Characteristics of MHD three-dimensional flow of nanofluid over a permeable stretching porous sheet

The aim of the present work is to focus on heat and mass transfer characteristics of the magnetohydrodynamic three-dimensional flow of nanofluid over a permeable stretching porous sheet. The significance of this study is the consideration of copper-based and aluminum oxide-based nanofluids. The physical parameters like a chemical reaction, Soret effect, radiation, and heat generation, and radiation absorption being involved in this examination are novel. The nonlinear partial differential equations are transformed into ordinary differential equations by adopting suitable similarity transformations. The numerical solutions are obtained by applying the Runge–Kutta method of fourth-order with the Shooting technique using MATLAB. The results obtained are presented through graphs and tables for various parameters. A comparison with published results has been done to validate the methodology and found good coincidence. It is claimed that the increase in heat generation parameters results in increasing the temperature. With an increase in the Soret effect, the skin friction coefficient along x-axis increases and skin friction coefficient along the y-axis, Nusselt number and Sherwood number decrease.     

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.     

Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption

This work is focused on steady flow and heat transfer in a porous medium saturated with a Sisko nanofluid (non‐Newtonian power‐law) over a nonlinearly stretching sheet in the presence of heat generation/absorption. Nonlinear PDEs are transformed into a system of coupled nonlinear ODEs with related boundary conditions using similarity transformation. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method (RKF45) with Maple 14.0 software. The solutions depend on the power‐law index n and the effect of pertinent parameter such as the Brownian motion parameter, thermophoresis parameter, Lewis number, the permeability, and the heat generation/absorption on the dimensionless velocity, temperature, and nanoparticles volume fraction and also on the skin friction, local Nusselt, and Sherwood numbers are produced for values of the influence parameter. A rapprochement of the numerical results of the actual study with formerly published data detected an excellent agreement.     

Stagnation point flow and heat transfer over a stretching/shrinking sheet in a porous medium

The steady stagnation point flow and heat transfer over a shrinking sheet in a porous medium is studied. A similarity transformation is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the Keller-box method. The behavior of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. The results indicate that dual solutions exist for the shrinking case.     

Influence of Hall current effect on hybrid nanofluid flow over a slender stretching sheet with zero nanoparticle flux

The present article explores steady, incompressible, and electrically conducting viscous hybrid-nanofluid flow through an impermeable slender stretching sheet. We have opted for water (H₂O) as base fluid and two nanoparticles namely Al₂O₃ and graphene for the hybrid-nanofluid. The consequence of nonuniform magnetic field and Hall current is accounted for in the flow distribution. Zero mass-flux boundary conditions have been included here. The leading partial differential equations of the acknowledged model revise to similarity variables. Next, the subsequent equations are numerically solved by a shooting scheme based on Runge–Kutta fourth-order procedure. The consequences of boosting flow factors on transport systems are achieved accurately through the requisite figures and charts. Concentration outlines are dual in nature when the wall-thickness factor intensifies. The rate of heat and mass transmit augments with wall-thickness factor.     

Numerical treatment of magneto Carreau nanofluid over a stretching sheet considering Joule heating impact and nonlinear thermal ray

In this essay, the magnetohydrodynamic flow of a Carreau nanoliquid upon a radiative stretching plate has been reviewed. The impacts of Joule heating and thermal ray are considered. The thermophoresis phenomenon and Brownian motion are applied to model nanoparticles (Buongiorno's model). Governing equations are solved numerically using Runge‐Kutta‐Fehlberg 4.5 after the transformation of partial differential equations into ordinary differential equations. In the obtained outcomes of investigating the impacts of different parameters on the change in velocity, concentration, and temperature profiles for two cases of shear‐thinning liquid and shear thickening liquid are reported as diagrams. Also, in the final segment of this essay, the impacts of diverse parameters on the skin friction coefficient and the local Nusselt number are investigated. The novel findings of current research illustrate that the values of local Nusselt number and surface drag force for shear thickening liquid are higher than shear‐thinning liquid. Also, the temperature profile has direct relationships with thermal radiation and magnetic field.     

Study of chemically reactive and thermally radiative Casson nanofluid flow past a stretching sheet with a heat source

Nanoparticle (NP) delivery is an exciting and rapidly developing field that adequately takes care of thermal radiation in blood flow and is likely to have bearing on the therapeutic procedure of hyperthermia, blood flow, and heat transfer in capillaries. The NP parameters such as size, shape, and surface characteristics can be regulated to improve nano-drug delivery efficiency in biological systems. The NPs outperform traditional drug delivery processes in drug carrying capacity and controlled release. The current article investigates the boundary layer flow and heat transfer of thermally radiative Casson nanofluid (NF) over a stretching sheet with chemical reaction and internal heat source. In our study, Cu and Al₂O₃ are taken as NPs in a suitable base fluid. The problem is analyzed by using similarity transformations and is solved with MATLAB's built-in solver bvp4c. The effects of pertinent parameters characterizing the flow model are presented through graphs and tables. The important findings of the investigation are noted as: the use of metallic oxide is more beneficial to attain higher temperature within a few layers close to the bounding surface; the appearance of convexity and concavity in the concentration profile attributed to flow instability, and the constructive and destructive heterogeneous reactions at the bounding surface have distinct roles to modify the NF flow in the boundary layer.     

Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet

The unsteady boundary layer flow of a nanofluid over a permeable stretching/shrinking sheet is theoretically studied. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. The results are obtained for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle fraction profiles for some values of the governing parameters, namely, the unsteadiness parameter, the mass suction parameter, the Brownian motion parameter, the thermophoresis parameter, Prandtl number, Lewis number and the stretching/shrinking parameter. It is found that dual solutions exist for both stretching and shrinking cases. The results also indicate that both unsteadiness and mass suction widen the range of the stretching/shrinking parameter for which the solution exists.     

Magnetohydrodynamics boundary layer flow and heat transfer in porous medium past an exponentially stretching sheet under the influence of radiation

Buoyancy forces result from the cooling or heating of a continuous stretching sheet, which causes a change in the resulting flow and thermal fields, and hence the heat transfer behavior in the manufacturing process. The study of the thermal buoyancy induced in boundary layer flow is important due to its recent advances in the areas of nuclear energy, electronics, and space technology. In this perspective, the aim of the present study is to investigate the effect of the buoyancy parameter on the magnetohydrodynamics boundary layer flow over an exponentially stretched sheet in the presence of nonlinear thermal radiation and porous media. Using similarity transformation, the flow model of partial differential equations is transformed into a set of coupled nonlinear ordinary differential equations. The efficient fourth‐order Runge‐Kutta scheme with the shooting method is used to solve the reduced equations. The impact of various associated parameters on velocity and temperature profiles were analyzed and computed through graphs. The major outcome of the present study shows the enhancement in the velocity distribution with the increase in the buoyancy parameter. Also, the increase in thermal buoyancy and thermal radiation leads to an increase in fluid temperature. Moreover, it is worth to note that the fluid velocity declines with the augmentation of the magnetic parameter.     

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.     

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.     

Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet

A boundary layer analysis is presented for the flow and radiative heat transfer of an incompressible micropolar fluid over stretching/shrinking sheet with power-law surface velocity and temperature distributions. Dual solutions are analytically obtained firstly by homotopy analysis method (HAM). It is found that dual solutions not only exist for the shrinking flow as reported in the previous literatures, but also exist for the stretching flow. The special case of the first branch (K = 0, classical Newtonian fluid) is compared with the existing numerical results of stretching flow in good agreement. Our results show that both solutions are physically meaningful (two solutions are closely related to each other), unlike the results previously reported that only one solution is acceptable. Moreover, the effects of the material parameter K, the radiative Prandtl number Pr_n, the velocity exponent parameter m and the temperature exponent parameter λ on the flow and heat transfer characteristics are analyzed in detail.     

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two‐dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter () and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin‐friction coefficient (C_fx(Re_Lξexp(ξ)^)1/2) and the local Nusselt number (Nu_x(Re_Lξexp(ξ)^)?1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement.     

Statistical analysis on three-dimensional MHD convective Carreau nanofluid flow due to bilateral nonlinear stretching sheet with heat source and zero mass flux condition

This study focuses on analyzing the response of a magnetohydrodynamic convective Carreau nanofluid flow over a bilateral nonlinear stretching sheet in the presence of a heat source and zero mass flux condition. The problem has been solved numerically using the MATLAB built-in function bvp5c. The findings of velocity, temperature, and concentration profiles based on the various parameters are illustrated using graphs. The impact of various parameters on the heat transfer rate is scrutinized using statistical techniques, like, correlation coefficient, probable error, and regression. The effect of various parameters on skin friction coefficients is studied via tables and slope of linear regression. It is observed that the statistical results coincide with the numerical results. It is also noticed that the stretching ratio parameter increases the Y-directional velocity profile. Accuracy of the numerical procedure has been validated through a restrictive comparison of the present work with previous published results and is found to be in good agreement.     

Effects of the viscous dissipation and chemical reaction on Casson nanofluid flow over the permeable stretching/shrinking sheet

A steady two‐dimensional Casson nanofluid flow over the permeable stretching/shrinking sheet along the viscous dissipation and the chemical reaction is studied in this article. The convective boundary condition is incorporated in energy equation. Similarity variables are applied to convert the governing partial differential equations into ordinary differential equations. The numerical solutions of the equations are obtained by using the shooting method with Maple implementation. The numerical findings indicate occurrence of the dual solutions for a certain range of stretching/shrinking and suction parameters. Therefore, a stability analysis is done to find the solution that is stable and physically realizable. The effects of the pertinent physical parameters on velocity, temperature, and concentration profiles are investigated graphically. Numerical results of various parameters involved for skin friction coefficient, the local Nusselt as well as Sherwood numbers are determined and also discussed in detail. The Casson and suction parameters decrease the velocity in the first solution, whereas they increase it in the second solution. The rate of heat transfer increases in both solutions with an increment in Eckert number, Biot number, thermophoresis, and Brownian motion parameters. Thermophoresis and Brownian motion parameters show opposite behavior in the nanoparticle's concentration. The nanoparticle concentration decreases in both solutions with increment in Schmidt number, Brownian motion, and chemical reaction parameters.     

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.