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1.
    
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.  相似文献   

2.
    
In the current communication, three-dimensional Williamson fluid flow past a bidirectional inclined stretching plate with novel Hall current, nonuniform heat source/sink, and nth-order chemical reaction features are investigated. Rosseland's diffusion model is defined for the radiation heat transfer. The nonlinear governing derivative equations satisfying the flow are transmuted to the coupled derivative equations by employing the local similarity quantities and then solved numerically through the Runge–Kutta–Fehlberg method utilizing the shooting quadrature. An inclusive analysis is reported via graphs for the flow rate field, temperature, and concentration distributions for different evolving terms of immense concern. Wall dragging effect and wall heat gradient and wall concentration gradient have been examined, plotted, and described. The detailed geometry reveals that dimensionless velocity field is monotonically rising as the Hall parameter rises. The chemical reaction concentration for the Williamson fluid is enhanced with expanding values of the magnetic field parameter. Transitional values of wall stress components upturn with an increase in Hall parameter while the Williamson term is boosted. Nusselt number is reduced as the Williamson term rises and the Sherwood number enhances with a rising chemical reaction term. The results are verified for limiting cases by comparing with various investigations and found to have excellent accuracy.  相似文献   

3.
    
The present study aims to investigate Marangoni‐forced convective nanofluid flow over an electromagnetic actuator (Riga plate). A first‐order homogeneous chemical reaction is considered. The thermocapillary and solutocapillary Marangoni effect developed by the surface tension is considered as a driving force for the nanofluid. In addition, Grinberg‐term is accounted to involve the impact of Lorentz force impinged by the actuator in the model. A set of nonlinear ordinary differential equations is obtained via suitable transformations for a nonsimilar analysis. Series solutions are achieved through homotopy to discuss the behavior of the velocity field, thermal distribution, and concentration of the nanoparticles graphically. The variation in Nusselt and Sherwood numbers is discussed. The outcomes declared that the flow parallel to the surface of the plate is assisted by the Lorentz forces generated by electromagnetic bars of the actuator resulting in an enhancement in the fluid motion. Furthermore, the stronger Marangoni effect resulted in the declining trend of the temperature profile. The concentration of nanoparticles near the surface reduced intensive chemical reaction inside the nanofluid.  相似文献   

4.
    
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.  相似文献   

5.
    
This article attempts to report the flow mechanism of Jeffrey nanofluid flow on a Riga plate integrating the influences of viscous dissipation, irregular heat source/sink, Brownian motion, and thermophoretic force. Nondimensionalization of mathematical model describing the flow system is accomplished by a set of compatible transformations. An accurate solution of ordinary differential equations is achieved by practicing spectral quasilinearization method. The present method is capable of giving results with good accuracy in few iterations, which infers speedy convergence. Solution‐based error norm (a measure of difference of approximate solution in two consecutive iteration level) is presented to authenticate precision of obtained approximate solution. The similarity between present approximate results and previously reported results is noted to check correctness. Obtained numerical solutions were replicated in a diagrammatic form to visualize the impact of flow parameters. Ratio of relaxation to retardation time produces an enhancing influence on momentum and nanoparticle concentration and a declining effect on the fluid temperature. Riga plate strengthens the momentum, which intensifies the transport of heat energy from boundary layer region, resulting in a reduction in fluid temperature.  相似文献   

6.
    
Minimizing entropy generation is a technique that helps improve the effectiveness of real processes by studying the associated irreversibility of system performance of nanofluid. This study examines the entropy generation analysis of electromagnetohydrodynamic radiative Casson flow induced by a stretching Riga plate in a non-Darcian porous medium under the influence of internal energy change, Arrhenius activation energy, chemical reaction, and melting heat transfer. The thermophysical features of the fluid are assumed constant in most of the literature. However, this current research bridges this gap by considering viscosity, conductivity, and diffusivity as temperature-dependent variables. Also, the exponential decaying Grinberg term is used as a resistive force in this investigation due to the electromagnetic properties of the Riga plate in the momentum conservation equation. Some suitable dimensionless variables are introduced to remodel the transport equations into unitless ones and then solved numerically by employing Galerkin Weighted Residual Method. Analyses reveal that the Casson parameter declines the fluid velocity, while the existence of the melting parameter has the opposite effect. Also, this article includes some future recommendations.  相似文献   

7.
    
Fundamental developments in nanotechnology have attracted the attention of scientists towards the interaction of nanoparticles due to their fascinating applications in thermal engineering and solar energy systems. Convinced by such motivating applications, the current research project addresses the utilization of nanoparticles in the unsteady three-dimensional chemically reactive flow of an Oldroyd-B fluid induced by a bidirectional oscillatory stretching surface. The effects of mixed convection are also considered here. The prime features of the nanofluid namely thermophoresis and Brownian motion characteristics are explored by introducing the famous Buongiorno's nanofluid model. The relevant equations for the formulated theoretical model have been reduced by the appropriate transformations for which the analytic solution is deliberated via the homotopic technique. Later on, a complete graphical analysis for distinct flow parameters is deliberated for dimensionless velocities, concentration, and temperature distributions with the relevant physical implications. Moreover, stimulating physical quantities like local Nusselt and Sherwood numbers are numerically calculated and discussed. The study emphasizes that decreasing variation in both components of velocities has been reported with an increment of relaxation time, while the impact of the retardation time constant is quite opposite. It is further claimed that the velocity distribution has an increasing tendency in the horizontal direction for a higher buoyancy ratio and mixed convection parameters. Moreover, an increment in thermophoresis parameter enhances both temperature and concentration distributions.  相似文献   

8.
    
The melting effect with the magnetic field performs a significant role in various manufacturing and industrial applications, such as welding, casting, magma-solidification, nuclear engineering, and so forth. The present study focuses on the impact of the melting effect and magnetic field with inhomogeneous heat origination and sink. The formulation of the mathematical model is done by considering fluid with hybrid nanoparticles and dust particles in two different phases. We have considered Fe2SO4 and Cu as nanoparticles dispersed in the base fluid water along with suspended dust particles. The set of partial differential equations is reduced by using apt similarity variables and boundary conditions to obtain ordinary differential equations. The numerical solution is approximated using MATLAB-bvp4c adopting the shooting technique. The impact of numerous pertinent physical parameters on the velocity and thermal profiles is plotted and deliberated. Furthermore, the rate of heat flow and friction factor is also tabulated and visualized through the graphs. Streamlines are also drawn to know the behavior of the fluid flow. The rise in values of ME quickly increases the velocity of the fluid motion but declines the thermal gradient and thickness of its related boundary layer. Also, inclining values of Pr enhance the thermal profile due to the impact of melting.  相似文献   

9.
    
This article presents the magnetohydrodynamic boundary layer flow, heat and mass transfer characteristics of a nanofluid over an inclined porous vertical plate with thermal radiation and chemical reaction. The new enhanced concentration boundary condition on the surface of the wall is considered in this analysis. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using the similarity variables and are solved numerically using the finite element method. The effect of key parameters such as magnetic parameter (M), buoyancy ratio (Nr), Prandtl number (Pr), thermal radiation (R), Brownian motion (Nb), thermophoresis (Nt), Lewis number (Le), and chemical reaction parameter (Cr) on velocity, temperature, and concentration distributions is discussed in detail and the results are shown graphically. Furthermore, the impact of these parameters on skin‐friction coefficient, Nusselt number, and Sherwood number is also investigated and the results are shown in tabular form. The developed algorithm is validated with works published previously and was found to be in good agreement. The thermal boundary layer thickness is elevated, whereas the solutal boundary layer thickness retards with the improving values of the Brownian motion parameter (Nb). The rates of nondimensional temperature and concentration both decelerate with higher values of the thermophoresis parameter (Nt).  相似文献   

10.
    
This investigation focuses on the influence of thermal radiation on the magnetohydrodynamic flow of a Williamson nanofluid over a stretching sheet with chemical reaction. The phenomena at the stretching wall assume convective heat and mass exchange. The novelty of the present study is the thermodynamic analysis in the nonlinear convective flow of a Williamson nanofluid. The resulting set of the differential equations are solved by the homotopy analysis method. We explored the impacts of the emerging parameters on flow, heat, and mass characteristics, including the rate of entropy generation and the Bejan number through graphs, and extensive discussions are provided. The expressions for skin friction, Nusselt and the Sherwood numbers are also analyzed and explored through tables. It is concluded that the rate of mass transfer may be maximized with the variation of the Williamson and chemical reaction parameters. Moreover, the entropy generation rate and the Bejan number are augmented via increasing the Williamson parameter.  相似文献   

11.
    
This study involvesthe numerical modeling of steady thermal radiation and chemical reaction on non-Newtonian fluid motion via a bidirectional stretching surface. We have taken convective boundary conditions, and heat sources on the stretching surface. The working fluid of the present study is Casson fluid (“non-Newtonian”) with couple stress. The self-similarity forms of the nonlinear thermal radiative flow model are obtained by using similarity variables. Furthermore, the numerical results are computed with the help of fourth-order Runge–Kutta–Fehlberg method with a shooting algorithm after reducing nonlinear partial differential equations have been translated into strong ordinary differential equations (ODEs). Impacts of the various flow physical parameters especially Biot number, nonlinear thermal radiation, and heat source parameters containing nonlinear ODEs are discussed in detail for distinct numerical values. A comparison of calculated results with the known numerical results made with the previously published literature is mentioned and obtained a good agreement. Finally, we found that the R e x 1 / 2 C f x $R{e}_{x}^{1/2}{C}_{fx}$ (“coefficient of skin friction”) declines along x * , y * $x* ,,y* $ directions, respectively, with β $beta $ via λ $lambda $ while the opposite direction follows M $M$ with respect to λ $lambda $ and the R e x − 1 / 2 N u x $R{e}_{x}^{-1/2}N{u}_{x}$ (“heat transfer rate”), R e x − 1 / 2 S h $R{e}_{x}^{-1/2}Sh$ (“mass transfer rate”) increase with Γ $Gamma $ via γ 1 ${gamma }_{1}$ while opposite direction follows γ 1 ${gamma }_{1}$ with respect to γ 2 ${gamma }_{2}$ .  相似文献   

12.
    
The Riga surface is composed of an electromagnetic actuator that comprises a span-wise associated array of discontinuous electrodes and an everlasting magnet mounted over a planer surface. The electro-magneto-hydrodynamic has an attractive role in thermal reactors, fluidics network flow, liquid chromatography, and micro coolers. Inspired by these applications, a laminar, two-dimensional nanofluid flow with uniform heat sink-source, thermophoretic depositions of the particles, and the Newtonian heating effect are investigated. The equations that describe the fluid motion are reduced into a system of ordinary differential equations with the help of spatial similarity variables. Numeric solutions of ordinary differential equations are executed through the Runge–Kutta–Felhberg 45 order technique via a shooting scheme. The role of various nondimensional factors on physically interesting quantities is elaborated graphically. The velocity profile rises for modified Hartmann number and decreases for porosity parameter. Thermal enhancement is high in the common wall temperature condition comparative to the case of the Newtonian heating conditions. The concentration profile is enhanced with Schmidt number, but the reverse trend is observed for the thermophoretic parameter. The rate of mass transfer is increased with Schmidt number.  相似文献   

13.
    
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14.
    
This study addresses the fully developed magnetohydrodynamic flow of non-Newtonian fluid in a microchannel using tangent hyperbolic fluid model. The physical situation has been modeled by accessing boundary layer theory along with the physical aspects of thermophoresis and Brownian motion. The heat and mass transport phenomena are depicted through graphical interpretations. The modeled equations are nondimensionalized using dimensionless variables. The obtained corresponding equations are solved by employing Runge–Kutta–Fehlberg scheme accompanied with shooting technique. The fluctuations in distinct entities of physical connotations, like, the Nusselt number, friction factor and Sherwood number are explored in this examination. A notable reduction in the concentration field of the tangent hyperbolic fluid has been obtained for a larger chemical reaction parameter. The result shows that non-Newtonian fluids exhibit higher Nusselt number than Newtonian fluids. Furthermore, a significant enhancement in Nusselt number has been attained through a rise in the power-law index and thermophoresis aspect.  相似文献   

15.
    
An analytical study is performed to investigate the thermal radiation effect on the unsteady two-dimensional magnetohydrodynamic flow of a viscoelastic incompressible fluid (Walters B ′ $B^{prime} $ fluid model) along an infinite hot vertical sheet embedded in a porous medium. Further, the addition of a heat source in the energy equation as well as a chemical reaction in the concentration equation renders the present analysis realistic in the field of engineering and technology. The governing equations of mass, momentum, energy, and concentration are solved with successive perturbation techniques. The effects of pertinent parameters on fluid velocity, temperature, concentration, and bounding surface coefficients are shown graphically and in tabular form. The salient feature of the present study is to impose control on magnetic field strength vis-à-vis electromagnetic force by regulating voltage in the electric circuit. The important findings are: the elasticity property of the fluid is more sensitive to heated bounding surface consequently free convection current in enhancing the velocity near the plate than the inherent property viscosity. This outcome contributes to the design requirement to control the flow near the heated surface, higher values of frequency parameters contribute to the attainment of a free stream state in temperature distribution. Besides the aforesaid outcome, the present model is conducive to thinning of boundary layer as the elasticity, magnetic as well as free convection parameters enhance the force coefficients at the bounding surface.  相似文献   

16.
    
This work examines the heat transfer properties of magnetohydrodynamic nanofluid flow. Through a similarity conversion, the leading structure of partial differential equations is changed to that of ordinary differential equations. A rigorous mathematical bvp4c methodology is used to generate numerical results. The purpose of this study is to characterize the different temperature, concentration, and velocity limitations on a nanofluid with a magnetic effect that is spinning. The findings for rotating nanofluid flow and heat transfer characteristics of nanoparticles are shown using graphs and tables. The influence of physical factors such as heat transfer rates and skin friction coefficients is studied. When the magnetic parameter M is raised, the velocity of the nanoliquid decreases. A rise in thermal radiation (Rd) causes the temperature graphs to grow substantially, although the concentration profiles exhibit the opposite tendency. The effect of the convective heat transfer factor Bi on temperature is shown to increase as Bi increases, but the concentration distribution decreases as Biot increases.  相似文献   

17.
    
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.  相似文献   

18.
    
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.   相似文献   

19.
    
The consequences of chemical reaction, on unsteady magnetohydrodynamic heat and mass transport laminar flows of a viscous, electrically conducting with heat-generating or absorbing fluid enclosed through a semi-infinite absorbent plate has been premeditated. The plate is assumed to be in motion with a constant velocity within the path of fluid flow. A homogeneous magnetic field performs at right angles to the absorbent surface; it is absorbing the fluid with a suction velocity varying with a certain instant of time. The nondimensional governing equations for the present configuration are solved systematically utilizing harmonic and nonharmonic terms. Graphical consequences for the velocity, temperature, and concentration profiles together supported by the investigative solutions are displayed and discussed computationally. The resulting velocity is reducing by an augment in the strength of the magnetic field and Prandtl number, whereas it is enhancing by growing in the permeability of the porous medium. The temperature delivery is reduces by an escalating heat source parameter and occurrence of fluctuation. It is significant to note that the temperature increases notably with growing the radiation absorption parameter. The influences of the chemical reaction and Schmidt number reduced the concentration in the entire fluid medium.  相似文献   

20.
    
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.  相似文献   

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