence of motile microorganisms over a vertically stretchable surface is explored. The consequence of heat absorption, the efficiency of heat flux in a porous medium, viscous dissipations, and Joule heating impacts are considered. The Brownian and thermophoretic diffusion effects have been evaluated. In addition, the binary chemical reaction is taken into account to evaluate the magnetohydrodynamics (MHD) mixed convection flow. Graphene nanoparticles are suspended in so-called engine oil (base fluid). The proposed liquid model depends on the governing nonlinear equations of velocity, temperature, the concentration of nanoparticles, and motile gyrotactic microorganisms. In order to transform highly nonlinear partial differential equations into nonlinear ordinary differential equations, an appropriate similarity transformation is exploited. For the solution of the present study, the homotopy analysis method-technique in Mathematica-12 is used. The fluctuation of velocity, temperature, concentration, and gyrotactic microorganisms’ characteristics for numerous flow parameters is discussed in detail. Some important fallouts of the existing study are that the Maxwell liquid parameter, Eckert number, and magnetic parameter lessen the nanoliquid velocity. But the fluid temperature becomes higher for growing estimates of the Brownian motion and thermophoretic factors. The radiation and chemical reaction parameters have declining impacts on the solutal profile. The motile microorganism profile shows a decrement in bioconvection Lewis and Rayleigh numbers. The nanofluid thermal profile is improved but the nanofluid velocity declined through the augmentation of volume fraction. Also, the coefficient of skin friction and Nusselt number are obtained versus various flow parameters.

Numerical Analysis on MHD mixed convection flow of Al_2O_3/H_2O (Aluminum-Water) Nanofluids in a Vertical Square Duct

In this work, we have considered steady laminar magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid in presence of nanoparticles while water as the base fluid in a vertical square duct. The walls of the duct are thermally insulated. In the energy equation, the effect of viscous dissipation and Joule heat is also considered. In this case, the walls of the duct are kept at a constant temperature. By using dimensionless quantities the governing equations of momentum, induction, and energy are first transformed into dimensionless equations. The velocity, temperature, and induced magnetic field profiles are plotted to analyze the effect of different flow parameters. It is found that the nanofluid motion expedite with the increase of the value of the parameters magnetic Reynolds number and Prandtl number. There are some important industrial applications and cooling shows in the industry of the current research. This study observed its importance with the view to increasing the heat transfer efficiency practical application relevant to industry and engineering issues. The issues discussed in this study have not been included in the earlier investigation for steady nanofluid flow due to a square duct. Numerical results are matched with an earlier published work and an excellent agreement between two are observed.&#x0D;

MHD Mixed Convection of Non-Newtonian Bingham Nanofluid in a Wavy Enclosure with Temperature-Dependent Thermophysical Properties: A Sensitivity Analysis by Response Surface Methodology

The numerical investigation of magneto-hydrodynamic (MHD) mixed convection flow and entropy formation of non-Newtonian Bingham fluid in a lid-driven wavy square cavity filled with nanofluid was investigated by the finite volume method (FVM). The numerical data-based temperature and nanoparticle size-dependent correlations for the Al2O3-water nanofluids are used here. The physical model is a two-dimensional wavy square cavity with thermally adiabatic horizontal boundaries, while the right and left vertical walls maintain a temperature of TC and TH, respectively. The top wall has a steady speed of u=u0. Pertinent non-dimensional parameters such as Reynolds number (Re=10,100,200,400), Hartmann number (Ha=0,10,20), Bingham number (Bn=0,2,5,10,50,100,200), nanoparticle volume fraction (ϕ=0,0.02,0.04), and Prandtl number (Pr=6.2) have been simulated numerically. The Richardson number Ri is calculated by combining the values of Re with a fixed value of Gr, which is the governing factor for the mixed convective flow. Using the Response Surface Methodology (RSM) method, the correlation equations are obtained using the input parameters for the average Nusselt number (Nu¯), total entropy generation (Es)t, and Bejan number (Beavg). The interactive effects of the pertinent parameters on the heat transfer rate are presented by plotting the response surfaces and the contours obtained from the RSM. The sensitivity of the output response to the input parameters is also tested. According to the findings, the mean Nusselt numbers (Nu¯) drop when Ha and Bn are increased and grow when Re and ϕ are augmented. It is found that (Es)t is reduced by raising Ha, but (Es)t rises with the augmentation of ϕ and Re. It is also found that the ϕ and Re numbers have a positive sensitivity to the Nu¯, while the sensitivity of the Ha and Bn numbers is negative.

Magnetohydrodynamic and Thermal Performance of Electrically Conducting Fluid along the Symmetrical and Vertical Magnetic Plate with Thermal Slip and Velocity Slip Effects

Numerical and physical simulations of the magnetohydrodynamic mixed convective flow of electrically conducting fluid along avertical magnetized and symmetrically heated plate with slip velocity and thermal slip effects have been performed. The novelty of the present work is to evaluate heat transfer and magnetic flux along the symmetrically magnetized plate with thermal and velocity slip effects. For a smooth algorithm and integration, the linked partial differential equations of the existing fluid flow system are converted into coupled nonlinear ordinary differential equations with specified streaming features and similarity components. By employing the Keller Box strategy, the modified ordinary differential equations (ODEs) are again translated in a suitable format for numerical results. The MATLAB software is used to compute the numerical results, which are then displayed in graphical and tabular form. The influence of several governing parameters on velocity, temperature distribution and magnetic fields in addition to the friction quantity, magnetic flux and heat transfer quantity has been explored. Computational evaluation is performed along the symmetrically heated plate to evaluate the velocity, magnetic field, and temperature together with their gradients. The selection of the magnetic force element, the buoyancy factor 0&lt;ξ&lt;∞ , and the Prandtl parameter range 0.1≤Pr≤7.0 were used to set the impacts of magnetic energy and diffusion, respectively. In the domains of magnetic resonance imaging (MRI), artificial heart wolves, interior heart cavities, and nanoburning systems, the present thermodynamic and magnetohydrodynamic issuesare significant.

Finite-amplitude instability of magnetohydrodynamic mixed convection flow of liquid metals in a vertical channel

The study of mixed convective liquid metal flow under a magnetic field has good potential for designing the next generation of advanced magnetohydrodynamic (MHD) devices. Flow instabilities play a crucial role in understanding flow dynamics in different applications. This paper reports the finite-amplitude instability of MHD mixed convection flow of electrically conducting liquid metals in a vertical channel under a transverse magnetic field. The cubic Landau equation is derived to determine the subcritical/supercritical bifurcations in the flow. The weakly nonlinear stability results are examined for a good range of Ha and Pr in the vicinity and far from the linear stability critical point (bifurcation point) at Reynolds number Re = 5000. The finite-amplitude results give only the supercritical type of instability for the considered range of Ha and Pr. The equilibrium amplitude increases by increasing the strength of the applied magnetic field. The impact of the nonlinear interaction of different harmonic modes on friction coefficient, heat transfer rate, and wave speed is also examined for the linearly unstable region. The results show that the distorted mean flow's heat transfer rate is higher than that calculated by the laminar basic state. Like linear stability analysis, the nonlinear analysis shows that the applied magnetic field stabilizes the basic flow. The supercritical instability shows that the linearly unstable flow shows a smooth transition.