The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential e...The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential equations which governed the model are first reduced to a set of ordinary differential equations by using the similarity transformation.Next,the BVP4C solver is applied to solve the equations by considering the pertinent fluid parameters such as the permeability parameter,the magnetic parameter,the Williamson parameter,the nanoparticle volume fractions and the wall mass transfer parameter.The single(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)nanoparticles are taken as the hybrid nanoparticles.It is found that the increase in magnetic parameter in SWCNT+MCWNT hybrid nanofluid results in an increase of 72.2%on skin friction compared to SWCNT nanofluid while maintaining reducing a small number of Nusselt number.This shows the potential of the Williamson hybrid nanofluid for friction application purposes especially in transportation like braking system,flushing fluid and mechanical engineering.展开更多
The thermal and velocity slips of boundary layer of Williamson nanofluid over a stretching sheet are studied numerically.Buongiorno model is used to explore the heat transfer phenomena caused by Brownian motion and th...The thermal and velocity slips of boundary layer of Williamson nanofluid over a stretching sheet are studied numerically.Buongiorno model is used to explore the heat transfer phenomena caused by Brownian motion and thermophoresis.Using similarity transformations,the governing equations are reduced to a set of nonlinear ordinary differential equations(ODEs).These equations are solved numerically by using Shooting method.The effects of non-Newtonian Williamson parameter,velocity and thermal slip parameters,Prandtl number,Brownian parameter,Schmidt number,Lewis number,Brownian motion parameter,thermophoresis parameter on velocity,temperature and concentration fields are shown graphically and discussed.The results found that the thickness of boundary layer decreases as the slip and thermal factor parameter increases.Further,present results indicate that the nanofluid temperature and concentration are enhanced with a rise of Williamson parameter.The Nusselt number is reduced with an increase of the Lewis and Prandtl numbers.展开更多
文摘The present study numerically investigates the flow and heat transfer of porous Williamson hybrid nanofluid on an exponentially shrinking sheet with magnetohydrodynamic(MHD)effects.The nonlinear partial differential equations which governed the model are first reduced to a set of ordinary differential equations by using the similarity transformation.Next,the BVP4C solver is applied to solve the equations by considering the pertinent fluid parameters such as the permeability parameter,the magnetic parameter,the Williamson parameter,the nanoparticle volume fractions and the wall mass transfer parameter.The single(SWCNTs)and multi-walled carbon nanotubes(MWCNTs)nanoparticles are taken as the hybrid nanoparticles.It is found that the increase in magnetic parameter in SWCNT+MCWNT hybrid nanofluid results in an increase of 72.2%on skin friction compared to SWCNT nanofluid while maintaining reducing a small number of Nusselt number.This shows the potential of the Williamson hybrid nanofluid for friction application purposes especially in transportation like braking system,flushing fluid and mechanical engineering.
基金The authors gratefully acknowledge the financial supports received from Ministry of Higher Education,University Malaysia Pahang(UMP),Malaysia,through vote number RDU 150101 and RDU 170358.The second author would like to acknowledge Ton Duc Thang University,Ho Chi Minh City,Vietnam for the financial support.
文摘The thermal and velocity slips of boundary layer of Williamson nanofluid over a stretching sheet are studied numerically.Buongiorno model is used to explore the heat transfer phenomena caused by Brownian motion and thermophoresis.Using similarity transformations,the governing equations are reduced to a set of nonlinear ordinary differential equations(ODEs).These equations are solved numerically by using Shooting method.The effects of non-Newtonian Williamson parameter,velocity and thermal slip parameters,Prandtl number,Brownian parameter,Schmidt number,Lewis number,Brownian motion parameter,thermophoresis parameter on velocity,temperature and concentration fields are shown graphically and discussed.The results found that the thickness of boundary layer decreases as the slip and thermal factor parameter increases.Further,present results indicate that the nanofluid temperature and concentration are enhanced with a rise of Williamson parameter.The Nusselt number is reduced with an increase of the Lewis and Prandtl numbers.
