Magnetohydrodynamic Flow Research Articles

Computational study of Jeffrey Hybrid nanofluid flow over on a non-uniformly heated permeable exponentially stretching surface with Arrhenius activation energy and inclined magnetic field

This study delves into the intricate dynamics of magnetohydrodynamic (MHD) flow, investigating the behaviour of a TiO2–Cu/H2O Jeffrey hybrid nanofluid cascading over a porous exponentially stretching surface. Employing MATLAB's bvp4c solver, we address a complex interplay of factors including aligned magnetic fields, radiation effects, non-uniform thermal fluxes, and the influence of Arrhenius activation energy. Our findings reveal a nuanced landscape wherein heightened Jeffrey fluid parameters amplify thermal and concentration gradients, yet diminish heat and mass transfer rates. Interestingly, variations in the Deborah number yield subtle effects, enhancing thermal and concentration profiles while moderating transfer rates. Augmented magnetic and porosity parameters deepen profiles but reduce velocity and transfer rates. Notably, magnetic field alignment reduces velocity while accentuating thermal and concentration gradients. Furthermore, non-uniform thermal fluxes elevate temperatures but restrain heat transfer rates. Activation energy augments concentration profiles distinctly from chemical reaction parameters. The comparison of Jeffrey hybrid nanofluid and its conventional counterpart reveals intriguing disparities: the former exhibits a notable 30 % increase in absolute skin friction while increasing heat transfer rate by 4.5 %. These insights underscore the pragmatic significance of our model for precise prognostication and evaluation across various applications.

Unfolding some numerical solutions for the magnetohydrodynamics Casson–Williamson nanofluid flow over a stretching surface

Abstract This research focuses on exploring the significance of chemical reactions and thermal radiation on the magnetohydrodynamic (MHD) flow of a Casson–Williamson nanofluid (CWNF) over a stretching sheet. The objective is to comprehend how these factors influence the flow and heat transfer. A mathematical model, comprising partial differential equations adjusted into ordinary differential equations (ODEs) via utilizing some transformation. These ODEs are then tackled by MATLAB’s BVP4C method, which is part of the finite difference technique. Results are verified by comparison with existing literature and are depicted visually and in tabular format. Additionally, the study explores the effects of external factors such as magnetic fields and the Lewis number on parameters like Nusselt number, friction factor, and Sherwood number. Furthermore, heat generation in MHD CWNF is analyzed, along with a thorough evaluation of heat transfer near a stretching sheet with a permeable layer. The findings suggest that growing Brownian motion factor (Nb) and thermophoresis coefficient (Nt) enhance the rate of heat transfer, signifying improved heat transfer rates. Similarly, higher Nt values are associated with enhanced Sherwood numbers, indicating better mass transfer. Conversely, higher Nb values lead in lower local Sherwood numbers. Physically, an increase in Brownian motion causes significant displacement of nanofluid particles, boosting their kinetic energy and thereby enhancing heat generation within the boundary layer. It is noted that the Eckert number (Ec) reflects the impact of different Ec values on temperature distribution. As Ec increases, there is a proportional increase in fluid temperature due to frictional heating, which stores heat energy within the fluid. This effect becomes more pronounced for non-linear stretching surfaces, demonstrating the response of the thermal region to viscous dissipation. Viscous dissipation has the potential to enhance convective heat transfer, leading to amplified temperature distribution and thickening of the thermal layer.

Correction: Abbas et al. Analysis of Entropy Generation on Magnetohydrodynamic Flow with Mixed Convection through Porous Media. Energies 2022, 15, 1206

In the original paper [...]

Numerical insights of fractal–fractional modeling of magnetohydrodynamic Casson hybrid nanofluid with heat transfer enhancement

Fractional calculus expands the idea of differentiation to fractional/non‐integer orders of the derivatives. It includes the memory‐dependent and non‐local system's behaviors while fractal–fractional derivatives is the generalization of fractional‐order derivatives which refers to a combination of fractional calculus and fractal geometry. In this article, we have considered the magnetohydrodynamic (MHD) flow of Casson hybrid nanofluid through a vertical open channel with the effect of viscous dissipation and Newtonian heating. The problem is modeled in terms of non‐linear and coupled integer‐order PDEs which is further generalized through fractal–fractional derivative of power law kernel. Due to non‐linearity and complexities, we have adopted the numerical procedure as it is used when the analytical solutions of PDEs are frequently difficult or impossible for complicated situations. We have established the numerical algorithms for both the classical and fractal–fractional‐order model and compared the results. The existence and uniqueness of the model's solution has been shown theoretically. The effect of various embedded parameters on the heat transfer and fluid flow has been simulated and presented through various figures while skin friction and Nusselt number are tabulated. The effect of fractional and fractal parameter is also shown. As the present model is taken for the hybrid nanofluid flow and for the heat transfer applications, we have considered mineral transformer oil as a base fluid while titania and cadmium telluride nanoparticles are dispersed in it. From the results, it is observed that hybrid nanofluid have a better heat transfer enhancement up to 19.71% while the unitary nanofluids are only capable to enhance the heat transfer up to 9%.

Modeling viscous dissipation in MHD boundary layer flow: A two-stage in time and compact in space finite difference approach

It is suggested that an explicit-implicit third-order in-time numerical scheme be used to solve time-dependent partial differential equations (PDEs). A fourth-order compact scheme in space is adopted for discretizing space variables. The work creatively blends a third-order explicit-implicit numerical scheme in time with a fourth-order compact scheme in space to solve time-dependent PDEs. Notably, the proposed numerical scheme demonstrates stability for scalar PDEs and exhibits convergence for both linear and nonlinear PDE systems. In addition, a mathematical model is given for the heat transfer of magnetohydrodynamic (MHD) flow over flat and oscillatory sheets, and the effect of viscous dissipation is also considered. For various governing parameters, features of the flow and heat transfer characteristics are discussed and examined. Some results are verified using an exact solution. We use an explicit-implicit finite difference method guaranteed to be stable and convergent under all conditions to solve the coupled nonlinear partial differential equations that describe this problem. Physical aspects of the problem are discussed in light of the system’s embedded parameters, and numerical and graphical results are presented. To sum up, progress in our knowledge of such systems relies heavily on creating an accurate and efficient numerical scheme for modeling MHD boundary layer flows while considering the influence of viscous dissipation. This study aims to improve the current state of MHD flow simulations and provide a useful resource for engineers and scientists engaged in developing and improving MHD-based technologies.

Comparative study of Hiemenz flow in hybrid Carreau nanofluid (Fe3O4-Cu/kerosene-engine oil): nonlinear effects, Newtonian heating and viscous dissipation

ABSTRACT This study is important because it helps us understand how different factors affect the flow of a special liquid with nanoparticles, giving us useful insights for real-world applications in engineering and technology. This research endeavours to explore and contrast the distinctive characteristics of steady, 2-D magnetohydrodynamic (MHD) and stagnation point (Hiemenz) flow in Carreau hybrid nanofluid {Fe3O4-Cu/kerosene-engine Oil} over a nonlinear stretching-shrinking surface with its counterpart, Carreau nanofluid. Employing the laws of conservation encompassing mass, momentum, energy, and concentration, our methodology probes into the multifaceted effects induced by factors like the suction-injection, viscous dissipation, Newtonian heating, Hiemenz flow, thermophoresis, and Brownian motion. This exploration involves the transformation of governing partial differential equations (PDEs) into a system of ordinary differential equations (ODEs) through similarity transformations. Subsequently, the intricate non-linear ODEs are meticulously solved using the bvp4c technique, an adept MATLAB built-in function, facilitating a comprehensive understanding of the intricate dynamics within the system. In addition, the study considers the Newtonian heating effect and a numerical comparison is performed to verify the results. Using two different types of nanoparticles dispersed in kerosene-engine oil, it was demonstrated that increasing Weissenberg parameter values resulted in significant improvements in thermal conductivity and thermal velocity. A comparison of Carreau nanofluid thermal and concentration velocities with Carreau hybrid nanofluid showed that Carreau nanofluid values are lower (Weissenberg parameter). Higher Biot numbers are associated with reduced temperature velocity and elevated concentration velocity.

A neural network approach to modeling magnetohydrodynamic stagnation point Ree-Eyring flow over a convectively heated stretched surface

ABSTRACT This study investigates the application of artificial intelligence (AI) in fluid dynamics, mainly using a neural network trained by the Levenberg – Marquardt method (NN-BLMM), to model magnetohydrodynamic (MHD) stagnation point Ree – Eyring flow. We focus on this flow over a convectively heated stretched surface by integrating the Cattaneo – Christov heat model. The initial complex nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable similarity variables. A dataset was generated using the Lobatto IIIA numerical solver to analyze the effects of various fluid flow and thermal parameters. The NN-BLMM model was then rigorously evaluated through training, testing, and validation phases and compared with reference data. This ensures the model’s precision and effectiveness. We observe that an increase in the Powell – Eyring fluid parameter notably reduces the fluid’s shear resistance, implying a decrease in viscosity. Concurrently, the heat transfer rate within the fluid medium increases with an increase in the internal heat generation parameter. These findings highlight the robustness of NN-BLMM in simulating complex fluid dynamics, emphasizing AI’s potential to provide a deeper understanding of non-Newtonian fluid behaviors. This research has important implications for industrial applications in which precise control over fluid properties and heat transfer is crucial.

Significance of shape factor on magnetohydrodynamic buoyancy thin film flow of nanofluid over inclined sheet with slip condition: Irreversibility analysis

This work aims to examine the entropy production, heat transport, and dynamics of the unsteady thin film magnetohydrodynamic (MHD) flow of a nanofluid composed of alumina (Al2O3) and water. The fluid flow is seen to pass over an inclined sheet, taking into account the effects of buoyancy force, viscous dissipation, and joule heating. The system of partial differential equations (PDEs) is optimized under the boundary layer assumptions. Appropriate transformations are used to convert the governing partial differential equations (PDEs) and boundary conditions into dimensionless forms. Using MATLAB’s bvp4c code and a local non-similarity technique with up to second-degree truncation, we can obtain the findings of the enhanced model. The effect of multi-shape Al2O3 nanoparticles on flow, heat, and entropy-generating features is also investigated after the calculated results have been successfully aligned with published data. Mixed convection, nanoparticle volume percent, inclination angle, magnetic field intensity, mass suction, Eckert number, and Biot number are only a few of the governing parameters whose effects are graphically shown for selected values. As a result, the local Nusselt number and skin friction coefficient may be calculated. The skin friction and Nusselt number profiles exhibit a decreasing trend as the values of nanoparticle volume fraction ([Formula: see text]) magnetic [Formula: see text] and unsteadiness (A) increase toward mixed convection ([Formula: see text]). On the other hand, Nusselt number profile increases with increasing values of mass suction parameter [Formula: see text] The profiles of entropy generation and Bejan number show an upsurge as the values of the magnetic parameter [Formula: see text] and Brinkman number (Br) increase. Conversely, the entropy generation reduces with an increase in the temperature difference parameter [Formula: see text] and Bejan number increases.

Unsteady magnetohydrodynamic squeezing Darcy-Forchheimer flow of Fe3O4 Casson nanofluid: Impact of heat source/sink and thermal radiation

The paper aims to investigate the unsteady magnetohydrodynamics (MHD) flow with Darcy-Forchheimer effect and heat transportation. The system incorporates a Casson nanofluid (CNF) with heat transfer during melting and slip velocity, influenced by heat source/sink and thermal radiation. The motivation of investigating the current topic comes because of the squeeze flow is of practical physics. The mathematical process involves converting nonlinear partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). The nonlinear ODEs are analytically solved via the Homotopy perturbation method (HPM), while considering the appropriate boundary conditions (BCs). Through a non-dimensional procedure, many dimensionless physical quantities are achieved. The primary results of velocity, temperature profiles, local skin-friction, and the local Nusselt number are shown and analyzed based on several non-dimensional parameters. It is found that the increasing of the radiation factor values, leads to a drop in the velocity and temperature of the CNF, as well as the local skin-friction and Nusselt number. Additionally, the increase of the slip velocity factor results in higher velocity, temperature, and local Nusselt number. Meanwhile, it reduces the local skin-friction.

Series solution of time-fractional mhd viscoelastic model through non-local kernel approach

The study of ramped condition in the context of unsteady incompressible magnetohydrodynamic Casson fluid flow over a moving vertical plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. In this study, Casson fluid is considered unsteady under the influence of magnetic field. The fractional mathematical model is proposed by considering the effect of chemical reaction parameter of the flowing fluid. The governing equations are transformed into the dimensionless form and developed fractional models like Caputo-Fabrizio and Atangana-Baleanu Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for velocity, energy and momentum balances developed in terms of series. MATHCAD software is being used for numerical computations and the physical attributes of material and fractional parameters are discussed. To analyze their behavior clearly, two-dimensional graphical results are plotted for velocity profile and temperature as well. It has been concluded that the fluid’s velocity are reduced for larger values of the fractional parameter and Prandtl number and is maximum for small values of both parameters. Further, the velocity behavior becomes larger for isothermal condition as compared to ramped conditions.

A numerical investigation of the two-dimensional magnetohydrodynamic water-based hybrid nanofluid flow composed of Fe3O4 and Au nanoparticles over a heated surface

Abstract In this research article, the viscous, steady, and incompressible two-dimensional hybrid nanofluid flow composed of Fe3O4 and Au nanoparticles on an extending sheet has been presented. An inclined magnetic field impact is used for evaluating the impacts of various factors in that case. Furthermore, the influences of porosity, Brownian motion, thermophoresis, thermal and space-dependent heat sources, and thermal radiation factors are also used in this work. The numerical analysis is done by using the bvp4c technique. Validation of the present results confirms that the present analysis is valid. The outcomes show that the higher magnetic factor reduces velocity distribution while increasing the frictional force at the surface due to Lorentz forces which oppose the fluid flow. The friction force at the sheet’s surface is higher when the sheet stretches as compared to the case when the sheet shrinks. Increase in the magnetic factor increases the skin friction of sheet’s surface which consequently increases the rate of thermal transmission at the surface along with thermal distribution. The higher values of thermal radiation and thermal-dependent heat source increase the thermal transportation rate of sheet’s surface. Insights from this investigation can improve electronics cooling systems, vital for devices prone to overheating. Optimizing heat transfer with magnetohydrodynamic water-based hybrid nanofluids containing Fe3O4 and Au nanoparticles ensures efficient heat dissipation, enhancing device performance and longevity.

Heat and mass transfer in magnetohydrodynamic boundary layer flow of second-grade nanofluid fluid past inclined stretching permeable surface implanted in a porous medium

ABSTRACT The current study deals with heat and mass transfer mechanisms in a non-Newtonian second-grade nanofluid model. The flow is induced by stretching the surface linearly and making it permeable and inclined at angle α=π/6. The fluid is saturated with a porous medium under transverse magnetic field and suction/injection effects. The proposed problem is in terms of partial differential equations, which are transformed into ordinary differential equations using the stream function formulation. The rigorous solver bvp4 has been used to solve the obtained differential equations. The results are presented in figures and tables and then discussed using physical justification. Graphs depict that the velocity of fluid increases and temperature distribution declines with the intensification of the second-grade fluid parameter at the considered angle of inclination of the stretching plate. It is observed that as the porous medium parameter is intensified, the velocity field declines rapidly. The temperature and concentration increase with increasing thermophoresis parameter. Increasing Brownian motion parameter results in augmentation in temperature and reduction in mass concentration. The current work’s results created with the use of this numerical method are compared with previously published results, which demonstrate great agreement between results, indicating accuracy and validation of the present results.

Constraint-based analysis of heat transport and irreversibility in magnetic nanofluidic thermal systems

Purpose This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems. Design/methodology/approach The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility. Findings This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor. Research limitations/implications Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study. Originality/value This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications. Graphical Abstract

Computational investigation of magnetohydrodynamic convective flow in a trapezoidal cavity with multiple obstacles via finite element analysis

The present research deals with magnetohydrodynamic (MHD) natural convection within a trapezoidal cavity under the influence of inner solid obstacles of different shapes. The cavity includes two horizontal plates and two heated circular cylinders and is subjected to a uniform horizontal magnetic field. The walls of the domain can either be heated or cooled isothermally. The finite element method is used to solve the Oberbeck-Boussinesq equations that govern the fluid flow and heat transfer process. Three different thermal conditions are considered for the horizontal plates: isothermal heating, isothermal cooling, and adiabatic. The investigation explores the impact of varying Rayleigh numbers (Ra = 104–106), Hartmann numbers (Ha = 0–100), and thermal boundary conditions for inner horizontal plates on the flow patterns and heat transfer efficiency. The results indicate that as the Rayleigh number rises and the magnetic field strength diminishes, a noticeable improvement in heat transfer is observed, particularly in cases where the horizontal plates are subjected to cooling. Conversely, the heated inner horizontal plates exhibit less effective energy transport across the considered three configurations. It should be noted that the heat transfer rate for Ra = 106 can be increased more than 5 % when cooled ones will replace the heated inner plates. Whilst a transition between the adiabatic inner plates to cooled ones allows improving the average Nusselt number at the bottom heated wall at about 3 %. Moreover, the convective flow intensity can be described using the kinetic energy, where a growth of the magnetic field strength from 0 till 100 for Ra = 105 decreases the total kinetic energy at 76 times for heated plates, at 100 times for cooled plates and at 92 times for adiabatic plates.

Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints

Abstract Hybrid nanofluid problems are used for augmentation of thermal transportation in various industrial applications. Therefore, the present problem is studied for the heat and mass transportation features of hybrid nanofluid caused by extending surface along with porous media. In this investigation, the authors have emphasized to analyze hybrid nanofluid flow containing diamond and copper nanoparticles on an extending surface. Furthermore, the velocity, temperature, and concentration slip constraints are adopted to examine the flow of fluid. Heat source, chemical reactivity, thermal radiation, Brownian motion and effects are taken into consideration. Nonlinear modeled equations are converted into dimensionless through similarity variables. By adopting the homotopy analysis method, the resulting equations are simulated analytically. The impacts of various emerging factors on the flow profiles (i.e., velocities, temperature, concentration, skin frictions, local Nusselt number, and Sherwood number) are shown using Figures and Tables. The major key findings reveal that the hybrid nanofluid temperature is higher but the concentration is lower for a Brownian diffusivity parameter. Moreover, increment role of heat transport is achieved due to the increment in radiation factor, thermophoresis, Brownian motion factors, and Eckert number. It has also been observed that velocity in x-direction converges in the region − 0.8 ≤ ℏ f ≤ 0.5 -0.8\le {\hslash }_{\text{f}}\le 0.5 , in y-direction velocity is convergent in the zone − 0.6 ≤ ℏ g ≤ 0.35 -0.6\le {\hslash }_{\text{g}}\le 0.35 , while temperature converges in the region − 0.6 ≤ ℏ θ ≤ 0.4 -0.6\le {\hslash }_{\text{θ}}\le 0.4 and concentration converges in the region − 0.5 ≤ ℏ φ ≤ 0.4 -0.5\le {\hslash }_{\text{φ}}\le 0.4 .

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

Influence of Chemical and Radiation on an Unsteady MHD Oscillatory Flow using Artificial Neural Network (ANN)

This paper delves into the intricate interplay between chemical and thermal radiation in the context of an unstable magnetohydrodynamic(MHD) oscillatory flow through a porous medium. The fluid under investigation is presumed to be incompressible, electrically conductive, and radiating with the additional influence of a homogeneous magnetic field applied perpendicular to the channel’s plane. Analytical closedform solutions are derived for the momentum, energy, and concentration equations providing a comprehensive understanding of the system’s behavior. The investigation systematically explores the impact of various flow factors, presenting their effects through graphical representations. The governing partial differential equations (PDE) of the boundary layer are transformed into a set of coupled nonlinear ordinary differential equations (ODE) using a closed-form method. Subsequently, an artificial neural network (ANN) is applied to these ODEs, and the obtained results are validated against numerical simulations. The temperature profiles exhibit oscillatory behavior with changes in the radiation parameter (N), revealing insights into the system’s dynamic response. Furthermore, the paper uncovers that higher heat sources lead to increased temperature profiles. Additionally, concentration profiles demonstrate a decrease with escalating chemical reaction parameters, with a reversal observed as the Schmidt number (Sc) increases. This study highlights the efficacy of an ANN model in providing highly efficient estimates for heat transfer rates from an engineering standpoint. This innovative approach leverages the power of artificial intelligence to enhance our understanding of complex fluid magnetohydrodynamics and porous media flows.

The Okubo–Weiss-type topological criteria in two-dimensional magnetohydrodynamic flows

The Okubo–Weiss (Okubo, Deep-Sea Res., vol. 17, issue 3, 1970, pp. 445–454; Weiss, Physica D, vol. 48, issue 2, 1991, pp. 273–294) criterion has been widely used as a diagnostic tool to divide a two-dimensional (2-D) hydrodynamical flow field into hyperbolic and elliptic regions. This paper considers extension of these ideas to 2-D magnetohydrodynamic (MHD) flows, and presents an Okubo–Weiss-type criterion to parameterize the magnetic field topology in 2-D MHD flows. This ensues via its topological connections with the intrinsic metric properties of the underlying magnetic flux manifold, and is illustrated by recasting the Okubo–Weiss-type criterion via the 2-D MHD stationary generalized Alfvénic state condition to approximate the slow-flow-variation ansatz imposed in its derivation. The Okubo–Weiss-type parameter then turns out to be related to the sign definiteness of the Gaussian curvature of the magnetic flux manifold. A similar formulation becomes possible for 2-D electron MHD flows, by using the generalized magnetic flux framework to incorporate the electron-inertia effects. Numerical simulations of quasi-stationary vortices in 2-D MHD flows in the decaying turbulence regime are then given to demonstrate that the Okubo–Weiss-type criterion is able to separate the MHD flow field into elliptic and hyperbolic field configurations very well.

A semi-analytical solution of the magnetohydrodynamic blood-based ternary hybrid nanofluid flow over a convectively heated bidirectional stretching surface under velocity slip conditions

This work inspects the thermal transportation of the magnetohydrodynamic Casson trihybrid nanofluid flow over a convectively heated bidirectional elongating sheet. The flow is considered as three dimensional passing over the sheet, which is placed in a porous medium. The effects of thermal radiations and space- and thermal-dependent heat sources are used in energy equations, while magnetic effects are used in momentum equations. Appropriate variables have been used to convert the modeled equations into a dimensionless form, which have then been solved using the homotopy analysis method. In this work, it is uncovered that both the primary and secondary velocities are weakened with an upsurge in porosity and magnetic factors. The thermal transportation is augmented with growth in thermal- and space-dependent heat source factors and the thermal Biot number. The convergence of the method used in this work is ensured through ℏ-curves. The results of this investigation have also been compared with the existing literature with a fine agreement among all the results that ensured the validation of the model and method used in this work.

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

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