Hartmann Number Research Articles

Synergistic effects of multi-segmented magnetic fields, wavy-segmented cooling, and distributed heating on hybrid nanofluid convective flow in tilted porous enclosures

This study investigates the complex thermal-fluid behavior within a tilted porous enclosure filled with a Cu−Al2O3-water hybrid nanofluid, subject to segmented magnetic fields, wavy cooling segments, and distributed heat sources. The research explores the intricate interplay between geometric factors and thermal-magnetic forces to enhance heat transfer in industrial applications. The finite volume method (FVM), coupled with the SIMPLE algorithm and a TDMA solver, is employed to solve the governing transport equations. A comprehensive parametric analysis examines the effects of key dimensionless parameters: Darcy-Rayleigh number (10–104), Darcy number (10-4–10-1), Hartmann number (0–70), magnetic field angle (0°-180°), nanoparticle volume fraction (0–2 %), porosity (0.1–1.0), wavy cooler undulation height (0–0.3), magnetic segment width (0–1), number of segmental magnetic fields (0–4), and enclosure tilting angle (0°–180°). The study elucidates the physical mechanisms underlying the transition from uniform to segmented heating scenarios. Results reveal a remarkable enhancement of up to 38 % in heat transfer performance when transitioning from a conventional square enclosure to the proposed configuration with partial waviness on opposing walls. This improvement stems from increased surface area and disrupted thermal boundary layers, promoting better fluid mixing. The application of a segmented magnetic field with strategic orientation resulted in up to 26 % enhancement by modulating flow patterns and creating localized convection cells. The segmented heating generates thermal plumes that interact with the magnetic field-induced Lorentz forces, further improving thermal transport. The findings provide valuable insights into the design and optimization of efficient heat transfer systems in various industries, including electronics cooling, solar thermal collectors, and nuclear reactors, demonstrating significant potential for energy savings and improved thermal management through the strategic integration of hybrid nanofluids, magnetic fields, and geometric modifications in porous media applications.

Application of Box-Behnken design with RSM to predict the heat transfer performance of thermo-magnetic convection of hybrid nanofluid inside a novel oval-shaped annulus enclosure

The study of flow around a stationary or rotating circular cylinder holds substantial importance in numerous engineering disciplines, including building, bridge, and structural engineering. This knowledge is utilized to manage flow-induced vibrations, implement blowing or suction techniques, control moving surfaces, and develop acoustic thrusters and synthetic jets. The current aims to analyze the numerical and RSM optimization with Box–Behnken design (BBD) for the buoyancy driven convective flow and heat management features of Magneto Fe3O4−MWCNTs/water hybrid nanofluid filled inside a novel oval-shaped annulus enclosure with concentric hot circular cylinder. The water used as base fluid and iron oxide and Multiwall carbon nanotubes as nanoparticles. The finite element method is employed to solve numerically the coupled equations. The RSM optimization with Box–Behnken design (BBD) is applied to optimize the heat transfer rate across different three factors. The stream lines, isotherms and line graphs are design for different flow parameters effect. The results indicated that heat transfer is enhanced by using of hybrid nanofluid. The velocity is reduced via increment in Hartmann number. The local Nusselt number is increases with increment in the values of the Rayleigh number. Furthermore the Heat transfer rate is boosted up with increases the concentration of nanoparticles.

A variational multiscale stabilized finite element method for double diffusive incompressible flow with application to mixed convection in a heated staggered cavity under magnetic field

In this work, a novel stabilized finite element scheme in a subgrid multiscale variational framework is proposed to efficiently solve double-diffusive incompressible Newtonian fluid flow in a complex geometry occurring in several real-life applications. Here, the fine scale effects are transferred to the course scale problem following algebraic subgrid analysis, and then, the course scale equations are computed and the key stabilization parameters are derived following the Fourier analysis. The influence of flow, heat, and mass transfer parameters such as Reynold’s Number, Hartmann Number, Richardson Number, and Lewis Number are analyzed under a magnetic field, through the streamlines, isotherms, and the local heat fluxes to understand the double-diffusive mixed convective process in a complex staggered cavity, which is relevant to engineering applications such as ventilation and contamination assessment systems. The study finds that maximum species contamination together with the maximum Sherwood Number (12.54) occurs when the Richardson number is 10, and the minimum contamination together with the minimum Sherwood Number (0.71) occurs when the Lewis number is 0.1 when other parameters are varied within the operational range. The results are validated with previously existing literature for simple cases.

Theoretical assessment of chemically reactive bioconvective flow of hybrid nanofluid by a curved stretchable surface with heat generation

ABSTRACT Bioconvection in hybrid nanofluids refers to the phenomenon where biological microorganisms such as algae or bacteria exhibit collective movement or pattern formation in a suspension containing nanoparticles. This phenomenon has significance in various fields, including biology, nanotechnology, and engineering. The current investigation emphasizes the bioconvective flow of a water (H2O)−ethylene glycol (C2H6O2)-based hybrid nanofluid flow by a curved stretched sheet. Copper (Cu) and silver (Ag) nanoparticles are suspended in the base fluid. The thermal field is analyzed in the presence of heat generation, dissipation, Joule heating, and the impact of thermal radiation. Binary reactions associated with Arrhenius energy are accounted in the modeling of mass concentration. The phenomenon of bioconvection is considered to regulate the random movement of tiny solid particles within the flow. Boundary layer constraints are implemented to eliminate ineffective terms from modeling. The transformation procedure is adopted to obtain the flow governing system of ODEs. The built-in code of Mathematica (NDSolve) is implemented to obtain the graphical and numerical results. The results show that the velocity field decreases with increasing porosity variable and Hartmann number. An opposite impression of the Eckert number and Schmidt variable on the thermal field is noticed. Bioconvection Peclet and Lewis numbers have a direct relationship with motile density.

Experimental investigation on magneto-convective flows around two differentially heated horizontal cylinders

Liquid metal buoyant flow around two differentially heated horizontal cylinders in the presence of a uniform vertical magnetic field is investigated experimentally. While magneto-convection in pipes or ducts has been studied theoretically and experimentally in recent years, data for heat transfer at immersed obstacles are rare and, to our knowledge, detailed experimental investigations on this fundamental magnetohydrodynamic problem do not exist. In the present work, two horizontal cylinders inserted into an adiabatic rectangular cavity filled with gallium–indium–tin are kept at constant temperatures to establish a driving temperature gradient in the surrounding liquid metal. The buoyancy-driven flow, quantified by the Grashof number $Gr$ , is varied in the range ${10^{6} \leq Gr \leq ~5\times 10^{7}}$ . With increasing magnetic field, expressed via the Hartmann number $Ha$ , different flow regimes are identified from measurements for $0 \leq Ha \leq ~3000$ . The effect of the electromagnetic force primarily consists in suppressing turbulence and damping the convective flow. The heat transfer is quantified in terms of the non-dimensional Nusselt number $Nu$ , and its dependence on $Gr/{Ha}^{2}$ , which is identified as the important group governing the flow, is discussed.

Buoyancy-driven heat transfer and entropy analysis of a hydromagnetic GO-Fe3O4/H2O hybrid nanofluid in an energy storage enclosure partially filled with non-Darcy porous medium under an oblique magnetic field

Purpose Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid. Design/methodology/approach The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles. Findings Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios. Originality/value The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.

Impact of double diffusion on solid particle dispersion in rotated cylinders with nano-enhanced phase change materials

This study introduces an innovative approach that combines the Incompressible Smoothed Particle Hydrodynamics method with Artificial Neural Networks to examine the dispersion of solid particles within rotated circular cylinders filled with nano-enhanced phase change materials. This method addresses the limitations of traditional numerical techniques by improving accuracy in complex geometries and dynamic boundary conditions. The various parameters are examined, including the lengths of low sources in boundary walls Lb, dimensionless time τ, Hartmann number (Ha), Darcy number (Da), thermal radiation parameter (Rd), and Rayleigh number (Ra). The solid particles are initially situated at the center gate between the two circular cylinders, maintained at elevated temperature Th and concentration Ch. Due to the upward direction of convection flow, the solid particles are consistently dispersed into the top circular cylinder. The findings offer valuable insights into the system's behavior. The dispersion of solid particles within the NEPCM is influenced by both τ and Lb, showcasing minimal dispersion for τ≤0.1 and intensified dispersion for τ≥0.2, particularly augmented by larger Lb. The heat capacity ratio (Cr) exhibits a decrease with increasing Lb at multiple time points. A decrease in the Darcy number significantly slows down the dispersion of solid particles because of the substantial resistance posed by the porous medium. As the Rayleigh number increases, there is an enhanced dispersion of solid particles into the upper circular cylinder and heightened temperature distributions. Additionally, the average Nusselt number Nu¯ and Sherwood number Sh¯ decrease with the increase in Lb due to the expansion of low-temperature and concentration source. When the length Lb was increased from 0.25 to 1, Nu¯ and Sh¯ decreased by approximately 76% and 67%, respectively, underscoring the impact of geometric configuration on heat and mass transfer efficiency. The study highlights the effectiveness of the MLP model in predicting Nu¯ and Sh¯ values through graphical analysis, showing significant agreement with the target values. The results demonstrated notable improvements in managing particle dispersion and heat/mass transfer, emphasizing the potential of this integrated approach for applications in thermal management and energy optimization.

Finite element analysis of Cu-water nanofluid flow and heat transfer in a dynamically bulging enclosure

PurposeThe main purpose of this study is to analyze the heat transfer phenomena in a dynamically bulging enclosure filled with Cu-water nanofluid. This study examines the convective heat transfer process induced by a bulging area considered a heat source, with the enclosure's side walls having a low temperature and top and bottom walls being treated as adiabatic. Various factors, such as the Rayleigh number (Ra), nanoparticle volume fraction, Darcy effects, Hartmann number (Ha) and effects of magnetic inclination, are analyzed for their impact on the flow behavior and temperature distribution.Design/methodology/approachThe finite element method (FEM) is employed for simulating variations in flow and temperature after validating the results. Solving the non-linear partial differential equations while incorporating the modified Darcy number (10−3 ≤ Da ≤ 10−1), Ra (103 ≤ Ra ≤ 105) and Ha (0 ≤ Ha ≤ 100) as the dimensionless operational parameters.FindingsThis study demonstrates that in enclosures with dynamically positioned bulges filled with Cu-water nanofluid, heat transfer is significantly influenced by the bulge location and nanoparticle volume fraction, which alter flow and heat patterns. The varying impact of magnetic fields on heat transfer depends on the Rayleigh and Has.Practical implicationsThe geometry configurations employed in this research have broad applications in various engineering disciplines, including heat exchangers, energy storage, biomedical systems and food processing.Originality/valueThis research provides insights into how different shapes of the heated bulging area impact the hydromagnetic convection of Cu-water nanofluid flow in a dynamically bulging-shaped porous system, encompassing curved surfaces and various multi-physical conditions.

Influence of thermal radiation and magnetic field on convective transfer within an inclined square enclosure filled with Cu-water nanofluid

The present work investigates the effects of thermal radiation and magnetic field on the laminar convective transfer process on copper-based nanofluid within an inclined square enclosure. The studied configuration is a rigid-walled cavity subjected to a horizontal temperature gradient where the left wall is maintained at a hot temperature Th and subjected to a magnetic field B0. In contrast, the right wall is kept at a cold temperature Tc. The horizontal walls are adiabatic. The dimensionless governing equations are solved using the finite difference method and the UPWIND scheme to solve the convective terms. Formulated using the stream function, vorticity, and temperature. Effects on mean Nusselt numbers are investigated at different Rayleigh numbers 104,105,106, Hartmann numbers HA=0to100, tilt angles γ=0,π/6,π/4andπ/3, nanofluid volume fractions 0%≤φ≤6% and different radiation parameters ( Rd=0,1,2,3 ). The findings show that the HTR increased 3.6 times by augmenting the Ra from 104 to 106. Also, increasing the Ha number from 0 to 100 causes an 83.16% reduction in the HTR. Considering the radiation mode of heat transfer causes an increase in HTR. The average Nusselt values increase by 59.72% for the concentration of 6% while increasing the radiation parameter from 0 to 3. On the other hand, an increase in volume fraction leads to a deterioration in mean Nusselt numbers (Numean).

An implication of entropy generation in Maxwell fluid containing engine oil based ternary hybrid nanofluid over a riga plate

ABSTRACT Nanoparticles enhance the heat transmission by recovering energy that was dissipated due to increased thermal conductivity. Engine oil, commonly known as a lubricant, facilitates the movement of energy between various substances. The purpose of this analysis is to investigate the impact of the Maxwell fluid and entropy generation on the movement of ternary hybrid nanoparticles as they flow past a Riga plate under convective boundary conditions. The ternary nanoparticles AA 7072 , AA 7075 , and CoF e 2 O 4 are combined with engine oil ( EO ) as the primary liquid. The heat transfer analysis involves the examination of heat sink/source and thermal radiation. The use of a similarity transformation is employed to convert partial differential equations (PDEs) into a dimensionless form. The altered equation is subsequently solved with the homotopy analysis method (HAM), a robust analytical technique. The current analysis is marked by convergence, which denotes the answer. The impact of flow properties, such as the Maxwell parameter, modified Hartmann number, thermal radiation, and Biot number, on the velocity distribution and temperature profile. Higher values of the Maxwell fluid parameter have been shown to result in an increase in the velocity curve. The skin friction and heat transmission variances are elucidated through the utilization of tables and figures. Moreover, the findings suggest that the thermal layer of the tri hybrid nanoliquid is strengthened in reaction to higher thermal radiation and Biot number. At the same time, the thermal layer is also strengthened.

The electrokinetic energy conversion and streaming potential analytical solutions of couple stress nanofluids in the circular polyelectrolyte-grafted nanochannel

The purpose of this study is to investigate the variation of streaming potential and EKEC efficiency of nanofluids with couple stress in the circular polyelectrolyte-grafted (PE-grafted) nanochannel under the combined effect of periodic pressure and magnetic field. The analytical solutions of the velocity field in the PEL region and electrolyte solution are obtained by solving the modified Navier-Stokes equation and the influence of several dimensionless parameters on the streaming potential and electrokinetic energy conversion (EKEC) efficiency are further discussed graphically. The results indicate that the streaming potential decreases with increasing Hartmann number and nanoparticle diameter within a certain parameter range. The dimensionless velocity shows an oscillating trend at different oscillating Reynolds numbers, and the oscillation is more pronounced at the interface between the PEL and the electrolyte solution. In addition, the EKEC efficiency of nanofluids in soft nanochannel is compared with that in a rigid one. It is shown that the EKEC efficiency is higher in PE-grafted nanochannel, and the couple stress plays an important role in improving the EKEC efficiency. We anticipate that these findings will help to reveal a novel understanding of energy conversion in the circular PE-grafted nanochannel.

Revolutionizing bioconvection: Artificial intelligence-powered nano-encapsulation with oxytactic microorganisms

Using incompressible smoothed particle hydrodynamics (ISPH), this study examines the bioconvection flow of oxytactic microorganisms in a porous annulus populated by nano-encapsulated phase change material (NEPCM). Artificial neural network (ANN) is joined with the ISPH method to accurately predict the values of average Nu‾. Between the outside hexagonal-shaped domain and the embedded wavy cylinder, a new annulus is produced. The ranges of the pertinent parameters are wave amplitude of an embedded cylinder A=0.1−0.5, Hartmann number Ha=0−80, a radius of the cylinder Rcyld=0.05−0.5, Darcy number Da=10−2−10−5, undulation number Kund=2−32, bioconvection Rayleigh number Rab=1−1000, Rayleigh number Ra=103−106, and Lewis number Le=1−20. The regulated geometric characteristics of an embedded wavy cylinder, such as wavy amplitude, cylinder radius, and undulation numbers, have been found to contribute significantly to widening the cooling region and minimizing the oxytactic microorganisms. Hence, the embedded wavy cylinder can be applied for various thermal uses including cooling devices and heat exchangers. The average Nu‾ is enhanced under an increment in the geometric parameters of the embedded cylinder. Increasing Rayleigh/bioconvection Rayleigh numbers enhances the buoyancy forces that accelerate the velocity field.

One-winged butterflies: mode selection for azimuthal magnetorotational instability by thermal convection

The effects of thermal convection on turbulence in accretion discs, and particularly its interplay with the magnetorotational instability (MRI), are of significant astrophysical interest. Despite extensive theoretical and numerical studies, such an interplay has not been explored experimentally. We conduct linear analysis of the azimuthal version of MRI (AMRI) in the presence of thermal convection and compare the results with our experimental data published before. We show that the critical Hartmann number ( $Ha$ ) for the onset of AMRI is reduced by convection. Importantly, convection breaks symmetry between $m = \pm 1$ instability modes ( $m$ is the azimuthal wavenumber). This preference for one mode over the other makes the AMRI wave appear as a ‘one-winged butterfly’.

A SUPS formulation for simulating unsteady natural/mixed heat convection phenomena in square cavities under intense magnetic forces

This paper presents stabilized finite element simulations of unsteady natural and mixed heat convection phenomena occurring in square enclosures. It is assumed that the enclosures are subject to intense uniform magnetic fields applied perpendicular to the vertical walls. It is well known that the classical Galerkin finite element method (GFEM) is prone to yielding nonphysical oscillations when simulating convection-dominated flows. Therefore, in order to handle such flows occurring at high Hartmann (0≤Ha≤100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 \\le {\\rm Ha} \\le 100$$\\end{document}) and Rayleigh (103≤Ra≤108\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{3} \\le {\\rm Ra} \\le 10^{8}$$\\end{document}) numbers, the stabilization of the GFEM is accomplished with the streamline-upwind/Petrov–Galerkin and pressure-stabilizing/Petrov–Galerkin formulations. Temporal discretizations are performed with the backward Euler formula. At each time step, the nonlinear systems are linearized with the Newton–Raphson (N–R) method, and the linearized systems are solved directly using the sparse lower–upper decomposition. The incompressible flow solvers are developed in-house, run in parallel within the FEniCS ecosystem, and tested on a comprehensive set of numerical experiments with various thermal boundary conditions. Numerical simulations and comparisons reveal that the proposed formulation performs quite well at high Hartmann and Rayleigh numbers without exhibiting any significant localized or globally spread numerical instabilities. Moreover, it achieves this by using uniform meshes and only linear elements, making the formulation much more computationally efficient. Mesh convergence analyses are also performed to demonstrate the reliability of the numerical results obtained.

The time‐fractional ISPH method for fin circular rotation on MHD bioconvection flow of oxytactic microorganisms and NEPCM within a hexagonal‐shaped cavity

AbstractThis work investigates the bioconvection flow of oxytactic microorganisms and nanoparticle‐enhanced phase change material (NEPCM) within a hexagonal‐shaped cavity containing a rotated cross fin, utilizing the incompressible smoothed particle hydrodynamics (ISPH) method based on a time‐fractional derivative. The study considers the circular rotation of an inner cross fin and the presence of two rectangular heat sources on the plane walls inside the hexagonal cavity. The novelty of this work is its integration of a hexagonal‐shaped cavity with a rotated cross fin and the use of a time‐fractional derivative in the ISPH method to analyze bioconvection flow, offering new insights into the interaction between microorganism motion and heat transfer dynamics in complex geometries. The effects of Darcy, Hartmann, Lewis, Peclet, Rayleigh, and bioconvection Rayleigh numbers on isotherms, heat capacity ratio, microorganism density, velocity fields, and average Nusselt number are analyzed. The key findings demonstrate the significant impact of Rayleigh and bioconvection Rayleigh numbers in enhancing heat distribution and velocity fields, thereby significantly influencing microorganism motion. Due to Lorentz forces, the velocity field decreases by with an increase in the Hartmann number from 0 to 50. The resistance of the nanofluid's velocity becomes apparent as the Darcy number decreases. Increasing Lewis and Péclet numbers cause the microorganisms to shift towards the cavity's boundaries.

Influence of solid cylinders on fluid flow and thermal analysis in a curved channel with constant magnetic field

The current study explores the numerical simulation of constant mixed convection heat transfer and fluid flow within a channel, driven by the inlet velocity. The investigation focuses on a curved irregular channel where the presence of three differently sized circular obstacles introduces an unpredictable element to the heat transfer process. For the two-dimensional physical scenario, mathematical equations are formulated to analyze velocity and temperature. Employing appropriate dimensional variables, the coupled partial differential equations are transformed into dimensionless form. Subsequently, the Finite Element Method (FEM) is employed to simulate the results for non-dimensional physical parameters such as Reynolds number, Richardson number, Hartmann number, nanoparticles' volume fraction, and various states of the circular obstacles on heated lines, flow structure, velocities, and temperatures at mean positions generating isotherms, streamlines, velocity, and temperature profiles for various parameter increments. The analysis reveals significant influences of Reynolds number (Re) and heated circular obstacles on the temperature profile, manifesting as heated lines within the system. The analysis brings to light the substantial impacts of nanoparticles on the temperature profile at both the vertical and horizontal mean positions. An elevated Hartmann number signifies a more robust magnetic field than viscous forces. A heightened magnetic field can hinder fluid movement and modify the patterns of heat transfer. Based on the graphical results, we infer that temperature differences tend to arise between strata as the Richardson number increases, leading to a heightened and more evident stratification.

Implication of electromagnetohydrodynamic flow of a non‐Newtonian hybrid nanofluid in a converging and diverging channel with velocity slip effects: A comparative investigation using numerical and ADM approaches

AbstractThis study delves into the intricate interplay of magnetic and electric fields (EMHD) on the flow characteristics of a non‐Newtonian bio‐hybrid nanofluid, consisting of Ag+Graphene/blood, within converging and diverging geometries. The investigation takes into account the effects of velocity slip at the walls, offering a comprehensive examination of this complex fluid system. A novel bio‐hybrid nanofluid model was introduced, featuring a unique combination of Ag+Graphene/blood nanoparticles. To address this multifaceted problem, the research employed mathematical modeling based on nonlinear partial differential equations (PDEs), encompassing continuity and momentum equations. These PDEs were then transformed into a system of nonlinear ordinary differential equations (ODEs) through similarity transformations. The study explored both numerical and analytical solutions, with a particular focus on the application of the Adomian decomposition method (ADM). To validate the findings, the study compared the analytical results with those obtained using the HAM‐based Mathematica package and the Runge–Kutta Fehlberg 4th–5th order (RKF‐45) method in specific scenarios. Active parameters, including nanofluid volume fraction, slip factors, and the influence of magnetic and electric fields, were systematically examined to unveil their impacts on velocity and skin friction within this multifaceted nanofluid system. It is found that the skin friction coefficient decreases with the Increasing both the nanoparticle volume fraction, Hartmann number and the angle in both channels. Results obtained also reveal an in the converging section, higher Casson parameters lead to increased yield stress but are offset by the higher shear rates, resulting in a higher velocity profile. In the diverging section, the fluid resists flow due to the reduced shear stress, leading to a decreased velocity profile.

Investigation of the unsteady MHD fluid flow and heat transfer through the porous medium asymmetric wavy channel

This paper uses three analytical methods to find the novel results in the two-dimensional time-dependent MHD oscillatory flow and heat transfer in an asymmetric wavy porous channel. The corresponding constitutive equations become complex by considering the pressure gradient as a complex function. This results in the existence of both real and imaginary solutions for fluid velocity and temperature. The changes in parameters like the Hartmann number, wavelength, Grashof number, and porous medium shape factor will affect the real fluid velocity. Still, only radiation parameter changes will affect the real fluid velocity and temperature. Increasing the Hartmann number, porous medium shape factor, and radiation parameter will drastically reduce real fluid velocity. The Reynolds number should theoretically affect the imaginary velocity, but according to the boundary condition definition, the imaginary velocity value becomes zero. Altering the frequency of the wavy walls and the Peclet number will only affect the imaginary temperature component, and increasing these parameters will increase the average imaginary temperature profile. The uniqueness of this study lies in the resolution of complex differential equations in a way that has not been attempted before. The results indicated that each set of three solutions was nearly identical, highlighting the outcomes' precision.

Numerical analysis of transient MHD natural convection in a channel with four heat-generating cylindrical solids filled with in a non-Newtonian Fe3O4 ferrofluid

This article presents a numerical investigation and analysis of the cooling effectiveness of thermomagnetic transient natural convection in a long channel, equipped with four cylindrical heat-generating blocks. A non-Newtonian power-law ferrofluid was employed for the present investigation to achieve optimum cooling. The governing equations are the continuity equation, the momentum equation and the energy equation. The finite volume method was used to solve the resulting algebraic system. From an energy-saving point of view, this configuration can provide a good approximation for selecting effective physical and geometrical parameters to design a reliable thermal system. For this purpose, the study was carried out for various geometric and thermophysical parameters. Different values of thermal conductivity, power law index, Rayleigh number, Hartmann number and ferrofluid volume fraction, were considered. The results are illustrated in the form of streamlines, isotherms, average Nusselt and a spatio-temporal characterization of the mean ferrofluid velocity. From the results presented, we can conclude that the choice of non-Newtonian, pseudoplastic ferrofluid with a low thermal conductivity ratio subjected to a uniform magnetic field proves to be a crucial solution for efficient and stable cooling of heat-generating cylindrical blocks, which will have to be close to the cold walls of the channel.

Computational study on torsional Casson fluid flow through concentric cylinders in a porous medium

The aim of this article is to gain a better knowledge of the non-Newtonian features of Casson fluid flow under torsional motion through two concentric cylinders in a porous medium. This study is crucial because it has the ability to control the flow characteristics of Casson fluids in porous media using rotating cylinders for the optimization of industrial processes. The flow-narrating differential equations are converted into a set of nonlinear differential equations. To obtain numerical results to flow problem, a computational model is developed. Numerical solutions are acquired employing the fourth-order exactness programme (Bvp4c), and findings are validated by comparing them to the Runge-Kutta fourth-order approach. Consequences of various distinct parameters for fluid flow and heat transfer are interpreted in graphical and tabular form. It is found that both fluid velocity and temperature increase with growing inputs of outer angular velocity (0.3≤Ω2≤0.9). Skin friction coefficient (CfsTa) is observed to decline in the case when both cylinders are rotating in same direction (Ω1=0.7andΩ2=0.7) with enhanced inputs of Hartmann number (0.5≤Ha≤2.0), while Nusselt number (Nus) profiles are enhanced with rising inputs of the Forchheimer parameter (0.2≤Fr≤0.8) when both cylinders are rotating in opposite direction (Ω1=0.7andΩ2≤−0.7).