Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Physical insight into thermal analysis of magnetohydrodynamic stagnation point flow of micropolar nanofluid across a flexible surface equipped with porous medium and Fourier and Fick's law

Nanofluids represent a novel heat transfer liquid, making them an efficient medium for enhancing energy transmission. Nevertheless, significant knowledge gaps still exist concerning current strategies for improving heat transfer in nanofluids, underscoring the necessity for comprehensive research on these fluid systems. Therefore, this study considered theoretical analysis retrieves the influence of radiative two-dimensional stagnation point flow of second-grade micropolar fluid flow about an elongated channel surface implanted in porous media with magnetic effect, and modified heat and mass flux is under consideration. The major novel effect of the current study is to analyze the activation energy and thermal aspect of the system in the presence of nonlinear radiation effects that are considered in the revised mathematical framework by utilizing the boundary layer theory. The resulting set of coupled partial differential equations is further reduced and transformed into a dimensionless system of ordinary differential equations through appropriate scaling invariants. We initiate the RKF-45 investigation scheme to numerically analyze the transformed dimensionless system, considering relevant parameters. The computational algorithm is implemented using MATLAB programming syntax. Plotted visuals are revealed for leading parameters against pertinent flow profiles graphically and with numerical data. Additionally, the convergence analysis of the numerical results for various flow profiles of the fluids were compared to establish the authenticity of the proposed flow problem. These research findings play a significant role in controlling heat transfer rates and fluid velocities in diverse manufacturing processes and industrial applications, ultimately aiding in achieving the desired product quality.     

Significance of heat source/sink on the radiative flow of Cross nanofluid across an exponentially stretching surface towards a stagnation point with chemical reaction

A numerical review on magnetohydrodynamics radiative motion of Cross nanofluid across an exponentially stretchable surface near stagnation point with varying heat source/sink is addressed. Brownian movement and thermophoretic impacts are assumed. The governing equations for this study are first altered as a system of ordinary differential equations by similarity transformation. With an aid of the Runge–Kutta 4th order mechanism together with the shooting procedure, the impacts of several pertinent parameters including chemical reaction on regular profiles (velocity, temperature, and concentration) are explicated. The consequences of the same parameters on surface drag force, transfer rates of heat, and mass are visualized in tables. From the analysis, it was noticed that the magnetic field parameter enhances the temperature and decreases the velocity of the Cross nanofluid. Also, fluid temperature is an increasing function with thermal radiation and nonuniform heat source/sink. The rate of heat transfer is increased with thermophoresis and diminished with Brownian motion. Sherwood's number is diminished with Brownian motion but it was boosted up with thermophoresis. The present results are compared with published results and those are in agreement.     

MHD stagnation point flow of a Maxwell nanofluid over a shrinking sheet (multiple solution)

In the current study, a realistic approach is used to investigate the MHD stagnation point flow of a Maxwell nanofluid past a shrinking sheet with a chemical reaction. First, the flow model is made non dimensionalized via an appropriate transformation. The non dimensionalized equations are numerically tackled by adopting the bvp4c technique. It is also analyzed that the dual solutions are obtained for a particular choice of shrinking parameter. A detailed analysis of the impact of several parameters on the velocity field, temperature distribution, and concentration distribution is carried out graphically. The computed result shows that the first solution significantly increases for higher values of the magnetic parameter, whereas the second solution decreases. Furthermore, it is noted that the first and second solutions decreases for the relaxation parameter. The physical quantities are observed graphically. It is exhibited that the Nusselt number shows a decreasing behavior for the both solutions via relaxation parameter.     

Effect of thermophoresis and Brownian motion on the melting heat transfer of a Jeffrey fluid near a stagnation point towards a stretching surface: Buongiorno's model

This analysis intends to address the coupled effect of phase change heat transfer, thermal radiation, and viscous heating on the MHD flow of an incompressible chemically reactive nanofluid in the vicinity of the stagnation point toward the stretching surface, taking a Jeffrey fluid as the base fluid. Convergent analytical solutions for the nonlinear boundary layer equations are obtained by the successive application of scaling variables and the highly efficacious homotopy analysis method. Error analysis is implemented to endorse the convergence of the solutions. Through parametric examination, influence of various physical parameters occurring in analysis of the profiles of velocity, temperature, and nanoparticle concentration, coefficient of surface drag, rates of mass and heat transfer is explored pictorially. The Deborah number and the melting parameter are found to enhance velocity, and the associated momentum boundary layers are thicker, whereas the magnetic field depreciates the flow rate. Temperature is observed to enhance with the thermophoresis parameter, Prandtl number and Eckert number, whereas a reduction is seen with the thermal radiation parameter and Brownian motion parameter. Nanoparticle concentration is depleted by the chemical reaction parameter, the thermophoresis parameter, and the Lewis number.     

Stagnation‐point flow of Maxwell fluid with magnetic field and radiation effects

The effect of heat transfer on the steady two‐dimensional stagnation point flow of a Maxwell fluid over a stretching sheet is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The radiation effect in the energy equation is taken into account. The arising nonlinear problem is solved by a homotopy analysis method (HAM). Convergence of the series solutions is checked. The values of skin friction coefficient and local Nusselt number have been computed and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20385     

Transport of thermal energy in the magnetohydrodynamic oblique stagnation point flow in a hybrid nanofluid with nanoparticle shape effect

In the present paper, the augmented heat characteristics of a hybrid nanofluid which is a blend of Al₂O₃ (alumina) and Ag (silver) in the host hybrid fluid (C₂H₆O₂-H₂O) (50%–50%) impinging obliquely on an elastic surface with magnetic lines of force are investigated. The properties of the nanofluid are assessed through the computational solutions established with the aid of the popular Runge–Kutta–Fehlberg fifth-order (RKF 5) numerical technique. Outputs of the analysis reveal that the rate of thermal energy transport in the hybrid (mono) nanofluid is enhanced by 11.5% (5.8%) by using blade-shaped nanoparticles in comparison to that of the spherical particles. Stream contours of both nanofluids are inclined to the left (right) of the stagnation-point for positive (negative) values of the stagnation flow parameter.     

Impact of the Cattaneo‐Christov thermal and solutal diffusion models on the stagnation point slip flow of Walters' B nanofluid past an electromagnetic sheet

The present study investigates the effect of Cattaneo‐Christov thermal and solutal diffusion on the stagnation point flow of Walters' B nanofluid past an electromagnetic sheet subject to velocity, thermal, and solutal slips. The study analyzed the role of electromagnetic fields. In addition, the authors introduced the heat transfer aspect due to Brownian motion and thermophoretic force. The numerical solution of the transformed governing equations employed the spectral local linearization method. Comparisons showed an excellent agreement with the numerical data presented in previous notable works. The study reveals that the developed electromagnetic field due to the arrangement of the sheet causes accelerated fluid motion, and diminution of nondimensional temperature and concentration. In addition, augmented velocity, thermal, and solutal slips develop the corresponding descending boundary layers. The augmented short memory coefficient enhances the skin friction coefficient. The Cattaneo‐Christov thermal and solutal diffusion upsurge the heat and mass transfer rates from the electromagnetic sheet, respectively.     

Tangent hyperbolic nanofluid with mixed convection flow: An application of improved Fourier and Fick's diffusion model

This article presents a tangent hyperbolic fluid with the effect of the combination of forced and natural convection flow of nanoparticle past a bidirectional extending surface. Modified Fick's and Fourier's diffusion theories are incorporated into concentration and energy equations, respectively. Convective boundary conditions and second‐order slip flow are taken in the boundary condition. Nonlinear partial differential equations result after boundary layer approximations of the mathematical formulation of the flow problem. Nonlinear high order ordinary differential equations (ODEs) are formed by applying similarity transformation on the nonlinear partial differential equations. The transformed equations are solved with the bvp4c algorithm from Matlab. The numerical solution of ODEs was obtained and the effect of interesting parameters, dimensionless velocity component along x‐ and y‐axis, temperature, and concentration particle, Re_x, Re_y, , and , were presented through tables and graphs and discussed thoroughly. The results indicated that a decrease in velocity along with the y‐axis results from the increasing behavior of S, M, and n. Decrease in both temperature and concentration results in an increase of but their elongation is a result of increase in Bi. An increase in concentration results in decrease of N and S but a decrease in concentration results in the widening of Sc, Nb, and . Furthermore, enlargement of and results in increase of and modules and elongation of both and results in increase of and (Sc and Nb), respectively. A comparison with previously published literature was performed and a good agreement was found.     

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface.     

Influence of heat transfer on the nonorthogonal stagnation point flow of a third‐order fluid towards a stretching surface

The present article looks at the theoretical analysis of a steady stagnation‐point flow with heat transfer of a third‐order fluid towards a stretching surface. The formulation of the problem has been carried out for a third order fluid and constructed partial differential equations are rehabilitated into ordinary differential equations. The consequential ordinary differential equations are solved analytically using the homotopy analysis method (HAM). Graphical illustrations are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients and heat flux are computed and presented through tables. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21042     

Mixed convection stagnation point flow and heat transfer of Cu‐water nanofluids towards a shrinking sheet

This work is focused on numerical simulations of mixed convection stagnation point flow and heat transfer of Cu‐water nanofluids impinging normally towards a shrinking sheet. Similarity transformation technique is adopted to obtain the self‐ similar ordinary differential equations and then solved numerically using symbolic software MATHEMATICA. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed through graphs and tables. Both cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21037 2000 Mathematics Subject Classification : 76M20, 76W05     

Bioconvective Casson nanofluid flow toward stagnation point in non-Darcy porous medium with buoyancy effects,chemical reaction,and thermal radiation

The emphasis on non-Newtonian fluid encountered in biomedical, pharmaceuticals, mining, food, chemical, and plastics industries and in noticeably enormous diverse industrial applications influenced this article. This study is accomplished in a non-Darcy porous stretching surface to investigate the stagnation point of bioconvective Casson nanofluid. Chemical reaction, applied consistent magnetic field, radiative heat transfer, and buoyancy force consequences are studied for numerical examination. Composed of nonlinear partial differential equations for the above presumptions and reforming them into ordinary differential equations by means of compatible transformations are enforced. Adopting the fifth order Runge–Kutta Felhberg method with the shooting technique obtained a numerical solution. Obtained solutions are authenticated by comparing previous solutions. The major finding includes the reduction of the Casson parameter on the skin friction coefficient.     

OHAM simulation of 3D transverse magnetic field in rotating flow of Maxwell nanofluid over a stretching sheet with chemical reaction and heat source/sink

In this article, we investigate the heat transfer characteristics of a Maxwell nanofluid along a stretching sheet with transverse magnetic field, considering the presence of heat source/sink and chemical reaction. We consider appropriate similarity transformation for transforming the governing nonlinear equations into nondimensional highly nonlinear coupled ordinary differential equations. The optimal homotopy analysis method is utilized for solving the resultant-coupled equations. The impact of all sundry parameters, like, Deborah number, Prandtl number, magnetic parameter, thermophoresis, rotation parameter, chemical reaction, velocity slip, Schmidt number, Brownian motion parameter, heat sources per sink, Biot number, and Eckert number, on the temperature, velocity, and concentration fields is reported, analyzed, and described through graphs and tables. It is noticed that higher values of magnetic parameter and Deborah number reduce the horizontal velocity field. Furthermore, it is observed that the Biot number and heat source/sink parameter enhance the temperature distribution.     

Aspects of second-order velocity slip and radiation absorption on hydromagnetic stagnation point flow of Jeffrey fluid with chemical reaction

The present article describes the magnetohydrodynamic flow of a moving Jeffrey fluid along a convectively heated porous stretching surface with second-order velocity slip and radiation absorption effects. Furthermore, chemical reactions and viscous dissipation impacts are also taken into account. The governing equations are converted into dimensionless ordinary differential equations (ODEs) using appropriate similarity transformations. The highly nonlinear ODEs are solved numerically by employing a shooting technique based on the Runge–Kutta Cash–Karp formula. The figures are used to study the variations in temperature, velocity, and concentration profiles for several physical factors. The numerical values of the local skin friction, Sherwood number, and Nusselt number are explained and shown in tables. The analysis reveals that the velocity profile is enhanced for amplifying values of velocity ratio parameter and first-order velocity slip parameter. However, the temperature profile of Jeffrey nanofluid is highlighted w.r.t. Eckert number and radiation absorption parameter. This study may find significant applications in polymer production, food processing, instrumentation, combustion modeling, catalytic chemical reactors, and so on.     

Unsteady MHD Stagnation‐Point Flow Toward a Shrinking Sheet with Thermal Radiation and Slip Effects

The problem of an unsteady magnetohydrodynamic stagnation point flow of an incompressible viscous fluid over a shrinking sheet is discussed in the presence of thermal radiation and boundary slip, which has not been documented to date in the literature. The governing boundary‐layer equations are transformed to high order nonlinear and ordinary differential equations by similarity transformations and then solved numerically. The effects of magnetic parameter, unsteadiness parameter, radiation parameter, velocity, and thermal slip parameters on velocity and temperature are analyzed and discussed. It is found that dual solutions of both velocity and temperature fields exist for negative values of the velocity ratio parameter. The results indicate that dual solution domains of velocity and temperature expand as the unsteadiness parameter increases.     

Impact of the magnetic dipole on stagnation point flow of ferromagnetic Walters-B liquid: A passive control approach with Buongiorno's model

The properties of ferromagnetic fluids make them suitable for a wide range of applications, including loudspeakers, magnetic resonance imaging, computer hard drives, magnetic drug delivery, and magnetic hyperthermia. Owing to all such potential applications, the present research work is established to explain the stagnation point flow, heat, and mass transfer of Walters-B liquid in the presence of magnetic dipole, Brownian diffusion, and thermophoresis. To control the nanoparticles concentration at the surface, a passive control condition is employed. Using suitable similarity transformations, the governing equations are converted into nonlinear ordinary differential equations. Noticeable behavior of significant parameters on flow fields is studied graphically. The significant outcomes of the present study are that the increased values of viscoelastic parameter decline the velocity but an inverse trend is seen in heat transfer. The increased values of the Brownian motion parameter decline the heat transfer but a contrary trend is seen for augmented values of the thermophoresis parameter. The heat transfer rate is increased for rising values of radiation parameter and Biot number. The upward values of the thermophoresis parameter decline the rate of mass transfer. The escalating values of ferromagnetic interaction and velocity ratio parameters improve the skin friction.     

Mixed convection of transient MHD stagnation point flow over a stretching sheet with quadratic convection and thermal radiation

This study investigates the influence of quadratic (nonlinear) convection in transient magnetohydrodynamic (MHD) combined convection over a two-dimensional stretching sheet. It explores the effects of thermal radiation, suction, and heat sources or sinks. The Crank–Nicholson implicit finite difference method is employed for numerical computations. The significance lies in considering secondary convection, which is crucial in understanding nonlinear convective effects affecting flow and heat transfer properties. The study aims to advance our comprehension of how secondary convection impacts the overall system behavior. Through numerical calculations validated against existing literature, strong agreement is demonstrated. The study evaluates secondary convection effects, magnetic, buoyancy, gravitational parameters, Prandtl number, and radiation parameters. Notably, strong quadratic convection alters flow patterns, affecting velocity and temperature profiles. Moreover, it is observed that when increasing the nonlinear (quadratic) convective factors, the temperature profile increases for $$ and decreases for $$. The prevalence of nonlinear or second-order convection highlights magnetic dominance. In essence, this research enhances our understanding of complex convection interactions in MHD flow, shedding light on the role of secondary convection in shaping system behavior.     

Thermal and solutal Marangoni stagnation point Casson fluid flow over a stretching sheet in the presence of radiation,Soret and Dofour effect with chemical reaction

The Marangoni flow is involved with microgravity and earth gravity, which causes undesirable effects in crystal growth experiments. Crystal growth experiments were designed in such a manner so as to appraise MIR (space station), which is one of the best platforms for protein crystallization and radiation experiments. In this article, a model is proposed with a stagnation point and a Casson fluid flow at the interface of the plate in the presence of Marangoni convection influenced by a magnetic field and chemical reaction. Furthermore, it is considered that both temperature and concentration surface tension vary linearly with the interface. It is important to choose similarity transformations for implementing nonlinear differential equations into linear ordinary differential equations. We solved the system of differential equations using fourth order Range‐Kutta method with suitable shooting techniques, and the results are displayed through graphs. A comparison is made with the earlier existing literature, and it shows a very good agreement. The results and a detailed discussion of velocity, temperature, and concentration have been shown graphically. The favorable and unfavorable buoyancy force to Marangoni flow, the features of temperature and concentration field, have been investigated.     

Features of Cattaneo‐Christov heat flux model for Stagnation point flow of a Jeffrey fluid impinging over a stretching sheet: A numerical study

The present work focuses on a two‐dimensional steady incompressible stagnation point flow of a Jeffery fluid over a stretching sheet. The Cattaneo‐Christov heat flux model is incorporated into this study. Simulation is conducted via the Runge‐Kutta fourth‐order cum shooting method for the transformed system of nonlinear equations. The influence of the governing parameters on the dimensionless velocity, temperature, skin friction, streamlines, and isotherms is incorporated. A significant outcome of the current investigation is that an increase in the relaxation time parameter uplifts temperature; however, a gradual decrease is observed in the velocity field. Another important outcome of the present analysis is that the momentum boundary layer augments due to an increase in the Deborah number; however, a decrease is observed in the temperature. Furthermore, it is also observed that the skin friction coefficient escalates with an increase in the relaxation time parameter for the assisting flow, but a reverse trend is observed for the opposing flow.