•Here three-dimensional flow of Oldroyd-B is addressed over a stretched surface.•Stagnation point is considered.•Electrically conducting fluid is considered.•Ohmic heating and radiative heat flux are ...used in the mathematical modeling of energy equation.
This study addresses the three-dimensional (3D) stagnation point flow of non-Newtonian material (Oldroyd-B) with magnetohydrodynamics. Furthermore, Ohmic heating and radiative flux are used in the modeling of energy expression. The surface is convectively heated. Equal strengths of diffusions for homogeneous and heterogeneous reactions are counted. Results are computed and presented graphically. Heat transfer rate is numerically discussed through table.
Here the nonlinear differential system first converted into ordinary differential equation through implementation of appropriate similarity variables. The obtained ordinary system is tackled through homotopy technique for convergent solutions. The outcomes are presented through different graphs and discussed in section six.
The remarkable results of the present communication which is obtained from the semi analytical method i.e., “homotopy method” is summarized as
(i) Opposite impact is noticed for velocity components i.e., (f′(ξ), g(ξ)) for rising fluid parameter and rotation parameter.
(ii) The temperature is direct relation with Biot number and radiative variable.
(iii) Heat transfer rate is more versus Biot number and radiation variable.
(iv) The concentration field shows opposite impact versus homogeneous and heterogeneous parameters.
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Entropy generation minimization (EGM) and heat transport in nonlinear radiative flow of nanomaterials over a thin moving needle has been discussed. Nonlinear thermal radiation and viscous dissipation ...terms are merged in the energy expression. Water is treated as ordinary fluid while nanomaterials comprise titanium dioxide, copper and aluminum oxide. The nonlinear governing expressions of flow problems are transferred to ordinary ones and then tackled for numerical results by Built-in-shooting technique. In first section of this investigation, the entropy expression is derived as a function of temperature and velocity gradients. Geometrical and physical flow field variables are utilized to make it nondimensionalized. An entropy generation analysis is utilized through second law of thermodynamics. The results of temperature, velocity, concentration, surface drag force and heat transfer rate are explored. Our outcomes reveal that surface drag force and Nusselt number (heat transfer) enhanced linearly for higher nanoparticle volume fraction. Furthermore drag force decays for aluminum oxide and it enhances for copper nanoparticles. In addition, the lowest heat transfer rate is achieved for higher radiative parameter. Temperature field is enhanced with increase in temperature ratio parameter.
•Nonlinear radiative flow of nanomaterials over a thin moving needle has been discussed.•Nonlinear thermal radiation and viscous dissipation terms are merged in the energy expression.•Entropy generation minimization (EGM) is discussed through second law thermodynamics.•Lowest heat transfer rate is achieved for higher radiative parameter.
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Our main focus here is to analyze the chemically reactive flow of Prandtl–Eyring nanofluid. Flow is caused by linear stretching of sheet. Heat transfer characteristics are examined ...subject to nonlinear radiative flux and heat source/sink. Moreover Joule heating and dissipation effects are considered. Entropy optimization is expressed as a function of temperature, velocity and concentration. Total entropy has been calculated. Buongiorno nanofluid model which incorporates important slip mechanisms like Brownian motion and thermophoresis diffusion is used. Chemical reaction is considered along with activation energy. Suitable transformations are implemented to convert the governing expressions into ordinary one. Built-in-shooting technique is used for the solution development. Results for the velocity, entropy, temperature, Bejan number and concentration are presented graphically. Particular attention is given to quantities of engineering interests such as skin friction coefficient and Nusselt and Sherwood numbers.
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•Entropy generation in rotating flow of hybrid nanofluid between two parallel plates is discussed.•Chemical reaction with novel aspect of activation energy is accounted.•MHD fluid is ...considered.•Thermal radiation, heat generation and Joule heating are used in mathematical modeling.
Study of nanofluids has been enormously increased for the last couple of years. Regardless of some irregularity in the revealed outcomes and lacking consistency, yet the mechanisms of heat transport have been emerged as highly efficient. In the continuation of nanomaterials research, the investigators and analyst have also attempted to utilize hybrid nanomaterial recently, which is designed by suspending unique nanomaterials (nanoparticles) either in mixture or composite structure. The theory of hybrid nanofluids can be further modified for heat transport and pressure drop attributes by trade-off between disadvantages and advantages of individual suspension, ascribed to great aspect ratio, better thermal system and synergistic impact of nanomaterials. Therefore, we have conducted a theoretical attempt on MHD entropy optimized viscous hybrid nanomaterial flow between two parallel plates. The boundaries of plates are fixed with velocity and thermal slip aspects. Chemical reaction with novel aspect of activation energy is accounted. Furthermore, thermal radiation, heat generation and Joule heating are examined.
The modeled system is numerically simulated through bvp4c technique.
Behaviors of pertinent variables on the velocity, skin friction, temperature, Nusselt number, entropy generation rate and concentration are presented and discussed through different graphs. Temperature field decays against higher values of Eckert number and thermal slip variable.
It is noticed that velocity of material particles increase against larger estimations of rotation parameter. Temperature declines versus larger Prandtl and Eckert numbers. Concentration decays when an enhancement is occurred in the Lewis number. Magnitude of surface drag force upsurges for rising values of Prandtl number and radiation parameter. Furthermore, magnitude of Nusselt number enhances through larger Eckert number, magnetic number and Prandtl number.
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•Chemically reactive flow of Williamson nanofluid by a nonlinear stretched surface.•Nanomaterial model comprises thermophoresis parameter and Brownian motion.•Bidirectional nonlinear stretching sheet ...of constant thickness is considered.•Non-uniform applied magnetic field is in z-direction.
Main theme of this article is to model and analyze the outcome of chemically reactive flow of nanomaterial. Nanomaterial comprises thermophoresis and Brownian motion. Bidirectional nonlinear stretching sheet of constant thickness is considered. Rheological expressions of Williamson fluid is used to develop formulation. Boundary layer approach and suitable transformations are utilized to simplify the governing equations. Optimal homotopy analysis method OHAM is utilized for values of convergence control parameters. Tabulated values of skin friction coefficients and Nusselt and Sherwood numbers via different parameters are calculated and examined. Physical features of various pertinent parameters are argued through graphs. It is observed that velocity decays in x-direction for higher values of magnetic parameter. Temperature and concentration have contrast behavior for larger Brownian motion.
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•Here Fourier law of heat conduction (CC) model is discussed subject to Riga plate.•Stagnation point flow is considered.•The flow is generated due to linear stretching.•Series solutions are obtained ...through homotopy analysis method.
This research article proposes an improved Fourier law of heat conduction (Cattaneo-Christov) in presence of heat source/sink. The heat transport characteristics are modeled for mixed convective stagnation point flow by a Riga plate. Flow is generated due to linear stretching velocity. The partial differential system is changed to ordinary differential system through implementing appropriate transformations. Series solutions are developed through semi-analytical method called as homotopy analysis method. Present research article is related to the improved Fourier law of heat conduction (Cattaneo-Christov) over a linear stretchable surface of Riga plate when fluid saturates porous space. The main outcomes of present communication are summarized as: (i) velocity of material particles decreases subject to larger inverse Darcy-number while it enhances via velocity ratio and magnetic parameters (ii) temperature distribution as well as layer thickness enhance for higher estimations of Eckert number and heat source parameter while it decays against Prandtl number (iii) skin friction coefficient decreases through higher values of inverse Darcy number and mixed convection parameter.
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•Mixed convective of CNTs based flow of viscous material is addressed.•Both single and multi-walls carbon nanotubes is discussed.•Darcy’s law is used to characterize porous medium.•Viscous ...dissipation is used for heat transport in energy equation.
In this article we focused on the mixed convection flow of SWCNT-Water and MWCNT-Water over a stretchable permeable sheet. The nanofluid occupied porous medium. Darcy’s law is used to characterize porous medium. The impact of viscous dissipation is considered. Transformation procedure is adopted to transform the governing PDE’s system into dimensionless form. In order to solve the dimensionless PDE’s system we used numerical method known as Finite difference method. Effects of flow variables i.e porosity parameter, suction parameter, Grashof number and Reynolds number on velocity, skin friction, temperature and Nusselt number are described graphically. The obtained results shows that velocity is dominant in SWCNT-Water over MWCNT-Water. Temperature is dominant in MWCNT-Water over SWCNT-Water.
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•Entropy optimization is discussed in flow of viscous materials.•Total entropy rate is calculated through second law of thermodynamics.•Two different types of nanomaterials are used as ...nanoparticles.•Water is considered as a continuous phase liquid.
Nanomaterials have higher inspiration in the growth of pioneering heat transportation fluids and good efforts were made in this field during the recent year. Nowadays numerous scientists and researchers have focused their struggle on nanomaterials study. Nanoliquids have advanced properties which make them efficient in various applications including engine cooling, hybrid-power engine, pharmaceutical processes, refrigerator and vehicle thermal management etc. Therefore such implication in mind the entropy optimization in magnetohydrodynamic nanomaterials (TiO2 − GO) flow between two stretchable rotating disks is discussed here. Energy expression subject to Joule heating, thermal radiation and viscous dissipation is modeled. Entropy optimization rate is based upon thermodynamic second law. Here titanium dioxide (TiO2) and graphene oxide (GO) and water (H2O) are used as nanoliquids. Homogeneous and heterogeneous reactions have been accounted.
Transformation process reduced nonlinear PDE's to ordinary differential systems. Formulated systems are solved due to implementation of Newton built in shooting method.
Salient behavior of influential variables on velocity, entropy optimization, temperature, Bejan number and concentration graphically illustrated for (TiO2 and GO). Surface drag force and gradient of temperature ((Cf1, Cf2) and (Nux1, Nux2)) are numerically computed for various interesting parameters at lower and upper disks respectively. Axial and radial velocities components boost up for larger (Re) but opposite is hold for tangential velocity. Entropy optimization and temperature are increased for higher Brinkman number (Br).
A significant augmentation occurs in radial and axial velocities (f′(ξ) and f(ξ)) versus stretching parameter, while opposite is hold for tangential velocity (g(ξ)). For larger values of Reynold and Brinkman numbers the temperature increases. Temperature and entropy optimization have opposite effect for radiation parameter. Concentration has similar results for Reynold and Schmidt numbers. Entropy optimization and Bejan number for radiation parameter have similar outcome. Bejan number decays for Brinkman number.
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•Here flow of Carreau–Yasuda fluid is addressed over a porous surface.•Energy equation is modeled subject to Soret and Dofour effects.•Mixed convection is considered.•Numerical results are calculated ...via bvp4c.
Newtonian fluids can be categorized by a single coefficient of viscosity for specific temperature. This viscosity will change with temperature; it doesn’t change with strain rate. Just a small group of liquids show such steady consistency. A fluid whose viscosity changes subject to relative flow velocity is called non-Newtonian liquids. Here we have summarized a result for the flow of Carreau–Yasuda fluid over a porous stretchable surface. Mixed convection is considered. Modeling of energy expression is performed subject to Soret and Dufour effects.
The nonlinear PDE’s are changed to ODE’s through suitable transformations and then solved for numerical solutions via Built-in shooting method (bvp4c).
Variation of important variables is studied on the concentration, temperature and velocity fields. Tabular representation for study of skin friction and heat transfer rate is presented for important variables. Our results show that velocity decreases versus higher estimations of Weissenberg number, porosity parameter, buoyancy ratio and mixed convection parameter. Temperature decays via Weissenberg number and porosity parameter. Increase in concentration is noticed through higher Soret number and porosity parameter. Skin friction and heat transfer rate (Nusselt number) boosts versus larger porosity parameter and Prandtl number respectively while it decays against Weissenberg number and Dufour and Eckert number.
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•Magnetohydrodynamics flow of viscous fluid is considered over a curved surface.•Buongiorno model is used in the mathematical modeling of flow problem.•Total entropy is calculated through second law ...of thermodynamics.•Homogeneous-heterogeneous reactions are considered at the stretchable surface.
Background:Magnetohydrodynamics or hydro-magnetics (MHD) is the study of dynamics in the presence of magnetic characteristics and impact of electrically conducting liquids which has a significant applications in engineering and biomedical sciences. Liquid metals, plasma, electrolytes and salt water are the examples of such magneto-fluids. MHD liquid flow in various geometries significant to engineering sciences is an interesting and noteworthy scientific area because of applications. The above applications of magnetohydrodynamics insist the engineers and analyst to develop new mathematical modeling in the field of fluid mechanics. Therefore, we considered electrical conducting viscous fluid flow over a curved surface with second order slip. The Buongiorno model is utilized in the modeling of flow problem with thermophoretic and Brownian diffusions. The effects of viscous dissipation, thermal radiation and Joule heating (Ohmic heating) is used in the modeling of energy equation. Homogeneous-heterogeneous reactions are further considered. The energy equation is modeled.
Method:The nonlinear ODE’s are obtained through utilization of appropriate transformations and numerical results are computed via NDSolve MATHEMATICA.
Results: Velocity field is decreasing function of first order slip parameter. Both Bejan number and entropy generation is upsurged versus heterogeneous reaction parameter.
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