Hartmann Number Research Articles

Oscillatory electro-magneto-kinetics of confined-Stokes-second-problem micro-flows

We semi-analytically investigate the electro-magneto-hydrodynamics of time periodic electroosmotic flow of a Newtonian electrolyte through microchannels with oscillating boundaries, resembling a confined-Stokes-second-problem type system. Herein, a constant orthogonal magnetic field and a constant transverse electric field have been used along with the driving time periodic electric field to have better control over mixing in the microchannel or to augment the pumping. The Poisson–Boltzmann equation has been solved with Debye–Hückel linearization for the thin electric double layer to obtain the electric potential distribution. We determine the flow field for low Hartmann number (Ha) cases by the regular perturbation method. Furthermore, Laplace transformation has been used to solve the flow field for each order in the obtained perturbation series. We have obtained the solution of flow field up to O(Ha) and found an excellent match with the complete numerical solution for our range of Ha. The dependence of flow field on dimensionless parameters, such as Ha, electrokinetic number (M), and Womersley number (Wo), has been discussed thoroughly, where Ha and M are functions of the strength of applied magnetic field and transverse electric field, respectively, and Wo is the function of Debye length, kinematic viscosity, and frequency of the time periodic electric field. Interestingly, for large values Wo, we find wave like motion in the flow field, which induces vorticity as well as better mixing caliber. Additionally, we find that the interplay between Ha and M controls the mixing and modifies the flow rate according to the need. Various combinations of such parameters have been discussed to promote mixing as well as pumping for such strongly coupled microfluidic phenomena.

Power-Law Nanofluid Magnetohydrodynamics Combined Convection in the Presence of Heat Absorption/Generation: A Lattice Boltzmann Analysis to Compute Thermal Performance Index

Endeavors to improve the performance of thermal systems have always been of great noticed due to their extremely high importance in industrial and engineering applications. For this intention, in the existing simulation, several effective strategies have been evaluated to determine the amount of heat transfer and entropy formation caused by the combined convection of non-Newtonian nanofluid with particles Brownian motion. Based on the findings via LBM simulation, it has been observed that changing the position and speed direction on the chamber wall helps to control the flow characteristics, and thus significantly changes the thermal performance of the system. The least effect of the magnetic field in reducing the value of the Nusselt number in all the positions of applying the speed belongs to the state where the wall direction is aligned with the force of gravity. In the case where the middle part of the vertical wall has speed, the formed flow power inside the chamber is 29% and 45% higher than when the first third and the last third of the wall have speed. The presence of a strong magnetic field leads to the reduction of convection effects, which is more evident for moving up the vertical wall. When the middle part of the wall has speed, if the magnetic field is applied to the middle part of the chamber to the highest value, the reduction of the average Nusselt number is about 35% and 39% more than the case when the magnetic field is applied to the first third and the last third of chamber. To have a higher average Nusselt number value, reducing the fluid power-law index and enhancing the Reynolds number value are effective strategies. To control the effects of the magnetic field, it is very effective to reduce the shear force on the chamber wall and expose the fluid flow to the heat absorption/production phenomenon. By reducing the value of fluid power-law index, the effect of magnetic field and heat absorption/production becomes more evident. In Re=200, the reduction of the thermal performance index for enhancing the Hartmann number value to the highest value is about 39% for n = 0.45, while this effect is about 31% and 24% for n = 0.7 and n = 0.95, respectively. By exposing the current to heat production, the effect of the magnetic field is reported to be about 55% higher than in other cases. Although heat production enhances the amount of Be value by about 66% compared to the heat absorption mode, it leads to an increase in the thermal performance index. The highest value of the system thermal performance index (0.82) can be achieved by upward moving the middle part of the chamber wall in the absence of magnetic field for heat absorption mode at the lowest power-law index and the highest Reynolds number value.

Influence of Heat Transform and Rotation of Sutterby Fluid in an Asymmetric Channel

In this research, the effect of the rotation variable on the peristaltic flow of Sutterby fluid in an asymmetric channel with heat transfer is investigated. The modeling of mathematics is created in the presence of the effect of rotation, using constitutive equations following the Sutterby fluid model. In flow analysis, assumptions such as long wave length approximation and low Reynolds number are utilized. The resulting nonlinear equation is numerically solved using the perturbation method. The effects of the Grashof number, the Hartmann number, the Hall parameter, the magnetic field, the Sutterby fluid parameter, and heat transfer analysis on the velocity and the pressure gradient are analyzed graphically. Utilizing MATHEMATICA software, numerical results are computed. It is discovered that velocity varies with parameters, while the pressure gradient is directly proportional to most parameters.

Mixed Convection in a Lid-Driven Cavity in the Presence of Magnetic Field with Sinusoidal Heating

Understanding mixed convection in engineering applications such as heat exchangers, electronics cooling devices, and solar energy collectors have urged researchers to investigate this phenomenon deeper. This study investigates the fluid flow and heat transfer pattern in a two-dimensional (2D) rectangular cavity with sinusoidal heating on the moving top lid numerically. The bottom wall is kept cool while the vertical walls are insulated. The effect of Hartmann number, Ha on the thermal characteristics and fluid flow are analyzed for Richardson number, Ri=1 which indicate mixed convection dominated regime. The governing equations are solved numerically using a SIMPLE algorithm with the finite volume method. The numerical results are displayed in streamlines and isotherms plots. The value of the Nusselt number indicating the heat transfer rate is also discussed. It is found that Ha has a significant effect on the heat transfer process and fluid flow. It can be seen clearly when the value of Ha=30, the rate of heat transfer dropped significantly on the cold wall. Generally, the heat transfer rate decreases with the increase of Ha.

Unsteady magneto-hydrodynamic behavior of TiO2-kerosene nanofluid flow in wavy octagonal cavity

The aim of this study is to mathematically model the behavior of magneto-hydrodynamics (MHD) in a two-dimensional unsteady flow, specifically focusing on natural convection (NC) and heat transfer (HT) within a wavy octagonal cavity. The study investigates how heat is transferred and fluid flows within this cavity under specific conditions. In particular, it examines the impact of various parameters, such as the Hartmann number (Ha), Rayleigh number (Ra), and the volume fraction of nanoparticles (ϕ) on the flow and HT patterns. This cavity includes a rectangular vertical wall (RVW) at the center of its bottom wall, filled with kerosene-TiO2 nanofluid of spherical shape. Within this setup, the RVW is maintained at a high temperature (T = Th), while the wavy wall is kept at a lower temperature (T = Tc, where Tc <Th). All other boundaries of the domain are assumed to be adiabatic. The finite element method (FEM) is employed as the solver for the relevant partial differential equations in numerical simulations. The results show excellent agreement with previously published research papers. The numerical solution transitions from an unsteady state to a steady state in approximately 0.68 dimensionless time units during the HT process. Throughout the study, various parameters are explored, including Ha, ranging from 0 to 100, Ra, ranging from 103 to 106, and ϕ, ranging from 0 to 0.05. The findings reveal distinct patterns in streamlines and isotherms. Specifically, a reduction in the rate of HT is observed as the Lorentz force increases, while the rate of HT is enhanced with increasing buoyancy force. Additionally, an expansion in ϕ led to an increase in the rate of HT. The study's findings could contribute to our understanding of fluid dynamics, heat transfer, and the behavior of nanofluids in complex geometries, potentially leading to improvements in various engineering and industrial applications.

Numerical computations for convective MHD flow of viscous fluid inside the hexagonal cavity having sinusoidal heated walls

This analysis deals the steady and the incompressible MHD fluid flow by sinusoidal walls of a hexagonal cavity with a cylindrical obstacle at the center. Finite element method (FEM), a numerical modeling method is used to examine the heat transfer and fluid flow controlled by the energy equation, the continuity equation and Navier-Stokes equations, which are converted to dimensionless form through suitable parameterization, which are tackled by finite element method. The temperature distribution and velocity fields are displayed for various parameters which are Richardson number, Hartmann number, Reynolds number, velocities’ amplitudes ratio, temperatures’ amplitudes ratio and phase deviation. This graphical study shows good convergent results of temperature and velocity for variation of involved parameters. At the end, the significant effects of the heat transfer rate are discussed in terms of the Nusselt number.

Develop the artificial neural network approach to predict thermal transport analysis of nanofluid inside a porous enclosure

This study explores the impacts of heat transportation on hybrid (Ag + MgO) nanofluid flow in a porous cavity using artificial neural networks (Bayesian regularization approach (BRT-ANN) neural networks technique). The cavity considered in this analysis is a semicircular shape with a heated and a cooled wall. The dynamics of flow and energy transmission in the cavity are influenced by various features such as the effect of magnetize field, porosity and volume fraction of nanoparticles. To explore the outcomes of these features on hybrid nanofluid thermal and flow transport, a BRT-ANN model is developed. The ANN model is trained using a dataset generated through numerical scheme. The trained ANN model is then used to predict the heat and flow transport characteristics for various input parameters. The accuracy of the ANN simulation is confirmed through comparison of the predicted results with the results obtained through numerical simulations. By maintaining the corrugated wall uniformly heated, we inspected the levels of isotherms, streamlines and heat transfer distribution. A graphical illustration highlights the characteristics of the Hartmann and Rayleigh numbers, permeability component in porous material, drag force and rate of energy transport. According to the percentage analysis, nanofluids (Ag + MgO/H2O) are prominent to enhance the thermal distribution of traditional fluids. The study demonstrates the potential of ANNs in predicting the impacts of various factors on hybrid nanofluid flow and heat transport, which can be useful in designing and optimizing heat transfer systems.

Numerical modeling of magnetohydrodynamic buoyancy-driven convection for enhanced energy applications

In the realm of thermal management for electronic systems, the efficacy of heat dissipation serves as a major predictor of the reliability and operational lifespan of electronic components. Simultaneously, within the realm of geothermal energy utilization, where harnessing the Earth’s inherent heat reservoirs is employed for power generation and direct heating applications, an intricate comprehension of temperature gradients and the dynamics governing heat transfer stands as an imperative prerequisite for optimizing the extraction of thermal energy. This work offers a complete mathematical model aimed at understanding the principles governing energy transfer inside naturally convected flows subjected to the impact of an external magnetic field. The analytical inspection involves a broad parametric study of the flow system, comprising variations in buoyancy-driven factors, as well as the magnetic field parameter, indicated as the Hartmann number (Ha), ranging from 0 to 50. This multifaceted study unveils the profound impact of magnetic fields on critical aspects of the flow, including isotherm alignment, velocity distributions, thereby paving the way for the development of advanced cooling systems poised to deliver elevated energy efficiency and enhanced performance in electronic devices. The computational analysis digs into the complicated temperature distributions, velocity profiles, and vorticity patterns. It is found that increment of the external magnetic force limits the variations in fluid’s horizontal and vertical velocities. Convective heat transfer is decreased with increasing Hartmann number at cold and hot sections of the fluid chamber. While for Rayleigh number this behavior is reversed.

MRT-lattice Boltzmann simulation of MHD natural convection of Bingham nanofluid in a C-shaped enclosure with response surface analysis

This paper focuses on the natural convection of heat transfer using magnetohydrodynamic (MHD) Bingham nanofluid. Utilizing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) within a C-shaped enclosure and the NVIDIA graphics processing unit (GPU)-based compute unified architecture (CUDA) C/C++ platform, the simulation is carried out numerically. Inside the cavity, the base fluid is water and the nanofluid is Al2O3. Boundary conditions are presented in accordance with the heated, cold, and adiabatic conditions present in the cavity's various walls. Several parameters including Bingham number (Bn=0,0.5,1,1.5,2), Rayleigh number (Ra=104,105,106), Hartmann number (Ha=0,10,20,30), and nanoparticle volume fraction (ϕ=0,0.01,0.02,0.03,0.04). The results of the numerical simulation are shown using streamlines and isotherms, velocity-temperature, Local Nusselt number, and average Nusselt number. From the obtained results it is found that for the variation of Bn, Ha, and ϕ with different Ra the rate of heat transfer decreases along the bottom wall and increases for the left and top walls. The average Nusselt number decreases while Bn, Ha rises. On the other contrary, the average Nu increases as ϕ increases. Response surface methodology (RSM) is added here to have better understanding of the effects of parameter used. RSM includes statistical table for the combination of data set and their graphs to understand the accuracy. Moreover, regression analysis shows how average Nu increases or decreases with the variation of different parameters. The C-shaped geometry provides an excellent option in heat exchanging or electronic cooling equipment the chip designing technology. This study is only for two-dimensional laminar flow.

Thermal analysis and optimization approach for ternary nanofluid flow in a novel porous cavity by considering nanoparticle shape factor

This study focuses on the numerical investigation and optimization of the heat-fluid transfer process within a novel cavity containing a ternary nanofluid (Cu–MgO–ZnO/water) influenced by a magnetic field. The research is conducted within a circular cavity featuring a cold wall and a complex internal heat source. The governing equations, converted into dimensionless form, are solved using a computational code based on the finite volume approach. The analysis encompasses the effects of a wide range of physical parameters, including the Rayleigh number (Ra), Hartmann number (Ha), magnetic field angle (α), radiation (Ra), nanoparticle shape factor (Sf), and porosity (ԑ). The results revealed that increasing the nanoparticle shape factor leads to a significant 61 % enhancement in the outer Nusselt number. This finding underscores the substantial influence of the nanoparticle shape factor (Sf) on heat transfer compared to other controlled variables. Furthermore, the response surface method is employed to determine the optimal conditions that yield the highest Nusselt number, resulting in optimal values for Ra, Ha, ԑ, Rd, α, and Sf of 2876, 44.26, 0.75, 0.073, 54.21, and 16.15, respectively. Consequently, the highest average Nusselt number attained is 20.01. As a result, this optimization approach establishes valuable correlations among various control parameters to enhance thermal energy, offering valuable insights for designers in the development of thermal devices.

Effect of viscous dissipation due to magnetohydrodynamic flow in an inclined channel

Graphene oxide nanoparticles with higher thermal conductivity aid in enhancing the flow and heat transport in magnetohydrodynamic (MHD) devices such as MHD pumps. Modelling such devices with promising applications inherently necessitates the entropy studies to ensure efficient models. In conventional fluids, Lorentz force controls the fluid velocity in the presence of magnetic field. Whereas, the use of graphene oxide hypothesized the enhancement of flow, despite the impacts of Lorentz force, due to high thermal conductivity. This paper is an investigation to computationally study the hypothesis and to analyse the entropy generation in magnetohydrodynamic flow of graphene oxide (GO) in an inclined channel. Buongiorno nanofluid model is used including the impacts of nanoparticle attributes namely thermophoretic and Brownian diffusion along with viscous dissipation effects. Spectral quasilinearization method with Chebyshev's polynomials is adapted to solve the differential equations under convective conditions. On studying the effects of implanted parameters, it is concluded that the flow velocity enhancement by Hartmann number is remarked and is proved to be achieved from the thermal conductivity of graphene oxide particles. A quantitative analysis is made with the previously published results for special cases. Furthermore, investigations conclude that the entropy is contributed primarily from the heat transfer.

Irreversibilities and heat transfer in magnetohydrodynamic microchannel flow under differential heating

This study investigates heat transfer and entropy generation in a microchannel subjected to differential heating, viscous dissipation, and Joule heating within a magnetohydrodynamic (MHD) fluid flow. A finite difference method with a fully implicit scheme is employed to accurately model temperature distribution and entropy generation. A comparison between the average Nusselt numbers (Nu) calculated using the classical method and the Bennett Formula reveals a notable discrepancy, particularly at the entry length (up to 14%). It has been found that when one plate is heated while the other is cooled and the Hartmann number (Ha) is low, the average Nu for both plates converges to 2. However, at high Ha values considering viscous dissipation and Joule heating, there is an 8% deviation between the Nu values of the two plates, with the higher Nu found on the cooling plate. Sensitivity analyses explore the impact of control parameters on entropy generation, emphasizing the significance of η as a key parameter that reflects the system's resistance to entropy generation. Increasing η from 0.1 to 0.5 results in a 32% reduction in entropy generation. In particular, for microchannels, substantial η high values imply reduced entropy generation, highlighting their efficiency in heat transfer.

Numerical simulation of MHD double-diffusive mixed convection in a closed cavity filled with liquid potassium alloy: Incorporating thermosolutal source

This numerical study investigates the effect of a magnetic field and discrete thermo-solutal source on steady double-diffusive mixed convection in a double-sided cavity filled with liquid potassium alloy using the finite volume method. The discrete thermo-solutal source is fixed on the cavity left wall, with three locations considered in three cases. In contrast, the right vertical wall is maintained at a low temperature and concentration. The remaining part of the enclosure is kept adiabatic. The investigation explores the effects of relevant parameters, including Reynolds number (102 ≤ Re ≤ 103), Hartmann number (0 ≤ Ha ≤ 50), Lewis number (1.0 ≤ Le ≤ 10.0), and source location (0 ≤ η ≤ 1.0), Prandtl number (Pr = 0.054), and Source length (0.2L) are held constant. The results show that heat and mass transfer rates increase with Reynolds number, decreasing with Hartmann number. By increasing Le, the heat transfer reduces, and mass transfer increases. By reducing η from 0.8 to 0, the proximity of the corresponding sources enhances thermal and solutal effects, leading to increased heat and mass transfer rates. Further, an empirical correlation is developed for the average Nusselt number (Nuavg) and the average Sherwood number (Shavg).

Wall mode dynamics and transition to chaos in magnetoconvection with a vertical magnetic field

Quasistatic magnetoconvection of a fluid with low Prandtl number ( ${\textit {Pr}}=0.025$ ) with a vertical magnetic field is considered in a unit-aspect-ratio box with no-slip boundaries. At high relative magnetic field strengths, given by the Hartmann number ${\textit {Ha}}$ , the onset of convection is known to result from a sidewall instability giving rise to the wall-mode regime. Here, we carry out three-dimensional direct numerical simulations of unprecedented length to map out the parameter space at ${\textit {Ha}} = 200, 500, 1000$ , varying the Rayleigh number ( ${\textit {Ra}}$ ) over the range $6\times 10^5 \lesssim {\textit {Ra}} \lesssim 5\times 10^8$ . We track the development of stable equilibria produced by this primary instability, identifying bifurcations leading to limit cycles and eventually to chaotic dynamics. At ${\textit {Ha}}=200$ , the steady wall-mode solution undergoes a symmetry-breaking bifurcation producing a state that features a coexistence between wall modes and a large-scale roll in the centre of the domain, which persists to higher ${\textit {Ra}}$ . However, under a stronger magnetic field at ${\textit {Ha}}=1000$ , the steady wall-mode solution undergoes a Hopf bifurcation producing a limit cycle which further develops to solutions that shadow an orbit homoclinic to a saddle point. Upon a further increase in ${\textit {Ra}}$ , the system undergoes a subsequent symmetry break producing a coexistence between wall modes and a large-scale roll, although the large-scale roll exists only for a small range of ${\textit {Ra}}$ , and chaotic dynamics primarily arise from a mixture of chaotic wall-mode dynamics and arrays of cellular structures.

Effects of anisotropic permeability on EMHD nanofluid flow and heat transfer in porous microchannel with wavy rough walls

This theoretical study thoroughly examines the complexities of fluid flow and heat transfer within microfluidic devices by employing anisotropic porous media with wavy walls. The effect of anisotropic permeability and electromagnetohydrodynamics (EMHD) on nanofluid transport is examined in a wavy microchannel under a constant pressure gradient. The nonlinear coupled governing equations for electric double-layer potential, velocity, temperature, and nanoparticle volume fraction are solved numerically using shooting techniques with the Runge–Kutta method. The numerical results are validated with the asymptotic analytical solutions. We explore the impact of parameters like the Hartmann number, Darcy number, and joule heating on nanofluidic flow. The interplay between anisotropic permeability ratio and angle significantly influences flow, temperature profiles, and nanoparticle volume fraction. Reduction in nanoparticle concentration is attributed to constrained entry into the porous medium due to elevated anisotropic permeability. Frictional heating, influenced by the Forchheimer inertial effect, enhances temperature and induces slug flow at low Darcy numbers. The Nusselt number peaks at low Darcy numbers with an anisotropic angle of φ=π/2, experiencing a minimum when φ=0. These findings deepen our understanding of the role of anisotropic permeability in shaping fluid flow and heat transfer in microfluidic systems influenced by EMHD effects.

The Impact of Inclined Magnetic Field on Streamlines in a Constricted Lid-driven Cavity

The influence of oriented magnetic field on the incompressible and electrically conducting flow is investigated in a square cavity with a moving top wall and a no-slip constricted bottom wall. Radial basis function (RBF) approximation is employed to velocity-stream function-vorticity formulation of MHD equations. Numerical results are shown in terms of streamlines for different values of Hartmann number M, orientation angle of magnetic field ϴ and the height of the constricted bottom wall hc with a fixed Reynolds number. It is obtained that the number of vortices increases as either hc or M increases. However, the increase in ϴ leads to decrease the number of vortices. Formation of vortices depends on not only the strength and the orientation of the magnetic field but also the constriction of the bottom wall.

Entropic behavior in bidirectional flow of CeO2-ZnO/water hybrid nanofluid with prescribed surface temperature/heat flux aspects

PurposeThe present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid.Design/methodology/approachThe transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters.FindingsIt is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints.Originality/valueTo the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation.

A rapid performance prediction method for Two-Phase liquid metal MHD generators based on Quasi-One-Dimensional model

Liquid metal magnetohydrodynamic (LMMHD) power generation is a novel and highly efficient technology with broad application prospects. In our previous study, a novel LMMHD enhanced Closed-Brayton-Cycle power generation system for hypersonic vehicles was proposed, and its excellent power generation performance was demonstrated by thermodynamic analysis. The most important component of LMMHD system is the power generation channel, and the rapid and accurate performance prediction and optimization design methods of which are the prerequisites for further research. In this study, a quasi-one-dimensional modeling method for LMMHD power generation channels based on a two-fluid model is developed. The performance variation laws with the geometric structure, magnetic field and boundary conditions, as well as the potential loss mechanisms are investigated. Results indicate that the most optimal or appropriate design can be achieved by optimizing the channel geometry and magnetic field, such as the optimal aspect ratio of 1 and the optimal Hartmann number of 2000. But it is difficult to balance the power output and efficiency through the boundary condition optimization. The gas–liquid slip can lead to approximately 20–40% of energy losses, making the elimination and suppression of slip effects a significant research focus in the relevant field.

On the entropy analysis and hydrothermal behavior of buoyancy-driven magnetized hybrid nanofluid flow within a semi-circular chamber fitted with a triangular heater: Application to thermal energy storage for energy management

Entropy generation is treated as a noteworthy criterion for effective operation in thermal storage systems. Buoyancy-driven laminar flows within the semi-circular chamber have wide-ranging applications within the aviation industry, solar thermal receivers, heat exchangers, chemical mixing chambers, electronic components, etc. Nanofluids do explore significant heat transport capabilities in industrial, technical, and commercial sectors. The stable dispersion of metallic or oxide tiny nano-level particles and water, named hybrid nanofluids signifies the extended version of classical nanofluids. Hybrid nanofluids reveal superior thermal conductivity and are significantly used as an advanced heat transport medium in thermal storage, solar receiver, electronic cooling, heat pipes, space, biomedical, etc. With such an objective, the performed analysis unfolds the hydrothermal and entropy investigation of magnetically driven buoyancy-induced Al2O3–TiO2–water hybrid nanofluids through a semi-circular chamber having a triangular heater fitted from the bottom wall. The curved periphery is made cold, while the remaining triangular parts and bottom walls are made heated and insulated, respectively. Several triangular-size heaters are set to the lower wall and variations in entropy plus hydrothermal scenario are noted. Leading equations are transferred to dimensionless form using apposite similarity transformation. The Galerkin finite element discretization procedure is merged to execute the numeric simulation. Both numeric and experimental studies are clutched to compare the present result’s accuracy. Various velocities, streamlines, isotherms, Bejan numbers, entropy profiles, and Nusselt number profiles are presented to address the parametric influence of Hartmann numbers, solid particle concentrations, and Rayleigh numbers.

Numerical solutions for MHD mixed convection flow in a square wavy cavity inside heated corrugated rods

Steady mixed convection flow in a square wavy cavity containing heated corrugated rods is investigated numerically. In the current work, the vertical walls are suited at a fixed temperature, and the upper and lower walls are adiabatically treated. Thermal conductivity has been calculated by Galerkin finite element methods in which computational region is discretized into small triangular portions. We have studied effects on temperature and streamlines for different Rayleigh numbers, Hartmann numbers, and numbers of undulations and fixed dimensionless amplitudeA=0.05 of right wavy wall and amplitude of corrugated rod C=0.02. The flow is entirely steady for the range of Ra. from 103to105 and Ha. from 0 to 50. Mixed convection of top-motivated streams covers the tenders, for example, cooling of electronic gadgets, elite execution building protections, multi-safeguard structures utilized for atomic reactors, food handling, float glass creation, heater. Various examinations on cover-driven cavity stream and intensity move including different mixes of cavity arrangements, different liquids, and forced temperature slopes have been distributed in the writing much of the time.