Influence of chemically reactive species and a volumetric heat source or sink on mixed convection over an exponentially decreasing mainstream

In this paper, we investigate mixed convection flow over an exponentially decreasing freestream velocity in presence of nonlinear chemically reactive species and a volumetric heat source or sink. Nonsimilar transformations are used to reduce the boundary layer equations into dimensionless equations and are further solved by the implicit finite difference scheme in combination with the quasi‐linearization technique. The influence of various governing parameters such as the volumetric heat source/sink parameter (Q), the ratio of buoyancy forces (N), the Richardson number (Ri), and the chemical reaction parameter (Δ) on the flow, thermal and species concentration fields are discussed and presented in terms of graphs. The numerical investigation reveals that the increase in volumetric heat source/sink parameter Q increases the temperature profile about 69% in presence of injection and the concentration profile decreases about 56% for and increases around 53% for as n increases from 1 to 2.     

Hydromagnetic mixed convection unsteady radiative Casson fluid flow towards a stagnation-point with chemical reaction,induced magnetic field,Soret effect,and convective boundary conditions

This article presents the two-dimensional mixed convective MHD unsteady stagnation-point flow with heat and mass transfer on chemically reactive Casson fluid towards a vertical stretching surface. This fluid flow model is influenced by the induced magnetic field, thermal radiation, viscous dissipation, heat absorption, and Soret effect with convective boundary conditions and solved numerically by shooting technique. The calculations are accomplished by MATLAB bvp4c. The velocity, induced magnetic field, temperature, and concentration distributions are displayed by graphs for pertinent influential parameters. The numerical results for skin friction coefficient, rate of heat, and mass transfer are analyzed via tables for different influential parameters for both assisting and opposing flows. The results reveal that the enhancement of the unsteadiness parameter diminishes velocity and induced magnetic field but it rises temperature and concentration distributions. Moreover, higher values of magnetic Prandtl number enhance Nusselt number and skin friction coefficient, but it has the opposite impact on Sherwood number. We observe that the amplitude is higher in assisting flow compared to opposing flow for skin friction coefficient and Nusselt number whereas opposite trends are noticed for Sherwood number. Our model will be applicable to various magnetohydrodynamic devices and medical sciences.     

Second law analysis in radiative mixed convective squeezing flow of Casson fluid between parallel disks with Soret and Dufour effects

The present communication deals the entropy generation by cause of heat and mass transform in an unsteady mixed convective radiative squeezing flow of a Casson fluid confined between two parallel disks in the presence of diffusion‐thermo and thermal‐diffusion effects and temperature jump. The lower disk is taken to be porous and the upper one is impermeable. The governing PDE is converted as nonlinear ordinary differential equations (ODE) by using well‐established similarity transformations; then, the reduced nonlinear ODE are solved by shooting method with Runge‐Kutta fourth‐order approach. The influence of distinct nondimensional fluid and geometric‐related parameters on the velocity profiles, temperature, concentration, entropy generation number, and Bejan number are studied in detail and represented in the form of graphs. The entropy of the Casson fluid is increased with the Eckert number, whereas the concentration profile is decreased by squeezing Reynolds number. The current results are correlated with existing results for the viscous case and found to be in better agreement.     

Effects of chemical reaction,Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

The aim of the current study is to explore the effects of heat and mass transfer on unsteady chemically reacted Casson liquid flow over an exponentially accelerated vertical plate in a porous medium. It is assumed that the bounding plate has varying temperatures as well as concentrations in a porous medium under a uniform magnetic field. This phenomenon is modeled in the form of a system of partial differential equations (PDEs) with boundary conditions. The governing dimensionless PDEs are solved using Laplace transform method for velocity, temperature, and concentration. The impact of nondimensional parameters, which are controlling the flow like Casson parameter, Soret number, magnetic parameter, heat generation parameter, Prandtl number, radiation parameter, and Schmidt number is analyzed through graphs. The incremental values of the Casson fluid parameter lead to a reduction in velocity and discovered that for large values of the Casson parameter, the fluid is near to the Newtonian fluid. Also, the Sherwood number increases with enhancing dissimilar estimators of the Schmidt and Soret numbers. A comparison has been made with the published work (Kataria et al.) for a particular case, which was in good agreement.     

Thermosolutal convective non-Newtonian radiative Casson fluid transport over a vertical plate propagated by Arrhenius kinetics with heat source/sink

In the current study, a mathematical formulation is developed by combining the non-Newtonian (Casson) fluid model to simulate the thermosolutal free convection radiative flow over a vertical surface. The current flow model is formulated with a heat sink/source and radiation driven by Arrhenius kinetics. The basic flow equations are transmuted into a nondimensional form via similarity transformations for which numerical simulations are performed utilizing the Runge-Kutta-Fehlberg method with shooting technique. The results obtained for velocity, energy, and species mass concerning various flow parameters are presented graphically. Computed results for skin friction, Nusselt number, and Sherwood number are tabulated. The results have been verified for limited cases by comparing with various investigations, revealing excellent accuracy. The detailed geometry reveals that an increase in the activation energy enhances the flow velocity and heat transport in the Casson fluid system due to exothermic heat reaction. With the increase of the Frank-Kamenetskii term, there is a substantial rise in temperature distribution and a decrease in concentration profiles due to high Arrhenius exothermic process, which revealed that the presence of Arrhenius kinetics is more effective to improve heat transportation phenomenon. Enhancement of the heat source/sink term completely boosts heat distribution. Rise in Radiation parameter, temperature field increases by reducing heat dissipation to the ambient.     

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.     

Nonlinear convection flow of dissipative Casson nanofluid through an inclined annular microchannel with a porous medium

The nonlinear convection study on the flow of a dissipative Casson nanofluid through a porous medium of an inclined micro-annular channel is presented. The cylindrical surfaces were conditioned to temperature increase and velocity slip effects. A uniform magnetic field strength was applied perpendicular to the cylinder surface. The heat source and Darcy number influence are explored in the examination of the blood rheological model (Casson) through the annular cylinder. Appropriate dimensionless variables are imposed on the dimensional equations encompassing Casson nanofluid rheology through an annular microchannel. The resulting systems of equations were solved and computed numerically via Chebyshev-based collocation approach. Thus, the solutions of flow distributions, volumetric flow rate, and other flow characteristics were obtained. The result shows that both nonlinear convection parameters decrease the nanoparticle volume fraction, whereas they increase the energy and momentum distributions. Moreover, the volumetric flow rate is upsurged significantly by a wider porous medium, annular gap, a higher Casson parameter, and nonlinear convection influence.     

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.     

Chemically reacting mixed convective Casson fluid flow in the presence of MHD and porous medium through group theoretical analysis

This paper explores the consequences of chemically reacting magnetohydrodynamic mixed convective fluid substances driven by the porous medium, slippery, incompressible, and laminar vertical channel flow. Casson fluid model in a vertical channel is strengthened with mixed convection flow. The effects of the heat source-sink parameter, the suction-injection parameter, slips on the slide wall, and thermal radiation are also considered. A Lie group method is taken into consideration and nonlinear partial differential equations are converted into nonlinear ordinary differential equations (ODEs). The NDSolve command solves these ODEs and shows the action of the related parameters in the velocity, temperature, and concentration figures. The Casson fluid parameter increases the velocity profile but reduces the concentration profile. The parameter of suction-injection enhances the velocity, temperature, and concentration profiles. The variations in skin-friction coefficient in the heat and mass transfer rate are addressed in the diagrams. Moreover, streamlines are plotted for suction-injection parameter.     

Numerical simulation of Dufour and Soret impacts on MHD Williamson nanofluid flow through an inclined surface

The carry-outs of Dufour and Soret, as well as radiation, and chemical response on a non-Newtonian MHD Williamson nanofluid flow through an inclined extended plane are discussed in this article. Keller-box analysis is being used to explore the influence of the Williamson factor here on the fluid domain quantitatively. Ordinary differential equations (ODEs) are recovered from boundary flow equations using appropriate similarity transformations. These ODEs are numerically addressed. Graphs and comparisons are used to simulate and study the features of flow characteristics such as velocity, temperature, and concentration of Williamson nanofluids distributions in response to various emerging parameters. The numerical computations show that our results are in reasonable harmony with previous studies. The numerical computations revealed that for the time being, the density of the momentum fluid layers is diminishing for the values of $ᴦ$, Le, $\Omega$, M, and increasing for Gc, Gr. The thickness of the thermal boundary layer is decreasing for Sr, Df, Pr, Gc, and Gr. M, $ᴦ$, $\Omega$, R, N, and Le are all on the rise. The concentration profile for R, Le, Nb, Nt, Gr, Gc, and N is decreasing, while Pr, Df, Sr, M, $ᴦ$, and $\Omega$ are increasing.     

Soret and Dufour effects between two rectangular plane walls with heat source/sink

This study addresses the thermo‐diffusion and the diffusion‐thermo phenomena in a semi‐infinite absorbent channel whose walls are contracting/expanding, with heat source/sink effects. The governing partial differential equations with suitable boundary conditions are transformed to a system of dimensionless ordinary differential equations. An analytic solution of the problem has been found using a technique called homotopy analysis method (HAM). HAM gives consistently valid answers to the problem over an extensive variety of parameters and also provides better accuracy. To validate the analytical results, a comparison has been presented with a numerical solution calculated by using the parallel shooting method. The effects of dimensionless parameters, that is, deformation parameter, Reynolds number, Soret and Dufour numbers, and heat source/sink parameter on the expressions of velocity, temperature, and concentration profiles are analyzed graphically to understand the physics of the deformable channel. It has been noted that the velocity across the channel is higher for the expanding channel, as compared to that for the contracting channel. Also the Soret and Dufour number increases the temperature of the fluid, and decreases the concentration. The temperature profile has an increasing behavior in the case of heat source, and a decreasing behavior in the case of heat sink.     

Unsteady MHD mixed convection flow of a micropolar fluid along an inclined stretching plate

In this research, the unsteady magnetohydrodynamic mixed convection flow of a micropolar fluid over an inclined plate has been investigated. The problem is reduced to a system of non‐dimensional partial differential equations, which are solved numerically using the implicit finite‐difference scheme. Velocity profiles, temperature profiles, concentration profiles, the skin friction coefficient, the rate of heat transfer, and the rate of mass transfer are computed numerically for various values of different physical parameters. In this study, we consider both assisting and opposing flow. It is found that in the assisting flow case, a solution could be obtained for all positive values of the buoyancy parameter λ, while in the opposing flow case the solution terminated at $\lambda = {\lambda _c}(\lambda < 0)$ . © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21034     

Impact of Soret and Dufour on MHD mixed convective flow of non-Newtonian fluid over a coagulated surface

In the present study, we investigated the steady, two-dimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo-diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth-order Runge–Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter.     

Impact of viscous dissipation and Dufour on MHD natural convective flow past an accelerated vertical plate with Hall current

The present research work concentrates on viscous dissipation, Dufour, and heat source on an unsteady magnetohydrodynamics natural convective flow of a viscous, incompressible, and electrically conducting fluid past an exponentially accelerated infinite vertical plate in the existence of a strong magnetic field. The presence of the Hall current induces a secondary flow in the problem. The distinguishing features of viscous dissipation and heat flux produced due to gradient of concentration included in the model along with heat source as they are known to arise in thermal-magnetic polymeric processing. The flow equations are discretized implicitly using the finite difference method and solved using MATLAB fsolve routine. Numerical values of the primary and secondary velocities, temperature, concentration, skin friction, Nusselt number, and Sherwood number are illustrated and presented via graphs and tables for various pertinent parametric values. The Dufour effect was observed to strengthen the velocity and temperature profile in the flow domain. In contrast, due to the impact of viscous dissipation, the local Nusselt number reduces. The study also reveals that the inclusion of the chemical reaction term augments the mass transfer rate and diminishes the heat transfer rate at the plate.     

Squeezing flow of Casson hybrid nanofluid between parallel plates with a heat source or sink and thermophoretic particle deposition

The investigations on the flow of non-Newtonian fluids are becoming one of the major topics in the research field. These liquids have substantial applications in industrial and engineering fields such as drilling rigs, food processing, paint and adhesives, nuclear reactors and cooling systems. On the other hand, hybrid nanofluids play a major role in the heat transfer process. Keeping this in mind, the motion of Casson hybrid nanofluid squeezing flow between two parallel plates with the effect of heat source and thermophoretic particle deposition is examined here. The partial differential equations that govern fluid flow are converted into ordinary differential equations using appropriate similarity variables and those equations are numerically solved using the Runge–Kutta–Fehlberg fourth–fifth-order method by implementing the shooting scheme. The graphs depict the effects of a number of key parameters on fluid profiles in the absence and presence of the Casson parameter. These graphs show that fluid velocity enhances with the augmentation of the local porosity parameter. Thermal dispersal upsurges for enhancement of heat source/sink parameter and the concentration profile escalates for an upsurge of the thermophoretic parameter. Skin friction enhances with enhancement in the local porosity parameter.     

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.     

Influence of Soret and Dufour on mixed convection flow across a vertical cone

This contribution examines the influence of Soret and Dufour on an incompressible viscous fluid flow across a vertical cone. The flow model is framed in the form of mathematical governing equations and a nondimensionalization is performed on them for ease of the numerical computations' examination; the obtained nonsimilarity equations are solved numerically through the bivariate Chebyshev spectral collocation quasi-linearization method. Outcomes of the flow characteristics, velocity, temperature, concentration, skin friction rate, heat, and mass transfer rates are analyzed with the variations of governing parameters, Prandtl number, buoyancy parameter, Schmidt number, buoyancy ratio, Soret and Dufour parameters at various stream-wise spots of the flow. To certify the exactness of the listed computations, we performed a comparison with prior published computations, which were found with great agreement, and the residual analysis study was also portrayed to reflect the convergence and stability of the adopted numerical technique.     

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.     

Study of an unsteady magnetohydrodynamic-free convective flow under parabolic ramped temperature and concentration in the presence of Soret and heat sink

The purpose of this paper is to investigate the effects of Soret, thermal radiation, and chemical reaction on an unsteady magnetohydrodynamic free convective flow past an impulsively initiated semi-infinite vertical plate with heat sink under parabolic ramped temperature and parabolic ramped concentration. Using some nondimensional parameters, the flow boundary equations in this case are first converted to dimensionless equations. The closed-form Laplace transform technique is employed here to solve the partial differential equations and get the solutions for fluid velocity, temperature, and concentration. The velocity, temperature, and concentration of the fluid tend to vary with the effect of various flow factors. These changes are graphically represented and analyzed. Differences in skin friction, Nusselt number, and Sherwood number for the different relevant parameters are also recorded. The Soret number hikes the fluid velocity and concentration. The rate of heat transfer, mass transfer, and momentum transfer improves due to the application of parabolic ramped conditions.     

Mixed convective heat and mass transfer on a peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel

In the present analysis we discuss the effects of mixed convective heat and mass transfer on the peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The governing equations for the present flow problem are first modeled and then discussed. The analytical solution of the present flow problem is discussed using regular perturbation technique. The graphical results are discussed to see the effects of various physical parameters of interest. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21020