We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the correspon...We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.展开更多
The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting ...The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.展开更多
The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted ...The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.展开更多
The non-Newtonian fluid model reflects the behavior of the fluid flow in global manufacturing progress and increases product performance.Therefore,the present work strives to analyze the unsteady Maxwell hybrid nanofl...The non-Newtonian fluid model reflects the behavior of the fluid flow in global manufacturing progress and increases product performance.Therefore,the present work strives to analyze the unsteady Maxwell hybrid nanofluid toward a stretching/shrinking surface with thermal radiation effect and heat transfer.The partial derivatives of the multivariable differential equations are transformed into ordinary differential equations in a specified form by applying appropriate transformations.The resulting mathematical model is clarified by utilizing the bvp4c technique.Different control parameters are investigated to see how they affect the outcomes.The results reveal that the skin friction coefficient increases by adding nanoparticles and suction parameters.The inclusion of the Maxwell parameter and thermal radiation effect both show a declining tendency in the local Nusselt number,and as a result,the thermal flow efficacy is reduced.The reduction of the unsteadiness characteristic,on the other hand,considerably promotes the improvement of heat transfer performance.The existence of more than one solution is proven,and this invariably leads to an analysis of solution stability,which validates the first solution viability.展开更多
This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into accoun...This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.展开更多
The axisymmetric stagnation point flow over a stretching/shrinking surface with second-order slip and temperature jump is studied numerically.The governing partial differential equations are transformed into ordinary(...The axisymmetric stagnation point flow over a stretching/shrinking surface with second-order slip and temperature jump is studied numerically.The governing partial differential equations are transformed into ordinary(similarity)differential equations.These equations along with the corresponding boundary conditions are solved numerically using a boundary value problem solver bvp4c in Matlab software.It is observed that dual(first and second)solutions exist for the similarity equations.The effects of different parameters on the velocity and the temperature distributions as well as the skin friction coefficient and the Nusselt number are analyzed and discussed.展开更多
Time-dependent,two-dimensional(2 D)magnetohydrodynamic(MHD)micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered.Mass and heat transfer characteristics are incorporated...Time-dependent,two-dimensional(2 D)magnetohydrodynamic(MHD)micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered.Mass and heat transfer characteristics are incorporated in the problem.A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations.The obtained equations are numerically solved by a shooting scheme in the MAPLE software.Dual solutions are observed at different values of the specified physical parameters.The stability of first and second solutions is examined through the stability analysis process.This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible.Furthermore,the natures of various physical factors on the drag force,skin-friction factor,and rate of mass and heat transfer are determined and interpreted.The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters,whereas it increases by increasing the unsteadiness parameter.The temperature of the micropolar nanofluid rises with increase in the Brownian motion,radiation,thermophoresis,unsteady and magnetic parameters,but it decreases against an increment in the thermal slip constraint and Prandtl number.The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.展开更多
We investigate the dual solutions for the MHD flow of micropolar fluid over a stretching/shrinking sheet with heat transfer. Suitable relations transform the partial differential equations into the ordinary differenti...We investigate the dual solutions for the MHD flow of micropolar fluid over a stretching/shrinking sheet with heat transfer. Suitable relations transform the partial differential equations into the ordinary differential equations.Closed forms solutions are also obtained in terms of confluent hypergeometric function. This is the first attempt to determine the exact solutions for the non-linear equations of MHD micropolar fluid model. It is demonstrated that the microrotation parameter helps in increasing Nusselt number and the dual solutions exist for all fluid flow parameters under consideration. The dual behavior of dimensionless velocity, temperature, microrotation, skin-friction coefficient,local Nusselt number is displayed on graphs and examined.展开更多
The intention of the current research is to address the conclusion of non-isothermal heterogeneous reaction on the stagnation-point flow of SWCNT-engine oil and MWCNT-engine oil nanofluid over a shrinking/stretching s...The intention of the current research is to address the conclusion of non-isothermal heterogeneous reaction on the stagnation-point flow of SWCNT-engine oil and MWCNT-engine oil nanofluid over a shrinking/stretching sheet.Further,exemplify the aspect of heat and mass transfer the upshot of magnetohydrodynamics(MHD),thermal radiation,and heat generation/absorption coefficient are exemplified.The bvp4 c from Matlab is pledged to acquire the numerical explanation of the problem that contains nonlinear system of ordinary differential equations(ODE).The impacts of miscellaneous important parameters on axial velocity,temperature field,concentration profile,skin friction coefficient,and local Nusselt number,are deliberated through graphical and numerically erected tabulated values.The solid volume fraction diminishes the velocity distribution while enhancing the temperature distribution.Further,the rate of shear stress declines with increasing the magnetic and stretching parameter for both SWCNT and MWCNT.展开更多
The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal m...The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow.The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid.The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model.The problem formulated in dimensionless form is solved by NDSolve MATHEMATICA.The graphical analysis for parameters governed by the problem is performed with physical applications.The affiliation of entropy generation and Bejan number for different parameters is inspected in detail.The numerical data for illustrating skin friction,heat and mass transfer rate is also reported.The motion of the fluid is highest for the viscosity ratio parameter.The temperature of the fluid rises via thermal Biot number.Entropy generation rises for greater Brinkman number and diffusion parameter.展开更多
This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic(MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes(NS) equations are transformed into a sim...This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic(MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes(NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation,and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.展开更多
基金LMP acknowledges financial support from ANID through Convocatoria Nacional Subvención a Instalación en la Academia Convocatoria Año 2021,Grant SA77210040。
文摘We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.
基金Project supported by the Ministry of Higher Education in Malaysia(No.FRGS/1/2012/SG04/UKM/2001/1)the Universiti Kebangsaan Malaysia(No.DIP-2012-31)
文摘The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.
基金the Ministry of Education of Malaysia(No.FRGS/1/2019/STG06/UKM/01/4)Ministry of Science of Romania(No.PN-III-P4-ID-PCE-2016-0036)。
文摘The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.
基金the Research Grant of University Kebangsaan Malaysia(No.GUP-2019-034)。
文摘The non-Newtonian fluid model reflects the behavior of the fluid flow in global manufacturing progress and increases product performance.Therefore,the present work strives to analyze the unsteady Maxwell hybrid nanofluid toward a stretching/shrinking surface with thermal radiation effect and heat transfer.The partial derivatives of the multivariable differential equations are transformed into ordinary differential equations in a specified form by applying appropriate transformations.The resulting mathematical model is clarified by utilizing the bvp4c technique.Different control parameters are investigated to see how they affect the outcomes.The results reveal that the skin friction coefficient increases by adding nanoparticles and suction parameters.The inclusion of the Maxwell parameter and thermal radiation effect both show a declining tendency in the local Nusselt number,and as a result,the thermal flow efficacy is reduced.The reduction of the unsteadiness characteristic,on the other hand,considerably promotes the improvement of heat transfer performance.The existence of more than one solution is proven,and this invariably leads to an analysis of solution stability,which validates the first solution viability.
文摘This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.
基金The authors wish to thank the reviewers for their very good comments and suggestions.The financial supports received from Ministry of Higher Education Malaysia,Malaysia(Project Code:FRGS/1/2015/SG04/UKM/01/1)Universiti Kebangsaan Malaysia,Malaysia(Project Code:DIP-2015-010)are gratefully acknowledged.
文摘The axisymmetric stagnation point flow over a stretching/shrinking surface with second-order slip and temperature jump is studied numerically.The governing partial differential equations are transformed into ordinary(similarity)differential equations.These equations along with the corresponding boundary conditions are solved numerically using a boundary value problem solver bvp4c in Matlab software.It is observed that dual(first and second)solutions exist for the similarity equations.The effects of different parameters on the velocity and the temperature distributions as well as the skin friction coefficient and the Nusselt number are analyzed and discussed.
文摘Time-dependent,two-dimensional(2 D)magnetohydrodynamic(MHD)micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered.Mass and heat transfer characteristics are incorporated in the problem.A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations.The obtained equations are numerically solved by a shooting scheme in the MAPLE software.Dual solutions are observed at different values of the specified physical parameters.The stability of first and second solutions is examined through the stability analysis process.This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible.Furthermore,the natures of various physical factors on the drag force,skin-friction factor,and rate of mass and heat transfer are determined and interpreted.The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters,whereas it increases by increasing the unsteadiness parameter.The temperature of the micropolar nanofluid rises with increase in the Brownian motion,radiation,thermophoresis,unsteady and magnetic parameters,but it decreases against an increment in the thermal slip constraint and Prandtl number.The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.
文摘We investigate the dual solutions for the MHD flow of micropolar fluid over a stretching/shrinking sheet with heat transfer. Suitable relations transform the partial differential equations into the ordinary differential equations.Closed forms solutions are also obtained in terms of confluent hypergeometric function. This is the first attempt to determine the exact solutions for the non-linear equations of MHD micropolar fluid model. It is demonstrated that the microrotation parameter helps in increasing Nusselt number and the dual solutions exist for all fluid flow parameters under consideration. The dual behavior of dimensionless velocity, temperature, microrotation, skin-friction coefficient,local Nusselt number is displayed on graphs and examined.
文摘The intention of the current research is to address the conclusion of non-isothermal heterogeneous reaction on the stagnation-point flow of SWCNT-engine oil and MWCNT-engine oil nanofluid over a shrinking/stretching sheet.Further,exemplify the aspect of heat and mass transfer the upshot of magnetohydrodynamics(MHD),thermal radiation,and heat generation/absorption coefficient are exemplified.The bvp4 c from Matlab is pledged to acquire the numerical explanation of the problem that contains nonlinear system of ordinary differential equations(ODE).The impacts of miscellaneous important parameters on axial velocity,temperature field,concentration profile,skin friction coefficient,and local Nusselt number,are deliberated through graphical and numerically erected tabulated values.The solid volume fraction diminishes the velocity distribution while enhancing the temperature distribution.Further,the rate of shear stress declines with increasing the magnetic and stretching parameter for both SWCNT and MWCNT.
文摘The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization.The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow.The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid.The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model.The problem formulated in dimensionless form is solved by NDSolve MATHEMATICA.The graphical analysis for parameters governed by the problem is performed with physical applications.The affiliation of entropy generation and Bejan number for different parameters is inspected in detail.The numerical data for illustrating skin friction,heat and mass transfer rate is also reported.The motion of the fluid is highest for the viscosity ratio parameter.The temperature of the fluid rises via thermal Biot number.Entropy generation rises for greater Brinkman number and diffusion parameter.
文摘This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic(MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes(NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation,and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.
