Chemically reactive and radiative flow of ferro-aluminum (AA7075) hybrid nanofluid past a stretching cylinder

The present investigation throws light on the heat transfer behavior of hybridized (ferro-aluminum alloy [AA7075]) nanofluid. In addition to that, influences of thermal radiation, magnetic effect, and chemical reaction are also considered for the exploration. Here, the flow is deliberated due to a porous stretching cylinder. The equations that portray the fluid flow are transfused to simple ordinary differential equations by applying similarity elements. Then, the procured equations have been solved by adopting the Runge–Kutta–Fehlberg 4th–5th order tool. The extracted solution are exported to plot graphs for velocity, thermal, and solutal profiles with the concerned parameters, and using these plots, the discussion has been produced for the behavior of all flow fields. The behavior of the thermal profile shows substantial enhancement with an increase in the solid volume fraction of hybrid nanofluid. The velocity and concentration panel de-escalates for larger values of Reynolds number. A significant discussion on the skin friction drag, Nusselt number, and Sherwood number has been produced.     

Second order velocity slip and thermal jump of Cu–water nanofluid over a cone in the presence of nonlinear radiation and nonuniform heat source/sink using homotopy analysis method

The purpose of the present paper is to explore the second order slip effects on nanofluid flow over a vertical cone. The effects of nonlinear thermal radiation and nonuniform heat source/sink are also taken into account. Water with copper nanoparticles is used as nanofluid in this investigation. The governing partial differential equations for the flow are converted into ordinary differential equations by using transformations and then are solved using homotopy analysis method. The influence of various important parameters on velocity, temperature, skin‐friction, and Nusselt number are presented through graphs. Results indicate that the velocity and magnitude of skin friction decrease with a rise in first and second order velocity slips. A raise in either first or second order temperature jump causes a fall in temperature. Nonlinear radiation increases the more rapidly when compared to the linear radiation case.     

Impacts of variable thermal conductivity and mixed convective stagnation‐point flow in a couple stress nanofluid with viscous heating and heat source

The current study examines mixed (combined) convection stagnation‐point couple stress nanofluid over a stretched cylinder of variable thermal conductivity in the presence of viscous dissipation and internal heat source. The basic governing partial differential equations have been converted to coupled nonlinear differential equations by using adequate similarity transformations. By applying semi‐analytic technique (BVPh2.0), the equivalent ordinary differential equations are successfully solved and validated with a bvp4c solver. Graphs are presented to study the impact of various parameters on axial velocity, temperature, and volumetric nanofluid concentration profiles. The coefficient of skin friction (quantifying resistance) and the rate of heat and mass transfer on the surface due to flow variables are computed and explained. The axial velocity and momentum thickness are decreased with increasing couple stress parameter, whereas the reverse trend is noted with mixed convection and buoyancy ratio parameters. The temperature distribution increases for increasing Brownian motion and thermal conductivity parameter, whereas it decreases for increasing stagnation parameter.     

Radiative nanofluid flow and heat transfer between parallel disks with penetrable and stretchable walls considering Cattaneo–Christov heat flux model

In this work, we explore the unsteady squeezing flow and heat transfer of nanofluid between two parallel disks in which one of the disks is penetrable and the other is stretchable/shrinkable, in the presence of thermal radiation and heat source impacts, and considering the Cattaneo–Christov heat flux model instead of the more conventional Fourier's law of heat conduction. A similarity transformation is utilized to transmute the governing momentum and energy equations into nonlinear ordinary differential equations with the proper boundary conditions. The achieved nonlinear ordinary differential equations are solved by the Duan–Rach Approach (DRA). This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of diverse active parameters, such as the suction/injection parameter, the solid volume fraction, the heat source parameter, the thermal relaxation parameter, and the radiation parameter on flow and heat transfer traits are examined. In addition, the value of the Nusselt number is calculated and portrayed through figures.     

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.     

Uncertainties in physical property effects on viscous flow and heat transfer over a nonlinearly stretching sheet with nanofluids

The purpose of this paper is to investigate a numerical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet utilizing nanofluid. The governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation. Different water-based nanofluids containing Cu, Ag, CuO, Al₂O₃, and TiO₂ are considered in our problem. Furthermore, four different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. The variations of dimensionless surface temperature, dimensionless surface temperature gradient as well as the flow and heat transfer characteristics with the governing parameters are graphed and tabulated. Comparison with published results for pure fluid flow is presented and it is found to be in excellent agreement.     

Nonsimilarity boundary layer flow of copper–water nanofluid near stagnation point in a porous medium

The effects of nanoparticle shape are first introduced to study the nonsimilar solutions of stagnation point boundary layer flow of water–copper nanofluid saturated in a porous medium. Two cases of solid matrix of porous medium, including glass balls and aluminum foam, are considered. By using a new empirical correlation for the heat capacitance, thermal conductivity, and thermal diffusivity of the nanofluid saturated in a porous medium, the governing equations of the problem are constructed and reduced by dimensionless variables and nonsimilar transformations, and the homotopy analysis method is adopted to solve the partial differential equations. The results indicate that the heat transfer is significantly enhanced with the increase of permeability of the porous medium on the surface of the stagnation point boundary layer flow. In addition, it is found that the empirical shape of the nanoparticle has an impact on the heat transfer.     

Heat and mass transfer analysis in unsteady MHD flow of aluminum alloy/silver-water nanoliquid due to an elongated surface

The current article presents an analytical study of an unsteady magnetohydrodynamic flow of Al₅₀Cu₅₀/Ag-water nanofluid over an elongated surface with thermal radiation and thermal diffusion effects. The flow is caused by an elongated plate, and the flow governing partial differential equations are transmuted into ordinary differential equations using suitable similarity transmutations. The regular perturbation technique is employed to resolve the transmuted equations. The results obtained describe the influence of pertinent parameters over usual flow fields, which are presented via plots, and the expressions procured for skin friction factor and rate of thermal and diffusion transport are comprehensibly portrayed in a tabular mode. The outcomes stipulate that the thermal transport performance of Al₅₀Cu₅₀-water nanofluid is moderately high as compared with Ag-water nanofluid. Also, the thermal radiation and chemical reaction parameters have a tendency to augment the rate of mass transfer.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk

The aim of this analysis is to examine the steady, laminar boundary layer flow of a micropolar nanofluid owing to a rotating disk in the presence of a magnetic field and thermal and solutal nonlinear convection and nonisothermal parameters. The governing joined partial differential equations are converted into nonlinear ordinary differential equations by means of available transformations. The equations are calculated using the method bvp4c from Matlab software. The convergence test has been maintained; for the number of spots greater than the appropriate mesh number of points, the precision is not influenced, but the set time is boosted. Moreover, various quantities of the main parameters on skin friction coefficients, wall couple stress coefficients, Nusselt number, Sherwood number, velocities, temperature, and concentration of nanofluid are analyzed by means of tables and graphs. The results indicate that the presence of the nonisothermal parameter boosts the radial skin friction, temperature, and Sherwood number but causes decaying concentration distributions, the azimuthal skin friction coefficient, and Nusselt number that indicate the diffusion of momentum occurs more around the surface of the rotating disk.     

Numerical simulation of mixed convective 3D flow of a chemically reactive nanofluid subject to convective Nield's conditions with a nonuniform heat source/sink

The present investigation aims to explore the influence of a mixed convection and nonuniform heat source/sink on unsteady flow of a chemically reactive nanofluid driven by a bidirectionally expandable surface. Convective heat transport phenomenon is used to maintain the temperature of the surface. Moreover, zero mass flux is also accounted at the surface such that the fraction of nanomaterial maintains itself on strong retardation. The governing nonlinear set of partial differential equations is transformed into a set of ordinary differential equations via a suitable combination of variables. The Keller‐Box scheme has been incorporated to make a numerical inspection of the transformed problem. The spectacular impacts of the pertinent constraints on thermal and concentration distributions are elucidated through various plots. Graphical outcomes indicate that the thermal state of nanomaterial and nanoparticles concentration are escalated for elevated amounts of Biot number, porosity parameter and nonuniform heat source/sink constraints. Furthermore, it is also seen that escalating amounts of unsteady parameter, temperature controlling indices, Prandtl number, and expansion ratio parameter reduce the thermal and concentration distributions. Numerical results for the rate of heat transference have been reported in tabular form. The grid independence approach is used to verify the convergence of the numerical solution and the CPU run time is also obtained to check the efficiency of the numerical scheme adopted for finding the solution.     

Effects of multislip and distinct heat source on MHD Carreau nanofluid flow past an elongating cylinder using the statistical method

This study focuses on studying the impact of multiple slip effects on the hydromagnetic Carreau nanofluid flow over an elongating cylinder considering a linear heat source and exponential space-based heat source. Suitable transformations are used in converting the highly nonlinear system of partial differential equations governing the flow into a system of ordinary differential equations and hence resolved using the Runge–Kutta method of order four coupled with the shooting method. BVP5C and RKF45 are used to compare the numerical accuracy and an excellent agreement is noted. The parallel effect of parameters on Nusselt number is studied using surface plots and the corresponding effects are scrutinized using multiple linear regression. It is observed that the linear heat source parameter, thermal slip parameter and exponential space-based heat source parameter demote the heat transfer rate. The consequence of different parameters on drag coefficient and mass transfer are quantified using a linear regression slope.     

Computation of Darcy-Forchheimer flow of Sisko nanofluid over a stretching cylinder

This study investigates the Darcy-Forchheimer flow of Sisko nanofluid with viscous dissipation and convective thermal boundary conditions. The Buongiorno two-component nanoscale model is deployed for nanofluid characteristics, which take into account the physical phenomena responsible for the slip velocity between the base fluid and the nanoparticles such as thermophoresis and Brownian diffusion. The Darcy- Forchheimer model employed here includes the effects of boundary and inertial forces. The nonlinear coupled partial differential equations governing the fluid flow are converted into the nonlinear ordinary differential equations by choosing suitable similarity transformations. The nondimensionalized differential equations are then solved utilizing the finite difference based bvp-4c tool in MATLAB software. The numerical solutions are presented graphically to demonstrate the impact of involved physical parameters on temperature, velocity, and nanoparticle volume fraction. Moreover, the rate of heat transfer, mass transfer, and skin friction are physically interpreted. The present investigation reveals that the Darcy number enhances the velocity and depleted the temperature while the Forchheimer number depleted the velocity and enhances the temperature of the Sisko nanofluid. The thermophoresis, Brownian diffusion parameters, and the Forchheimer number contribute to the reduction in the heat transfer rate while the Darcy number enhances it. The skin friction at the wall can be controlled by controlling the values of Darcy number.     

Convective instability in binary nanofluids with an internal heat source in the presence of thermodiffusion and nanoparticles

This paper investigates the effect of internal heat source on the convective instability under the effect of thermodiffusion of nanoparticles and solute in binary nanofluids theoretically using stability criterion based on linear stability theory. A horizontal layer of binary nanofluid at constant and different temperatures is considered, and the problem is modeled by the system of highly nonlinear partial differential equations. These coupled equations are transformed into ordinary differential equations using nondimensional variables. To study the convective instability of a binary nanofluid, the Rayleigh numbers are derived analytically for stationary and oscillatory convections and the addition factor F_a is proposed. The comparison of the obtained results is favorable with previously published results. The Brinkman model for viscosity and the Bruggeman model for thermal conductivity are used to study the effect of nanoparticle on the system. The effects of various parameters, namely internal Rayleigh number, volume fraction of nanoparticles, Soret coefficients of nanoparticles, and solute on the system are shown through graphs. To check the variation in stability, we have considered NH₃/H₂O+Ag binary nanofluid and the effect of addition factor on the concentration profiles are explained with the help of a graph.     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Unsteady squeezing flow of water‐based nanofluid between two parallel disks with slip effects: Analytical approach

The squeezing flow of an unsteady water‐based nanofluid between two parallel disks has been analyzed in the current study. Thermal and solutal buoyancy along with heat source enhance the flow phenomena of free convective flow through a porous medium. In addition to that velocity slip and temperature slip are also accounted for in the boundary conditions. The similarity transformation is adopted to formulate the governing equations that convert the complex partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). These transformed equations are handled analytically by using the variation parameter method (VPM). For computational purposes, the fixed numeric values of physical parameters are used and their behaviors are shown by means of graphs. The calculated results for the physical quantities of interest are shown in tables. The conformity of the solution is obtained in comparison to an earlier study in a particular case. The major findings are (i) the velocity profile has distinct variations, which are separated by the middle layer of the channel and (ii) enhancement in the heat transfer coefficient is noted due to the interaction of buoyancy parameter.     

Numerical computation on Marangoni convective flow of two‐phase MHD dusty nanofluids under Brownian motion and thermophoresis effects

The current theoretical study describes the Marangoni thermal convective flow of magnetohydrodynamic dusty nanofluids along a wavy vertical surface. The two‐phase mathematical model is developed under the influence of thermal radiation and exponentially varying space‐dependent heat source. Pure and hybrid nanoparticles together with dust particle suspension in the base fluid are taken into consideration to characterize the behavior of the flow. Brownian motion and thermophoresis mechanisms are considered, since it enhances the convection features of dusty nanofluid. Appropriate transformations are adopted to modify the flow governing equations and boundary conditions to dimensionless form. The forward finite difference scheme is implemented to illustrate the resultant coupled partial differential equations. The Newton quasi‐linearization technique is utilized to reduce the nonlinear system into a linear form, which is solved thereafter by Thomas algorithm. The responses of velocity, temperature, concentration, friction factor, and heat and mass transfer rate profiles with various governing parameters are discussed and portrayed graphically. The study evidences that the radiation and space‐dependent heat generating parameters strengthen the temperature distribution. Also, the heat transfer rate appreciably rises with the increment in Marangoni convection. The solution methodology and accuracy of the model is validated by generating the earlier outcomes for nonradiating nanofluid flow without heat source/sink.     

Nonlinear thermal radiation on MHD tangential hyperbolic hybrid nanofluid over a stretching wedge with convective boundary condition

In this study, two distinct nanoparticles: aluminum oxide (Al₂O₃) and copper (Cu) are chosen as nanomaterials to examine the effects of nonlinear electrically conducting magnetohydrodynamic radiation on the flow of tangential hyperbolic hybrid nanofluid across a nonlinearly stretched sheet with convective boundary conditions. The equations that regulate fluid flow are represented as partial differential equations. These equations are reduced to their equivalent ordinary differential equations, which are solved using the homotopy analysis approach with the help of similarity variables. The effect of essential physical factors on fluid velocity, temperature, skin friction coefficient, and local Nusselt number is investigated and discussed. Results ascertain that the heat transfer rate of Cu/H₂O nanofluid becomes high when equated to Cu–Al₂O₃/H₂O nanofluid. Furthermore, the temperature distribution enhances with the rise in solid volume fraction while it diminishes with improved magnetic field for both nanofluid and hybrid nanofluid.     

Analytical study of heat and mass transfer in unsteady MHD radiant flow of Williamson nanofluid over stretching sheet with heat generation and chemical reaction

This paper presents the analytical study of heat and mass transfer in a two-dimensional time-dependent flow of Williamson nanofluid near a permeable stretching sheet by considering the effects of external magnetic field, viscous dissipation, Joule heating, thermal radiation, heat source, and chemical reaction. Suitable transformations are introduced to reformulate the governing equations and the boundary conditions convenient for computation. The resulting sets of nonlinear differential equations are then solved by the homotopy analysis method. The study on the effects of relevant parameters on fluid velocity, temperature, and concentration profiles is analyzed and presented in graphical and tabular forms. Upon comparison of the present study with respect to some other previous studies, a very good agreement is obtained. The study points out that the transfer of heat can substantially be enhanced by decreasing viscoelasticity of the fluid and the transfer of mass can be facilitated by increasing permeability of the stretching sheet.