The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface genera...The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method(OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.展开更多
In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differen...In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.展开更多
The two-dimensional flow of a viscous nanofluid is investigated. The flow is caused by a nonlinear stretching surface with the slip effects of the velocity, the temperature, and the concentration. The fluid is electri...The two-dimensional flow of a viscous nanofluid is investigated. The flow is caused by a nonlinear stretching surface with the slip effects of the velocity, the temperature, and the concentration. The fluid is electrically conducted in the presence of an applied magnetic field. Appropriate transformations reduce the nonlinear partial differential system to an ordinary differential system. The convergent solutions of the governing nonlinear problems are computed. The results of the velocity, the temperature, and the concentration fields are calculated in series forms. The effects of the different parameters on the velocity, the temperature, and the concentration profiles are shown and analyzed. The skin friction coefficient, the Nusselt number, and the Sherwood number are also com-puted and investigated for different embedded parameters in the problem statements.展开更多
A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using su...A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.展开更多
In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation ...In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined.The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method(GFEM)is used to solve the proposed problem.The effect of local Deborah numbers 0,and ft.local buoyancy parameter z,Prandtl number Pr,Deborah number y,and heat generation/absorption parameter<5 on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms.The result shows the enlargement in the local buoyancy parameter A will improve the velocity field and the heat transfer rate of the boundary layer flow.Moreover,our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect.The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.展开更多
Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transfor...Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by finite difference technique known as Keller Box method. The various parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic parameter (M), Casson parameter (β) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Casson fluid parameter (β) decreased both the fluid velocity and temperature whereas an increase in (β) increased both the heat transfer rate and wall skin-friction coefficient.展开更多
The objective of this work is to examine how temperature-dependent thermal conductivity and concentration-dependent molecular diffusion affect Reiner-Philippoff nanofluid flow past a nonlinear stretching sheet. At the...The objective of this work is to examine how temperature-dependent thermal conductivity and concentration-dependent molecular diffusion affect Reiner-Philippoff nanofluid flow past a nonlinear stretching sheet. At the interface of the elongated surface zero-mass flux and melting heat condition are incorporated. The formulated mathematical problem is simplified by implementing suitable similarity transformations. For the numerical solution bvp4c is utilized. The parameters emerging in the model are discussed versus allied profiles through graphical illustrations. It is perceived that the velocity of the fluid decays on incrementing the Bingham number. The gyrotactic microorganism profile declines on amplifying the Peclet number. The validation of the proposed model is also added to this study. .展开更多
This work investigates thermal enhancement in fluid flow over a nonlinear stretching sheet.The thickness of the sheet is variable and the flow of the fluid is affected by solar radiation energy with Thompson and Troia...This work investigates thermal enhancement in fluid flow over a nonlinear stretching sheet.The thickness of the sheet is variable and the flow of the fluid is affected by solar radiation energy with Thompson and Troian slip effects.The flow is magnetized by applying a magnetic field in the normal direction to the flow system.Moreover,thermal transport is controlled by incorporating the Cattaneo-Christov heat fluid model into the flow problem.The governing equations,initially framed in their dimensional form,are meticulously transformed into a dimensionless framework to simplify the analysis.These dimensionless equations are then solved using the homotopy analysis method(HAM).It is observed in this study that upsurges in the stagnation parameter,critical shear rate and velocity slip factor augment the velocity distribution while reducing the thermal profiles.The velocity distribution deteriorates while the thermal profiles are amplified with expansions in the magnetic factor and power law index.The thermal distribution also increases with rising Prandtl number and radiation factor.Augmentation of the power-law index,velocity slip parameter,critical shear rate,magnetic factor and stagnation parameter leads to an increased Nusselt number.The modeled problem is validated by comparing the current results with established work for different values of nonlinear stretching factor n in terms of the drag force and thermal flow rate at η=0,and a good agreement is observed between the current and established results.展开更多
This article manages Darcy-Forchheimer 3D flow of water based carbon nanomaterial(CNTs).A bidirectional nonlinear stretchable surface has been utilized to make the flow.Disturbance in permeable space has been represen...This article manages Darcy-Forchheimer 3D flow of water based carbon nanomaterial(CNTs).A bidirectional nonlinear stretchable surface has been utilized to make the flow.Disturbance in permeable space has been represented by Darcy Forchheimer(DF)expression.Heat transfer mechanism is explored through convective heating.Outcomes for SWCNT and MWCNT have been displayed and compared.The reduction of partial differential framework into nonlinear common differential framework is made through reasonable variables.Optimal series scheme is utilized for arrangements advancement of associated flow issue.Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables.Moreover surface drag coefficients and heat transfer rate are analyzed through plots.展开更多
Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments.A Cass...Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments.A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation.Slip boundary conditions are used for velocity,temperature and concentration of the nanoparticles.Brownian diffusion and thermophoresis is attended.An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid.The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity.A fourth order Runge-Kutta(RK)scheme is enforced to solve the system numerically.Graphs are prepared for various progressive values of non-dimensionalized parameters whereas;variation in wall drag factor,heat and mass transfer rates is analyzed through numerical data.Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow.Temperature is found as a progressive function for the Brownianmotion factor and thermophoresis.The magnitude of wall drag factor,heat transfer and masstransfer rates shows reduction for progressive values of slip parameters.展开更多
文摘The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy–Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method(OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.
文摘In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.
文摘The two-dimensional flow of a viscous nanofluid is investigated. The flow is caused by a nonlinear stretching surface with the slip effects of the velocity, the temperature, and the concentration. The fluid is electrically conducted in the presence of an applied magnetic field. Appropriate transformations reduce the nonlinear partial differential system to an ordinary differential system. The convergent solutions of the governing nonlinear problems are computed. The results of the velocity, the temperature, and the concentration fields are calculated in series forms. The effects of the different parameters on the velocity, the temperature, and the concentration profiles are shown and analyzed. The skin friction coefficient, the Nusselt number, and the Sherwood number are also com-puted and investigated for different embedded parameters in the problem statements.
基金UGC,New Delhi,India under the Special Assistance Programme DSA Phase-1
文摘A boundary layer analysis is presented for non-Newtonian fluid flow and heat transfer over a nonlinearly stretching surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained with the shooting method. The effect of increasing Casson parameter is to suppress the velocity field. However the temperature is enhanced with the increasing Casson parameter.
文摘In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined.The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method(GFEM)is used to solve the proposed problem.The effect of local Deborah numbers 0,and ft.local buoyancy parameter z,Prandtl number Pr,Deborah number y,and heat generation/absorption parameter<5 on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms.The result shows the enlargement in the local buoyancy parameter A will improve the velocity field and the heat transfer rate of the boundary layer flow.Moreover,our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect.The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.
文摘Study to analyze the MHD stagnation point flow of a Casson fluid over a nonlinearly stretching sheet with viscous dissipation was carried out. The partial differential equations governing this phenomenon were transformed into coupled nonlinear ordinary differential equations with suitable similarity transformations. These equations were then solved by finite difference technique known as Keller Box method. The various parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic parameter (M), Casson parameter (β) and non linear stretching parameter (n) determining the velocity and temperature distributions, the local Skin friction coefficient and the local Nusselt number governing such a flow were also analyzed. On analysis it was found that the Casson fluid parameter (β) decreased both the fluid velocity and temperature whereas an increase in (β) increased both the heat transfer rate and wall skin-friction coefficient.
文摘The objective of this work is to examine how temperature-dependent thermal conductivity and concentration-dependent molecular diffusion affect Reiner-Philippoff nanofluid flow past a nonlinear stretching sheet. At the interface of the elongated surface zero-mass flux and melting heat condition are incorporated. The formulated mathematical problem is simplified by implementing suitable similarity transformations. For the numerical solution bvp4c is utilized. The parameters emerging in the model are discussed versus allied profiles through graphical illustrations. It is perceived that the velocity of the fluid decays on incrementing the Bingham number. The gyrotactic microorganism profile declines on amplifying the Peclet number. The validation of the proposed model is also added to this study. .
基金supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446)。
文摘This work investigates thermal enhancement in fluid flow over a nonlinear stretching sheet.The thickness of the sheet is variable and the flow of the fluid is affected by solar radiation energy with Thompson and Troian slip effects.The flow is magnetized by applying a magnetic field in the normal direction to the flow system.Moreover,thermal transport is controlled by incorporating the Cattaneo-Christov heat fluid model into the flow problem.The governing equations,initially framed in their dimensional form,are meticulously transformed into a dimensionless framework to simplify the analysis.These dimensionless equations are then solved using the homotopy analysis method(HAM).It is observed in this study that upsurges in the stagnation parameter,critical shear rate and velocity slip factor augment the velocity distribution while reducing the thermal profiles.The velocity distribution deteriorates while the thermal profiles are amplified with expansions in the magnetic factor and power law index.The thermal distribution also increases with rising Prandtl number and radiation factor.Augmentation of the power-law index,velocity slip parameter,critical shear rate,magnetic factor and stagnation parameter leads to an increased Nusselt number.The modeled problem is validated by comparing the current results with established work for different values of nonlinear stretching factor n in terms of the drag force and thermal flow rate at η=0,and a good agreement is observed between the current and established results.
文摘This article manages Darcy-Forchheimer 3D flow of water based carbon nanomaterial(CNTs).A bidirectional nonlinear stretchable surface has been utilized to make the flow.Disturbance in permeable space has been represented by Darcy Forchheimer(DF)expression.Heat transfer mechanism is explored through convective heating.Outcomes for SWCNT and MWCNT have been displayed and compared.The reduction of partial differential framework into nonlinear common differential framework is made through reasonable variables.Optimal series scheme is utilized for arrangements advancement of associated flow issue.Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables.Moreover surface drag coefficients and heat transfer rate are analyzed through plots.
文摘Present article aims to discuss the characteristics of Casson type nanofluid maintained to flow through porous medium over non-linear stretching surface in the perspective of heat and mass transfer developments.A Casson type incompressible viscous nanofluid passes through the given porous medium via Darcy-Forchheimer relation.Slip boundary conditions are used for velocity,temperature and concentration of the nanoparticles.Brownian diffusion and thermophoresis is attended.An induced magnetic field effect is involved to accentuate the thermo-physical characteristics of the nanofluid.The model incorporates boundary layer formulations and small magnetic Reynolds for practical validity.A fourth order Runge-Kutta(RK)scheme is enforced to solve the system numerically.Graphs are prepared for various progressive values of non-dimensionalized parameters whereas;variation in wall drag factor,heat and mass transfer rates is analyzed through numerical data.Results indicate that momentum boundary layer reduces for stronger inertial impact and the resistance offered by the porous media to the fluid flow.Temperature is found as a progressive function for the Brownianmotion factor and thermophoresis.The magnitude of wall drag factor,heat transfer and masstransfer rates shows reduction for progressive values of slip parameters.
