Maxwell nanofluid heat and mass transfer analysis over a stretching sheet

The Buongiorno model Maxwell nanofluid flow, heat and mass transfer characteristics over a stretching sheet with a magnetic field, thermal radiation, and chemical reaction is numerically investigated in this analysis. This model incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a coupled nonlinear ordinary differential equation by using the similarity transformation technique. The resultant nonlinear differential equations are solved by using the Finite element method. The sketches of velocity, temperature and concentration with diverse values of magnetic field parameter (0.1 ≤ M ≤ 1.5), Deborah number (0.0 ≤ β ≤ 0.19), radiation parameter (0.1 ≤ R ≤ 0.7), Prandtl number (0.5 ≤ Pr ≤ 0.8), Brownian motion parameter (0.1 ≤ Nb ≤ 0.7), thermophoretic parameter (0.2 ≤ Nt ≤ 0.8), Chemical reaction parameter (1.0 ≤ Cr ≤ 2.5) and Lewis number (1.5 ≤ Le ≤ 3.0) have investigated and are depicted through plots. Moreover, the values of the Skin-friction coefficient, Nusselt number, and Sherwood numbers are also computed and are shown in tables. The sequels of this analysis reviewed that the values of Skin-friction coefficient and Sherwood number intensified with hiked values of Deborah number (β), whereas, the values of Nusselt number decelerate as values of (β) improves.     

Analysis of second law on Eyring‐Powell nanoliquid flow in a vertical microchannel considering magnetic field and convective boundary

Studies related to enhancing heat transfer has attained much attention of researchers to avail optimized heat‐transfer devices. High viscous fluids are of great importance as they are widely used in petroleum products, organic chemistry, coating, printing, and so forth. In this study, heat transfer mechanism driven by Eyring‐Powell nanoliquid flow in a vertical microchannel is examined. Impact of considering buoyancy force, magnetic field, and convective boundary on the thermal system is demonstrated. The modeled nondimensional equations are computed by using the Runge‐Kutta‐Fehlberg method. The vital roles of thermophoresis and Brownian motion are discussed in detail. The significance of second law analysis for thermal systems is presented. The causes of irreversibilities in a microchannel due to Eyring‐Powell nanoliquid flow is also demonstrated in the current research study. The upshots of the current investigations are visualized through graphical elucidation. It is established that minimization of entropy generation can be achieved by enhancing the mechanism of thermophoresis. The convective boundary helps in transmitting heat from the thermal system to the ambience hence the lower thermal field is attained.     

Squeezed MHD tangent hyperbolic fluid flow across a sensor surface

In the present numerical study, the combined effect of temperature-dependent thermal conductivity, linear thermal radiation, and magnetic effect on shear-thinning tangent hyperbolic fluid past a sensor surface has been studied. After converting the modelled partial differential equations into ordinary differential equations by using similarity transformation, the system of equations is tackled with the aid of the shooting method. The influence of important parameters on the fluid motion and energy distribution is displayed graphically and analyzed in detail. The presented simulations depict that a significant rise in fluid velocity is noticed for an enhancement in the magnetic parameter while an opposite trend is observed for the temperature distribution. Moreover, the skin friction coefficient decreases as the squeezed flow index is increased.     

Heat and mass transfer effect on an unsteady MHD radiative chemically reactive Casson fluid over a stretching sheet in porous medium

The objective of the present study is to investigate the effects of the variable magnetic field, chemical reaction, thermal radiation, Soret effect, and variable heat absorption on the fluid flow and heat and mass transfer of an unsteady Casson fluid past a stretching surface in a saturated porous medium. Velocity slip near the plate and conjugate heating boundary conditions in heat and mass transfer have been considered in this study. Due to the complexities in boundary conditions, the analytic solution of the governing equations of the present model is not possible. Thus, to overcome these issues, the coupled partial differential equations of the model are converted into a set of ordinary differential equations using similarity transformation. These equations have then been solved numerically using the fourth-order Runge-Kutta technique via the shooting method. The effects of various pertinent flow parameters on the velocity, concentration, and temperature field have been studied graphically. For the field of engineering, to get an insight into the physical quantities, especially Nusselt number, Sherwood number, and skin friction, their numerical values have been estimated against various parameters and presented in tables. From the tabulated values, it has been perceived that the shear stress increases with an increase in magnetic parameter, unsteadiness parameter, Casson parameter, and heat source parameter, whereas the Biot number shows the reverse trend. The mixture of porous media has justified that the heat transport process over a stretching sheet results in averting heat loss and accelerating the process of cooling, which is a significant outcome of the study. Furthermore, it has also been revealed that with the increase in the Soret effect and magnetic field, there is a reduction in the fluid velocity and temperature near the plate, whereas there is an increase in the species concentration. It has also been mentioned that the effects of the variable magnetic field have been widely applied in various engineering applications like magnetohydrodynamic (MHD) propulsion forces, rate of cooling, MHD power generation, and so on.     

Influence of relaxation-retardation viscous dissipation on chemically reactive flow of Oldroyd-B nanofluid with hyperbolic boundary conditions

The present analysis is meant to explore the computational solution of the problem dealing with the impact of relaxation-retardation viscous dissipation and chemical reaction on the flow of Oldroyd-B nanofluid over a Riga plate. Hyperbolic time-varying boundary conditions are taken into consideration. The basic modeled problem being transformed into nonlinear differential equations are solved numerically by efficient fourth-order Runge-Kutta method along with shooting technique. Characteristics of controlling parameters on velocity, temperature, and concentration along with skin friction, Nusselt number, and Sherwood number profiles are presented with the help of well-featured graphs. The relaxation and retardation parameters affect well flow profiles. In addition, an accelerated flow pattern is accomplished due to the augmentation of the modified Hartmann number. Furthermore, the presence of relaxation-retardation viscous dissipation improves the temperature field.     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy

In this communication, the dynamics of a non‐Newtonian tangent hyperbolic fluid with nanoparticles past a nonuniformly thickened stretching surface is discussed. We examine the impact of nonlinear mixed convection flow of a hyperbolic tangent fluid with the Cattaneo‐Christov heat and mass diffusion model past a bidirectional stretching surface. The effects of activation energy and magnetic field are incorporated in the analysis. The variables of transformations are used to change the nonlinear partial differential equations into ordinary differential equations (ODEs). Then, these ODEs are numerically solved using the Matlab routine of the bvp4c algorithm. The derailed analysis of the influences of the governing parameters on velocities along the x‐ and y‐axes, temperature and concentration profiles are presented using tables and figures. The outcomes of these parameters reveal that the velocities along the x‐ and y‐axes are decreased for the values of We increasing but the opposite behavior is observed as the value of $A$ increases. The results also show that the values of $e$ and $Nb$ rise as the temperature profiles increase. Similar influences are observed on the profile of concentration as the values of $F$ and $f$ rise. As the values of $N1$ go from 0.27 to 0.25, the skin‐friction coefficient increases, and similarly, as $Nb$ goes from 0.3 to 0.1, $?\theta \prime (0)$ is enhanced.     

The onset of natural convection in a horizontal nanofluid layer heated from below

A linear stability analysis is performed for the onset of natural convection in a horizontal nanofluid layer heated from below. The motion of nanoparticles is characterized by both the thermophoresis and Brownian diffusion effects. Different from previous studies in the literature, both the dependences of thermophoresis on nanoparticle volume fraction and Brownian motion on temperature are taken into consideration in the theoretical model. The result reveals that the base flow is mainly dominated by the effect of thermophoresis and the Brownian diffusion coefficient can be treated as a constant reasonably when a finite temperature difference is imposed across the nanofluid layer. Accordingly, a novel base solution of nanoparticle volume fraction is derived. It is found that the profile of nanoparticle concentration depends heavily on the magnitude of thermophoretic diffusion, which may exhibit a nonlinear distribution across the nanofluid layer once the effect of thermophoresis is significant. The suspended nanoparticles produce a strong destabilizing effect and a tiny volume fraction of nanoparticles is sufficient to trigger the onset of convection and make the nanofluid layer become unconditionally unstable. The dispersion spectra of unstable modes are demonstrated and the most unstable mode with the maximum growth rate is explored. The growth rate of the most unstable mode is found to increase significantly with increasing nanoparticle concentration, while the influence of heat capacity ratio of nanoparticle to base fluid on the behavior of thermal convection is negligible.     

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

In this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are , , , , , , and . It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number, whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.     

Heat and mass transfer in a MHD non‐Darcian micropolar fluid over an unsteady stretching sheet with non‐uniform heat source/sink and thermophoresis

The effect of heat and mass transfer in a MHD non‐Darcian flow of a micropolar fluid over an unsteady stretching sheet with thermophoresis and non‐uniform heat source/sink is discussed. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The arising nonlinear problem is solved by the Keller box method. The effects of various physical parameters on skin friction, local Nusselt number, and Sherwood number are presented graphically and in tabular form. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21018     

Heat transfer analysis of inclined magnetic field and activation energy in Maxwell nanofluid with thermophoresis effects

Numerical analysis is performed for incompressible Maxwell nanofluid model flow under the implications of thermophoresis and inclined magnetic field over a convectively stretched surface. The system that comprises differential equations of partial derivatives is remodeled into the system of ordinary differential equations via similarity transformations and then solved through by Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerge from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios. The significant outcomes of the current investigation are that the velocity field decays for higher fluid parameters while that peter out the fluid temperature. Further, the heat transfer rate is reduced with the incremental values of fluid and thermophoresis parameters while it uplifts with Biot and Prandtl numbers.     

Numerical analysis of MHD nanofluid flow over a wedge,including effects of viscous dissipation and heat generation/absorption,using Buongiorno model

The key purpose of this article is to examine magnetohydrodynamics flow, generative/absorptive heat, and mass transfer of nanofluid flow past a wedge in the presence of viscous dissipation through a porous medium. The investigation is completely theoretical, and the present model expresses the influence of Brownian motion and thermophoresis using the nanofluid Buongiorno model. The fundamental model of partial differential equations is reframed into the structure of ordinary differential equations implementing the nondimensional similarity transformation, which are tackled through the fourth–fifth-order Runge–Kutta–Fehlberg algorithm together with the shooting scheme. The analysis of sundry nondimensional controlling parameters, such as magnetic parameter, Eckert number, heat generation/absorption parameter, porosity parameter, Brownian motion parameter, and thermophoresis parameter on velocity, temperature, and concentration profiles are discussed graphically. The effects of the physical factors on the rate of momentum and heat and mass transfer are also determined with appropriate analysis in terms of skin friction, Nusselt number, and Sherwood number. The outcomes illustrate that the local Nusselt number and local Sherwood number are reduced for higher values of the thermophoresis parameter. Besides, it is found that higher estimations of heat generation/absorption and viscous dissipation parameters increase temperature. Moreover, it is found that the temperature profile increases with the involvement of the Brownian motion parameter, while an opposite trend is observed in the concentration profile. A comparison is also provided for limiting cases to authenticate our obtained results.     

Numerical illustrations of 3D tangent hyperbolic liquid flow past a bidirectional moving sheet with convective heat transfer at the boundary

Convective heat transfer plays a central role in the numerous industrial devices because it perturbs the mechanical behavior of a system along with its thermodynamics. Keeping such applications in mind, analysis of heat transportation in three‐dimensional tangent hyperbolic fluid flow is investigated here. Convective heat transportation at the boundaries is considered. Rosseland's approximation has been used for the radiation effects. Closed form analytical solutions for the governing equations are difficult to obtain even after the use of similarity transformations. Therefore, the numerical solutions are presented through the Runge‐Kutta‐Fehlberg forth‐fifth method. Graphical analysis of the numerical results has been carried out. Roles of sundry constraints on flow are studied. It is also noted that the rates of heat transportation and skin‐friction are higher in the presence of convective heat transfer near the boundary.     

Linear stability of convection in a vertical channel filled with nanofluid saturated porous medium

The convection in a vertical channel filled with a porous medium saturated by a nanofluid is studied numerically. The effects of Brownian motion and thermophoresis are incorporated in the model used for nanofluid. Also, the flow within the porous region is governed by Brinkman's equation. The generalized eigenvalue problem for the perturbed state is obtained from a normal mode analysis and solved using the Chebyshev spectral collocation method. The Rayleigh number is expressed as an implicit function of the wavenumber with other parameters. The critical wavenumber and the critical Rayleigh number are calculated for different parameters. The preferred modes under critical conditions are detected.     

Mixed convection flows of tangent hyperbolic fluid past an isothermal wedge with entropy: A mathematical study

The nonlinear, steady, and mixed convective boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian fluid over an isothermal wedge in the presence of magnetic field are analyzed numerically using the implicit Keller-Box finite-difference technique. The entropy analysis due to MHD flow of a tangent hyperbolic fluid past an isothermal wedge and viscous dissipation is also included. The numerical code is validated with previous Newtonian studies available in the literature. Graphical and tabulated results are analyzed to study the behavior of the fluid velocity, temperature, concentration, shear stress, heat transfer rate, entropy generation number, and Bejan number for various emerging thermophysical parameters, namely Weissenberg number (We), power-law index (n), mixed convection parameter (λ), pressure gradient parameter (m), Prandtl number (Pr), Biot number (γ), Hartmann number (Ha), Brinkmann number (Br), Reynolds number (Re), and temperature gradient (Π). It is observed that velocity, entropy, Bejan number, and surface heat transfer rate are reduced with the increase in the Weissenberg number, but temperature and local skin friction are increased. An increase in pressure gradient enhances velocity, entropy, local skin friction, and surface heat transfer rate, but reduces temperature and Bejan number. An increase in an isothermal power-law index (n) is observed to increase velocity, Bejan number, and surface heat transfer rate, but it decreases temperature, entropy, and local skin friction. An increase in the magnetic parameter (Ha) is found to decrease temperature, entropy, surface heat transfer rate, and local skin friction, and it increases velocity and Bejan number. The research is applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water-soluble solution thermal treatment.     

A two-component modeling for free stream velocity in magnetohydrodynamic nanofluid flow with radiation and chemical reaction over a stretching cylinder

This analysis explores the influence of magnetohydrodynamic (MHD) nanofluid flow over a stretching cylinder with radiation effect in presence of chemically reactive species. The thermal radiation phenomenon is incorporated in the temperature equation. The mathematical modeling of the physical problem produces nonlinear set of partial differential equations corresponding to the momentum and energy equations that can be transformed into simultaneous system of ordinary differential equations with appropriate boundary conditions by applying similarity transformations. Shooting technique is used to solve the molded equations after adoption of Runge–Kutta–Fehlberg approach and ODE45 solver in MATLAB. A parametric analysis has been carried out to investigate the impacts of physical parameters that are considered in the current study. The attractive pattern studied the consequence of Brownian motion along with thermophoresis parameter. The outcomes of prominent fluid parameters, especially heat radiation, Lewis number, free stream velocity, chemical reaction, thermophoresis, and Brownian motion on the concentration, temperature, as well as velocity have been examined and are displayed through graphs and tables. The present study reveals that the temperature phenomenon enhances with an increase in radiation parameter, while nanoparticle concentration phenomenon reduces with an increase in chemical reaction parameter.     

Thermal performance of Ag–water nanofluid flow over a curved surface due to chemical reaction using Buongiorno's model

An analysis of heat and mass transfer is carried out under the influence of chemical reaction, friction heating, and heat generation/absorption over a curved surface. The impacts of random motion attributes of nanoparticles and thermophoresis are also applied in the expressions of energy and concentration. With the help of assigned transformations, the nonlinear partial differential equations are changed to dimensionless nonlinear ordinary differential equations. Then, the numerical solution is obtained using fourth‐fifth order Runge‐Kutta‐Fehlberg method via the shooting technique. The impacts of relevant parameters on velocity, temperature, and concentration are depicted through graphs and tables. The results illustrate that the lowest concentration distribution of nanofluid is related to the higher value of chemical reaction parameter. Moreover, it is found that thermophoresis and Brownian motion parameters have a propensity to increase the temperature profile while curvature parameter decreases the velocity profile. Also, velocity and temperature fields show a similar behavior for the increasing values of volume fraction of the nanoparticles, while a reverse trend is observed in the concentration profile under the same condition. To authenticate the results of the current study, the obtained data were compared with previously published data.     

Heat and mass transfer of two immiscible flows of Jeffrey fluid in a vertical channel

In this article, we examined the effect of heat and mass transfer flow of two immiscible Jeffrey fluids in a vertical channel. The highly nonlinear coupled ordinary differential equations are evaluated using regular perturbation parameters, for small values of perturbation parameter. The effect of Jeffrey's parameter on the flow and the effects of various physical parameters entering into the problem on dimensionless velocity, temperature, and concentration distribution is illustrated graphically. We observe that the Jeffrey parameter, thermal, and mass Grashof number enhance the fluid flow, while the chemical reaction parameter suppresses the fluid flow, also it is established that the Nusselt number is boosted by enhancing the thermal and mass Grashof number. We observed that the results are in very good agreement with the results obtained for a viscous fluid.     

Double‐Diffusive Convective Transport in a Nanofluid‐Saturated Porous Layer with Cross Diffusion and Variation of Viscosity and Conductivity

The onset of double‐diffusive nanofluid convection in a fluid‐saturated horizontal porous layer is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. The Darcy model has been used for the porous medium, while the nanofluid incorporates the effects of Brownian motion along with thermophoresis. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation in the vertical direction of conductivity and viscosity. In addition, the thermal energy equation includes regular diffusion and cross diffusion terms. The linear stability analysis is based on the normal mode technique, while for nonlinear analysis, minimal representation of the truncated Fourier series representation involving only two terms has been used. It is found that for the stationary mode the Soret parameter, Dufour parameter, viscosity ratio, and conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret parameter, Dufour parameter, and viscosity ratio have a stabilizing effect while the solutal Rayleigh number and conductivity ratio destabilize the system. For steady finite amplitude motions, the heat and mass transport decreases with an increase in the values of the Dufour parameter and solutal Rayleigh number. The Soret parameter enhances the solute concentration Nusselt number while it retards the thermal Nusselt number and concentration Nusselt number. The viscosity ratio and conductivity ratio enhances the heat and mass transports. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large, all three transient Nusselt values approach a steady value. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 628–652, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21102