Magnetohydrodynamic Boundary Layer Research Articles

Significance of heat transfer in a reversible esterification of Arrhenius activation energy with partial slip

The significance of heat transfer during a reversible esterification process in a magnetohydrodynamic boundary layer Casson fluid flow along a vertical stretching plate is examined. The multi-slip conditions are considered in a porous medium. The presence of chemical process requiring an activation energy is considered in the analysis. The study also investigates the hydromagnetic boundary layer Casson fluid flow alongwith partial slip conditions across a vertical stretching plate. The incorporation of multi-slip constraints in a porous medium, alongside magnetic fields and other parameters, highlights its relevance in diverse engineering fields such as thermal engineering, polymerization, and biodiesel industries. Understanding the characteristics of such fluids under complex conditions is vital for optimizing heat and mass transfer in industrial applications, making this investigation timely and valuable. The nonlinear differential set of equations are solved numerically involving Runge Kutta based shooting approach of fourth order and the results are verified with the bvp4c tool and the findings are explored using graphical plots. The predominance of significant factors on flow configurations are analyzed and presented in graphs and tables. A comprehensive analysis is provided on the effects on velocity, concentration, and temperature of diverse parameters such as reaction rate constant, magnetic parameter, suction parameter, mass Grashof number, Prandtl number, Casson parameter, thermal radiation parameter and slip parameters. The tabular representation of the adverse effects of drag coefficient, rate of mass transfer and Nusselt number on flow configurations for various significant parameters is presented. It is inferred that for the case of reversible and irreversible flows, the shear stress rate escalates by 29% when the magnetic parameter elevates from 0.5 to 1.5 and about 35% when the Casson parameter elevates from 0.5 to 1.5. For the suction parameter, the coefficient of drag increased by 27% and 26% for irreversible and reversible flows respectively. When the reaction rate increases from 0.5 to 1.5, the rate of shear stress elevates by 0.5% and 0.02% for irreversible and reversible flows in order. The Nusselt number decreased about 7% and 8% when the magnetic parameter and Casson parameter rises from 0.5 to 1.5 respectively, for irreversible and reversible flows. It is noteworthy that the previous studies are in precise agreement with the present investigation.

Numerical Simulation of MHD Oldroyd-B Fluid with Thermal Radiation and Chemical Reactions Using Chebyshev Wavelets

The study has been carried out to analyze the Magnetohydrodynamic (MHD) boundary layer flow, heat and mass transfer of the two-dimensional viscoelastic Oldroyd-B fluid over a vertical stretching sheet in the presence of thermal radiation and chemical reaction with suction/injection in a steady state. The governing equations of the system are partial differential equations, which then give rise to a set of highly nonlinear coupled ordinary differential equations using similarity transformations. The nonlinearity in the differential equations is dealt with quasilinearization technique. The resultant equations are numerically solved using Chebyshev wavelet collocation method. The effects of magnetic field, radiation, chemical reaction and buoyancy parameters are investigated. The numerical values of local skin friction coefficient, local Nusselt number and local Sherwood number are also tabulated and analyzed. We observe that the increase in buoyancy parameters enhances the velocity profiles and larger values of magnetic field decrease the velocity profiles but increases the temperature and concentration profiles. Error analysis has been done to check the convergence of the numerical scheme.

Magnetohydrodynamic Stagnation Point Flow and Heat Transfer of Casson Fluids Over a Stretching Sheet

This research investigates the effects of heat transfer on the stagnation-point flow of a non-Newtonian Casson fluid in a two-dimensional magnetohydrodynamic (MHD) boundary layer over a stretched sheet, considering thermal radiation impacts. By employing similarity transformations, the governing partial differential equations are transformed into nonlinear ordinary differential equations. The obtained self-similar equations are numerically solved using the Optimal Homotopy Analysis Method (OHAM). The numerical results are graphically represented, showcasing the influence of various parameters on fluid flow and heat transfer characteristics. The study uncovers important dynamics in transport phenomena. Examining and illustrating the effects of dimensionless parameters on velocity, temperature, and concentration profiles reveal significant insights. Moreover, skin friction and Nusselt number results for Casson fluids are analyzed and presented. The findings indicate that the Casson parameter and Hartman number act in opposition to fluid momentum, while the thermal conductivity parameter enhances fluid temperature. Thus, this research provides valuable insights into MHD boundary layer flows of non-Newtonian Casson fluids with thermal radiation effects, and the OHAM solution method proves effective in predicting flow transport properties.

Investigation of the Impact of a Chemical Reaction on the Magnetohydrodynamic Boundary Layer Flow of a Radiative Maxwell Fluid over a Stretching Sheet Containing Nanoparticles Employing the Variational Iteration Method

The heat and mass transmission properties of a 2-D electrically conducting incompressible Maxwell fluid past a stretched sheet were studied under thermal radiation, heat generation/absorption, and chemical reactions. This issue has a variety of real-world applications, most notably polymer extrusion and metal thinning. The transport equations account for both Brownian motion and thermophoresis during chemical reactions. Using similarity variables allows for non-dimensionalization of the stream's PDEs and associated boundary conditions. The resulting modified ODEs are solved with the variational iteration approach. The impact of embedded thermo-physical variables on velocity, temperature, and concentration was studied quantitatively. When compared to the RK-Fehlberg approach, the findings are very similar. Raising the chemical reaction parameter narrows the concentration distribution, whereas increasing the temperature increases thermal radiation's impact. As the amount of N_t increases, the thickness of the boundary layer develops, causing the surface temperature to rise, resulting in a temperature increase.

Heat and mass transfer effects on an unsteady MHD boundary layer flow of fractionalized fluid

This research investigates the transient magnetohydrodynamic (MHD) flow of a non-integer Maxwell fluid over a vertical plate, taking into account the effect of diffusion-thermo and parameter of heat absorption. The fractional derivative Caputo-Fabrizio is employed to model the problem. Using the Laplace integral transform technique, we solve the dimensionless governing equations to obtain the profiles of velocity, concentration, and temperature, which are then presented in graphical form for easy comparison and interpretation. The influence of several parameters—specifically, the fractional parameter and heat absorption is thoroughly analyzed and illustrated through a series of graphical representations. Furthermore, a comparison between traditional as well as fractionalized velocity fields is provided. The results show that chemical reactions and magnetic fields reduce the velocity profile, while diffusion-thermo and mass Grashof number increase the fluid velocity.

Computation of SWCNT/MWCNT-doped thermo-magnetic nano-blood boundary layer flow with non-Darcy, chemical reaction, viscous heating and Joule dissipation effects

CNTs have been shown to exhibit exceptional electrical and thermal conductivities, chemical and mechanical stability and physiochemical reliability in wide-ranging applications covering biomedicine, energy and aerospace. Motivated by emerging applications in nano-drug delivery in medicine and radiative ablation therapy, a steady-state mathematical model is established for magnetohydrodynamic boundary-layer transport of chemically reactive carbon nanotubes (CNTs)-doped electrically conducting blood along a porous stretching wall of a blood vessel. Multiple and single walls CNTs are considered using the model developed by Xue (2005). Heat generation, radiative flux, wall mass (concentration) slip, viscous heating and Joule magnetic dissipation are incorporated. Chemical reaction effects are addressed utilizing homogenous first-order model. The Darcy-Forchheimer drag force model is utilized for bulk matrix and inertial drag effects in the porous medium. Radiative heat-transport is studied considering Rosseland's diffusion model. The governing partial differential conservation equations for mass, momentum, energy and species are formulated in a two-dimensional Cartesian coordinate system with allied wall and free-stream boundary conditions. Via scaling transformations, a nonlinear boundary value problem is derived. Numerical computations are achieved through bvp4c scheme. The impact of selected parameters on dimensionless quantities (velocity, temperature, concentration, skin friction, local Nusselt and Sherwood numbers) are computed and elaborated through tables and graphs. A good correlation of the numerical solutions with earlier simpler models from the literature is included. The simulations show that with augmentation in Hartmann magnetic number and Forchheimer inertial drag number, significant damping in the nano-doped blood flow is produced for both SWCNTs and MWCNTs. Temperature is elevated with increment in dissipation effect i. e. Eckert number. Higher values of mass (solutal) slip parameter induce a depletion in the concentration. Nusselt number i. e. heat transfer rate to the blood vessel wall is improved with greater values of solid volume fraction for both CNTs. The present model is relevant to radiative ablation therapy combined with nano-medical treatments in blood vessels wherein constant mechanical loading via blood pressure and flow can elevate internal stresses (circumferential wall stress and endothelial shear stress) and induce morphological alterations in blood vessel wall (stretching) and endothelium in conjunction with biochemical reactions.

Unraveling heat transfer mechanisms in MoS 2/SO−water nanofluid for flow over a stretching cylinder

Nanofluids, advanced heat transfer fluids with improved thermophysical properties, have proven effective in enhancing the efficiency of various devices. Widely applied in electronic devices and automotive industry, consisting of nanoparticles and base fluids, serve as efficient coolants to optimize heat transfer performance. This article investigates the physical effects of magnetohydrodynamic (MHD) boundary layer flow of H 2 O base fluid over a stretched cylinder subjected to heat generation and thermal radiation. The present nanofluid investigation incorporate Mo S 2 nanoparticles into a base fluid mixture of SO / H 2 O . The mathematical model, employing similarity transformations, is developed, leading to the formulation of similarity equations. Simulations are conducted using MATLAB’s bvp4c solver to analyze the resulting flow patterns. Simulation results for various physical parameters demonstrate that the inclusion of hybrid nanoparticles in the fluid mixture significantly enhances heat transfer compared to the conventional nanofluids. Our finding highlights the necessity of considering hybrid nanoparticles over single-type counterparts for creating efficient thermal systems. Moreover, investigation underscores the vital role of hybrid nanofluids in fluid transmission, showcasing their ability to achieve higher temperature distribution.

Numerical simulation for MHD slip flow with heat transfer over a stretching bullet‐shaped object

AbstractThis paper investigates magnetohydrodynamic (MHD) boundary layer slip flow with heat transfer over a bullet shaped object. The study addresses a significant problem in fluid dynamics and heat transport with applications in various engineering and industrial domains, including aerospace, material processing, and energy systems. The governing equations are resolved using the bvp4c, an inbuilt MATLAB tool, and the arithmetic computation for the momentum and thermotic equations are executed. The results are exhibited graphically. Numerical outcomes are graphically depicted with the aid of velocity and temperature profiles for several model variables. The achieved results exhibit a promising agreement with the previously established findings available in the open literature. The heat transfer processes and fluid flow are remarkably influenced by means of the ratio of surface thickness and stretching potential. The results obtained designated that the Mixed convection parameter λ increases momentum BL thickness, whereas the temperature profile diminishes. Furthermore, momentum and temperature profile improve for surface thickness parameter . The current investigation highlights the potential utility of heat transport rate and friction factor in the industrial divisions for regulating cooling rates and enhancing the quality of end products.

An analytical study on the influence of magnetic field-dependent viscosity on viscous and ohmic dissipative second-grade fluid boundary layers

This article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Magnetohydrodynamics flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate

In this work, the unsteady magnetohydrodynamics boundary layer flow and heat transfer of novel generalized Kelvin–Voigt viscoelastic nanofluids over a moving plate are investigated. The classical Kelvin–Voigt constitutive relation is generalized to incorporate a time-fractional derivative to characterize the fluid behavior, which is proved to be of significance and physically justified. The newly developed fractional Kelvin–Voigt constitutive correlation and a dual-phase-lagging constitutive equation are applied to the momentum and energy equations, respectively, for a nanofluid model over a moving plate. The formulated integrodifferential velocity and thermal boundary layer equations are solved using the finite difference method together with a fast algorithm, which reduces the consumed central processing unit time significantly. Several numerical examples are presented to illustrate the influence of the critical parameters on the nanofluid motion and thermal characteristics. Compared to the fractional Maxwell nanofluid model, the velocity boundary layer for the fractional Kelvin–Voigt nanofluid model is thinner. Although the fractional indexes show similar effects on the velocity boundary layer, the impacts of the relaxation parameters are in contrast. This work provides valuable insights into the feasibility of using the fractional Kelvin–Voigt viscoelastic model to depict the fluid flow and heat transfer characteristics of nanofluids.

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.

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.

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.

Influence of Nanofluids on Boundary Layer Flow over an Inclined Stretching Sheet in a Porous Media along with Magnetic Field

The current study intends to analyse the magnetohydrodynamics boundary layer flow of a water-based nanofluid of Silver, Copper and Ferrous Ferric Oxide nanoparticles over a Permeable inclined stretched sheet in a porous media. A similarity transformation is utilized to convert the governing partial differential equations into non-dimensional, non-linear ordinary differential equations. The Keller box finite difference implicit approach is then applied to solve these nonlinear equations numerically. The impacts of several parameters, namely, inclination parameter, magnetic parameter, Soret Number, Eckertnumber and nano particles volume fractionon velocity, temperature and nanoparticle concentration are explored.

UTLIZATION OF GENERALIZED HEAT FLUX MODEL ON THERMAL TRANSPORT OF POWELL-EYRING MODEL VIA OHAM WITH HEAT GENEARTION ASPECTS

The focus of this work is on the flow of a spinning Powell-Eyring nanofluid in the boundary layer in three dimensions using magnetohydrodynamics (MHD). The research simulates mass transfer processes and heat transfer processes using non-Fick's mass flux theory and non-Fourier heat flux theory, respectively. Heat transport phenomena are analyzed by the integration of non-linear heat generation/absorption and thermal radiation properties. The boundary layer method is employed to solve a system of nonlinear partial differential equations (PDE) in the mathematical formulation. These equations are converted into nonlinear ordinary differential equations (ODES), and then the optimal OHAM with convergence control parameters is used to solve them. The impact of various physical movement circumstances on concentration and temperature profiles is visually represented through the generation of diagrams. This study provides important new understandings for both applied and scholarly research on complex heat transfer and fluid dynamics mechanisms in the context of three-dimensional MHD boundary layer flows of rotating Powell-Eyring nanofluids.

Insight into the dynamics of slip and radiative effect on magnetohydrodynamic flow of hybrid ferroparticles over a porous deformable sheet

AbstractIn the present work, we explored the magnetohydrodynamic boundary layer flow in the presence of pressure gradient across a flat plate. The effects of the slip velocity conditions, thermal Radiation the addition of hybrid Ferroparticles (i.e., a mixture of two types of magnetic nanoparticles for example, (magnetite () and cobalt ferrite ()) in base fluid ( ) and Porous wall (suction/ injection) are also considered in this study. Basic partial differential equations are transformed into nonlinear ordinary differential equations using the appropriate similarity transformations. Then, this equation was treated numerically by using the Runge–Kutta–Fehlberg 4th–5th order method with the shooting technique and analytically via an efficient method called the Generalized Decomposition Method. The effects of various physical parameters on the velocity and temperature profiles are shown graphically. It is found that the incorporation of hybrid nanoparticles demonstrates a relatively substantial impact on the behavior of dynamic and thermal field; outperforming both non‐hybrid nanoparticles and regular fluid in terms of speed and temperature enhancement. The slip and permeability parameters significantly alter the flow structure. The positive values of the slip and permeability parameters enhance the flow velocity and reduce the temperature, leading to the desired flow behavior. Conversely, adopting negative values of these parameters reverses the effect. Furthermore, the radiation parameter enhances the temperature distribution. Additionally, the boundary layer separation tends to disappear with the increase in the magnetic parameter. The results obtained clearly show the accuracy of the proposed method and also indicate an excellent agreement between analytical and numerical data.

Integrated intelligence of inverse multiquadric radial base neuro‐evolution for radiative MHD Prandtl–Eyring fluid flow model with convective heating

AbstractIn this communication, a new stochastic numerical paradigm is introduced for thorough scrutinization of the magnetohydrodynamic (MHD) boundary layer flow of Prandtl–Eyring fluidic model along a stretched sheet impact on thermal radiation as well as convective heating scenarios by exploiting the accurate approximation knacks of ANNs (artificial‐neural‐networks) modeling by using the inverse multiquadric (IMQ) function optimized/trained with well‐reputed global search with genetic algorithms (GAs) and local search efficacy of sequential quadratic programming (SQP), that is, ANNs‐IMQ‐GA‐SQP. The mathematical model of the Prandtl–Eyring fluid flow is portrayed in the form of PDEs and then converted in the form of a nonlinear system of ODEs by utilizing suitable similarity transformation to calculate/analyze the solution dynamics. The kinematic and thermodynamic properties of MHD Prandtl–Eyring fluid flow are examined/observed by varying the sundry physical parameters. The obtained intelligent computing designed solver‐based numerical results are consistently found in good agreement with reference results obtained through the Adams numerical technique. First and second‐order cumulant‐based statistical assessments are extensively exploited to endorse trustily the efficacy of ANNs‐IMQ‐GA‐SQP solver based on exhaustive simulations for the Prandtl–Eyring fluidic system.

Analysis of magnetohydrodynamic laminar boundary layer flow, heat, and mass transfer of nanofluids on a moving surface with thermal radiation via Bernoulli wavelets technique

This study investigates the nanofluid’s magnetohydrodynamic boundary layer flow (BLF) in the presence of thermal radiation using the Bernoulli wavelet collocation method (BWCM). The governing nonlinear partial differential equations (PDEs) are transformed into nonlinear coupled ordinary differential equations (ODEs) using the appropriate similarity transformations. The obtained ODEs are then transformed into a nonlinear system of algebraic equations using BWCM. By contrasting the BWCM with the NDSolve Mathematica command and the Haar wavelet method, the BWCM's validity is examined. The influence of the physical parameters on temperature, concentration, velocity, mass, and heat transfer rates are discussed through tables and graphs. It was found that the Prandtl number, thermophoresis parameter, Brownian motion parameter, radiation parameter, and Lewis number do not influence the skin friction coefficient.

An MHD boundary layer flow of Casson fluid due to a moving wedge analyzed by the Bernoulli wavelet method

AbstractThe current study adopts a Bernoulli wavelet technique to explore the magnetohydrodynamic (MHD) boundary layer flow of a Casson fluid through a wedge. A nanofluid across a wedge has been investigated for its stable laminar MHD flow, heat, and mass transport characteristics. By choosing worthwhile non‐dimensional parameters, the governing boundary layer equation is reformed into a dimensionless Falkner–Skan equation. The consequent nonlinear equation is addressed via the Bernoulli wavelet method. For a range of different values of the physical parameters, the nature of the boundary layer flow is visually observed. Fluid velocity rises with rise in the values of Casson parameter, wedge parameter, and magnetic parameter. Local wall skin friction increases with increase in wedge parameter and magnetic parameter values. To ensure the accuracy of the findings, local wall skin friction is estimated and tested with other techniques that are already reported in the existing research.

Local existence of solutions to the 2D MHD boundary layer equations without monotonicity in Sobolev space

<abstract><p>In this work, we investigated the local existence of the solutions to the 2D magnetohy-drodynamic (MHD) boundary layer equations on the half plane by energy methods in weighted Sobolev space. Compared to the existence of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays an important role, we used the initial tangential magnetic field with a lower bound $ \delta > 0 $ instead of the monotonicity condition of the tangential velocity.</p></abstract>