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Response surface optimization of heat transfer rate in Falkner-Skan flow of ZnO ? EG nanoliquid over a moving wedge: Sensitivity analysis
In this work, the optimization of the heat transfer rate in the Falkner-Skan flow of ethylene glycol-based ZnO nanoliquid passing through a moving wedge is performed using the Response Surface Methodology (RSM). The experimentally estimated nanoliquid properties are included in the calculations for realistic modeling. The heat transfer rate is optimized through the use of the numerical experiment based on the face-centered central composite design (CCF). The sensitivity of the heat transfer rate is evaluated using the obtained quadratic model. The impact of the relevant parameters is displayed graphically using the finite difference method-based solution procedure and analyzed in detail. The interactive impacts of the key parameters are also evaluated using three-dimensional surface plots. The maximum sensitivity of the heat transfer rate is towards the moving wedge parameter. The optimized rate of heat transfer occurs at the high levels of the radiation aspect, moving wedge parameter, and nanoparticle volume fraction. The interactive impacts of the nanoparticles volume fraction and the Falkner-Skan index were found to be non-linear. The movement of the wedge was found to have a significant impact on both the flow field and the rate of heat transfer. 2021 Elsevier Ltd -
Flow of nanoliquid past a vertical plate with novel quadratic thermal radiation and quadratic Boussinesq approximation: Sensitivity analysis
The effects of quadratic thermal radiation and quadratic Boussinesq approximation are investigated on the heat transport of a 36 nm Al2O3 ? H2O nanofluid over a vertical plate. The modified Buongiorno model is used in the analysis that includes the effectual thermophysical properties of the nanofluid and the key slip mechanisms. Experimentally verified correlations are used for the thermophysical properties. The reduced nonlinear differential problem is solved numerically by the Finite Difference Method (FDM). Flow profiles are displayed and analyzed for changes in dimensionless parameters. Further, the heat transfer flux at the wall is analyzed for interactive impacts of the buoyancy ratio, Brownian random motion, and thermophoresis parameters using the face-centered Central Composite Design (CCD) of the Response Surface Methodology (RSM). A sensitivity analysis is carried out for the heat transfer flux of the nanoliquid. Quadratic thermal radiation was found to improve the temperature profile. Furthermore, the mechanisms of Brownian random motion and thermophoresis have a negative sensitivity towards the rate of heat transfer. In various thermal applications like solar collectors, the density variation in terms of temperature differences is significantly high. Such phenomena can be accurately modeled by utilizing the quadratic Boussinesq approximation and the novel quadratic thermal radiation aspect. 2020 Elsevier Ltd -
Effects of chemical reaction and partial slip on the three-dimensional flow of a nanofluid impinging on an exponentially stretching surface
The three-dimensional mixed convection boundary layer flow of a nanofluid induced by an exponentially stretching sheet is numerically investigated in the presence of thermal radiation, heat source/sink and first-order chemical reaction effects. The adopted nanofluid model incorporates the effects of Brownian motion and thermophoresis into the mathematical model. The first-order velocity slip boundary conditions are also taken into account. The governing boundary layer equations are transformed into a set of nonlinear ordinary differential equations by employing suitable similarity variables. The resultant equations are solved numerically using the Runge-Kutta-Fehlberg method. Obtained solutions are compared with previous results in a limiting sense from the literature, demonstrating an excellent agreement. To show the typical trend of the solutions, a parametric study is conducted. The axial velocity, transverse velocity, temperature and nanoparticle volume fraction profiles as well as the skin-friction coefficient, Nusselt and Sherwood numbers are demonstrated graphically as a representative set of numerical results and discussed comprehensively. 2017, SocietItaliana di Fisica and Springer-Verlag Berlin Heidelberg. -
Significance of exponential space- and thermal-dependent heat source effects on nanofluid flow due to radially elongated disk with Coriolis and Lorentz forces
In this paper, the nanofluid flow near an infinite disk which stretches in the radial direction in the presence of exponential space-based heat source (ESHS) and thermal-based heat source (THS) is investigated. The Brownian motion and thermophoresis effects are accounted to study the nanofluids. Effects of radial magnetism and the Coriolis force are also deployed. The pertinent nonlinear equations are approximated under boundary layer notion and modified von Km transformations. The subsequent nonlinear differential system is treated via shooting method. The impacts of controlling parameters on flow profiles are discussed and depicted with the aid of graphs. Results show that as the ESHS and THS parameters increase, the thermal field increases. However, ESHS phenomenon is highly influential than THS phenomenon on energy transport and its gradient. Further, it is found that thermophoresis slip mechanism has more effect on heat transport rate than the Brownian motion. 2019, Akadiai Kiad Budapest, Hungary. -
Nonlinear convective and radiated flow of tangent hyperbolic liquid due to stretched surface with convective condition
The current study compacts with effect of nonlinear convection and radiation on tangent hyperbolic fluid flow of through a convectively heated vertical surface. The converted set of boundary layer equations are solved numerically by Runge-Kutta-Fehlberg method. The effect of various pertinent parameters on flow and heat transfer characteristics are discussed with tabulated numerical values and deliberate figures. Additionally, the skin friction coefficient and Nusselt number are also presented. We noticed that, the skin friction factor and heat transfer rates are higher in presence of nonlinear convection than its absence. Further, velocity profile decreases by increasing power law index but establishes opposite results for skin friction. 2017 -
Dynamics of magneto-nano third-grade fluid with brownian motion and thermophoresis effects in the pressure type die
The non-transient dynamics of the non-Newtonian third-grade liquid driven by pressure type die in the presence of nanoparticles is studied. The fluid is dissipating and its properties are taken as unvarying. The governing partial differential equations system is developed and they are numerically solved after non-dimensionalization. The significance of pertinent parameters on flow fields is analyzed and discussed. The thermal field shows dual behaviour in the flow domain due to the impact of magnetism, Brownian motion and thermophoresis. 2019 by American Scientific Publishers All rights reserved. -
Nonlinear convection in nano Maxwell fluid with nonlinear thermal radiation: A three-dimensional study
The combined effects of nonlinear thermal convection and radiation in 3D boundary layer flow of non-Newtonian nanofluid are scrutinized numerically. The flow is induced by the stretching of a flat plate in two lateral directions. The mechanism of heat and mass transport under thermophoretic and Brownian motion is elaborated via implementation of the thermal convective condition. The prevailing two-point nonlinear boundary value problem is reduced to a two-point ordinary differential problem by employing suitable similarity transformations. The solutions are computed by the implementation of homotopic scheme. At the end, a comprehensive parametric study has been conducted to analyze the typical trend of the solutions. It is found that the nanoparticle volume fraction and temperature profiles are stronger for the case of solar radiation in comparison with problem without radiation. 2017 Faculty of Engineering, Alexandria University -
Magnetohydrodynamic squeezing two-phase flow of particulate suspension in a rotating channel with transpiration cooling
This article addresses the time-dependent two-phase magnetohydrodynamic squeezing flow of dusty liquid. The fluid flow is considered in a rotating channel. The flow is constructed by squeezing of an upper plate and stretching of the lower plate and relevant equations are obtained. Numerical results are computed by utilizing shooting method along with the RKFehlberg scheme. The obtained solutions are validated by comparison with the existing analytical solutions. The effects of pertinent parameters on velocities of both phases are comprehensively discussed through graphical results. The numerical values of shear stress of both phases at lower and upper walls are also tabulated. Furthermore, the slope of the linear regression line through data points is determined in order to quantify the increase/decrease. Numerical simulations disclosed that the normal and transverse velocities are decreased due to stronger Coriolis force. It is also established that the velocities of the fluid phase are higher than that of the dust phase IMechE 2018. -
Nonlinear radiative flow of casson nanoliquid past a cone and wedge with magnetic dipole: Mathematical model of renewable energy
Solar energy is an important source of energy for all the living things. Other sources of energy such as electricity and heat can be converted from solar radiation. The recent advanced technologies are utilized to convert solar energy into electricity. In this direction, nanoliquids are quite useful because they directly absorb or scatter solar radiation. Nanofluids are selected to be best aspirant for the development of renewable energy. They are successfully utilized in the processes of renewable energy. Due to such importance of nanofluids, we investigate the effects of nanoparticles on nonlinear convective and radiative flow of Casson liquid. Two cases are considered namely flow due to a cone and flow due to a wedge. In addition to traditional temperature dependent heat source aspect an exponential space dependent heat source effect is examined. Explicitly heat/mass transfer mechanism is analysed due to prescribed linear surface temperature/particles volume fraction. Problem formulation is presented using conservation laws of mass, momentum, energy and nanoparticles volume fraction under boundary layer approximations. The solutions to the dimensionless problem are computed via Runge-Kutta-Fehlberg based shooting method. Results are plotted and examined. The exponential space dependent and thermal dependent heat source aspects are dominates on thermal field. Further, heat and mass transfer rates are higher in case of flow created by cone than flow created by wedge. The liquid velocity is higher in the case of flow due to wedge than flow due to cone case. 2018 by American Scientific Publishers All rights reserved. -
Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition
This research is made to visualize the nonlinear radiated flow of hydromagnetic nano-fluid induced due to rotation of the disk. The considered nano-fluid is a mixture of water and Ti6Al4V or AA7072 nano-particles. The various shapes of nanoparticles like lamina, column, sphere, tetrahedron and hexahedron are chosen in the analysis. The irregular heat source and nonlinear radiative terms are accounted in the law of energy. We used the heat flux condition instead of constant surface temperature condition. Heat flux condition is more relativistic and according to physical nature of the problem. The problem is made dimensionless with the help of suitable similarity constraints. The Runge-Kutta-Fehlberg scheme is adopted to find the numerical solutions of governing nonlinear ordinary differential systems. The solutions are plotted by considering the various values of emerging physical constraints. The effects of various shapes of nanoparticles are drawn and discussed. 2018 Elsevier B.V. -
Analysis of a magnetic field and Hall effects in nanoliquid flow under insertion of dust particles
In this study, the two-phase hydromagnetic flow of a viscous liquid through a suspension of dust and nanoparticles is considered. The influence of the Hall current is also taken into account. The similarity variables are utilized to transform the problem into one independent variable. The obtained expressions in one independent variable are solved through the RungeKuttaFehlberg scheme connected with the shooting procedure. The computed results are sketched for employing multiple values of physical constraints on the temperature and velocity of the nanofluid and dust phase. The characterization of various nanoparticles like Cu, Al2O3, TiO2, and Ag on velocities and temperatures of both phases is made through plots. A comparative analysis in the limiting approach is presented to justify the present solution methodology. The range of emerging parameters is taken as 0 ? l ? 3, 0.1 ? ?t ? 3, 0 ? m ? 2.5, 0 ? M2 ? 2, 0.1 ? ?v ? 3, 0 ? ? ? 0.4, and ?0.8 ? ? ? 0.8. From the study, it is revealed that ?t has theopposite effect on the temperature of dust and nanofluid phases. The Hall parameter mraisesthe profiles of velocities in the nanoliquid and dust phases. Also, it is found that the transverse velocities h(?) and H((?) andtemperatures ?(?) and ?p(?) rise for larger ?. 2020 Wiley Periodicals, Inc. -
Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection
The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth- and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non-linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation. 2017, Shanghai University and Springer-Verlag Berlin Heidelberg. -
Marangoni convective MHD flow of SWCNT and MWCNT nanoliquids due to a disk with solar radiation and irregular heat source
Present study addresses the Marangoni transport of dissipating SWCNT and MWCNT nanofluids under the influence of magnetic force and radiation. A novel exponential space dependent heat source is considered. The flow is generated due to a disk with surface tension created by thermal gradient. The partial differential equations system governing the flow of carbon-water nanoliquids and heat transfer through Marangoni convection is established. Subsequent system is reduced to nonlinear ordinary boundary value problem via generalized Karman transformations. Numerical solutions are developed of the arising nonlinear problem via Runge-Kutta based shooting approach. Impacts of embedded parameters are focused on Nusselt number, velocity and heat transport distributions through graphical illustrations. Our simulations figured out that the heat transfer rate increased via Marangoni convection; however it is decayed by applied magnetic force. The temperature of SWCNT-H2O nanoliquid dominates MWCNT-H2O nanoliquid. 2017 Elsevier B.V. -
Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects
Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Km transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect. 2018 -
Cattaneo-Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source
Melting and exponential space dependent internal heat source effects on magnetohydrodynamic of upper convected Maxwell liquid towards a horizontal flat surface are addressed. The combined effect of Brownian motion and thermophoresis in nanofluid modeling are retained. The Cattaneo-Christov heat flux model is imposed. Impacts of thermal and solutal stratifications are also accounted. A set of similarity variables are utilized to form ordinary differential system from the prevailing partial differential equations. The problem of ordinary differential system is analyzed numerically through Runge-Kutta-Fehlberg based shooting method. Graphical results of pertinent parameters on the velocity, temperature and nanoparticle concentration are studied. Skin friction coefficient, local Nusselt number and Sherwood number are also addressed. 2017 -
Marangoni convection radiative flow of dusty nanoliquid with exponential space dependent heat source
The flow of liquids submerged with nanoparticles is of significance to industrial applications, specifically in nuclear reactors and the cooling of nuclear systems to improve energy efficiency. The application of nanofluids in water-cooled nuclear systems can result in a significant improvement of their economic performance and/or safety margins. Therefore, in this paper, Marangoni thermal convective boundary layer dusty nanoliquid flow across a flat surface in the presence of solar radiation is studied. A two phase dusty liquid model is considered. Unlike classical temperature-dependent heat source effects, an exponential space-dependent heat source aspect is considered. Stretching variables are utilized to transform the prevailing partial differential system into a nonlinear ordinary differential system, which is then solved numerically via the Runge-Kutta-Fehlberg approach coupled with a shooting technique. The roles of physical parameters are focused in momentum and heat transport distributions. Graphical illustrations are also used to consider local and average Nusselt numbers. We examined the results under both linear and quadratic variation of the surface temperature. Our simulations established that the impact of Marangoni flow is useful for an enhancement of the heat transfer rate. 2017 -
Magneto-Thermo-Marangoni convective flow of Cu-H2O nanoliquid past an infinite disk with particle shape and exponential space based heat source effects
The exponential space dependent heat source (ESHS) process is utilized to explore the thermal transport characteristics of Marangoni convective flow in a Cu-H2O nanoliquid due to an infinite disk. Flow is driven by linear temperature. Five distinct nanoparticle shapes such as sphere, tetrahedron, column, hexahedron and lamina are accounted. Impacts of Joule heating, radiation and viscous dissipation are also retained. Hamilton-Crosser's expression is employed to deploy effective thermal conductivity of nanoliquid. Multi degree partial differential equations system is reduced by Km transformations and then solved via shooting method. It is figured out that the heat transfer rate is enhanced for stronger Marangoni convection and nanoparticle volume fraction. Also, shape of the nanoparticles significantly affects the flow fields. 2017 The Authors -
Effect of viscous dissipation and joule heating on three-dimensional mixed convection flow of nano fluid over a non-linear stretching sheet in presence of solar radiation
The present exploration deals the study of viscous dissipation and Joule heating effects on three-dimensional flow and heat transfer of nanofluid over a nonlinear stretching sheet. The fluid is assumed to be electrically conducting and the flow is persuaded by a stretching of an elastic sheet in two lateral directions. The governing partial differential equations are reduced to a set of nonlinear ordinary differential equations by applying the suitable similarity transformations. The so obtained similarity equations are solved by employing the fourth-fifth order Runge-Kutta-Fehlberg method. The impact of various pertinent parameters on the velocities, temperature, skin friction coefficients and Nusselt number are computed and illustrations are provided by the inclusion of figures and tables. The present results have an excellent agreement with previously published results in a limiting sense. It is found that the heat transfer rate increases when radiation parameter is increased and the effect of nanoparticle volume fraction and thermal radiation stabilizes the thermal boundary layer growth. 2017 by American Scientific Publishers All rights reserved. -
Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study
A numerical simulation for mixed convective three-dimensional slip flow of water-based nanofluids with temperature jump boundary condition is presented. The flow is caused by nonlinear stretching surface. Conservation of energy equation involves the radiation heat flux term. Applied transverse magnetic effect of variable kind is also incorporated. Suitable nonlinear similarity transformations are used to reduce the governing equations into a set of self-similar equations. The subsequent equations are solved numerically by using shooting method. The solutions for the velocity and temperature distributions are computed for several values of flow pertinent parameters. Further, the numerical values for skin-friction coefficients and Nusselt number in respect of different nanoparticles are tabulated. A comparison between our numerical and already existing results has also been made. It is found that the velocity and thermal slip boundary condition showed a significant effect on momentum and thermal boundary layer thickness at the wall. The presence of nanoparticles stabilizes the thermal boundary layer growth. 2016, The Natural Computing Applications Forum. -
Unsteady three-dimensional MHD flow of a nano Eyring-Powell fluid past a convectively heated stretching sheet in the presence of thermal radiation, viscous dissipation and Joule heating
The purpose of this study is to investigate the unsteady magnetohydrodynamic three-dimensional flow induced by a stretching surface. An incompressible electrically conducting Eyring-Powell fluid fills the convectively heated stretching surface in the presence of nanoparticles. The effects of thermal radiation, viscous dissipation and Joule heating are accounted in heat transfer equation. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis. The highly nonlinear partial differential equations are reduced to ordinary differential equations with the help of similarity method. The reduced complicated two-point boundary value problem is treated numerically using RungeKuttaFehlberg 45 method with shooting technique. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. At the end, the effects of influential parameters on velocity, temperature and nanoparticles concentration fields are also discussed comprehensively. Further, the physical quantities of engineering interest such as the Nusselt number and Sherwood number are also calculated. 2016 University of Bahrain