This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquir...This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquired from the partial differential equations,which are resulting from conservation of momentum,energy and species.By means of similarity transformations these ODEs were alerted into dimensionless form and solved numerically by means of bvp4c solver.The effects of different parameters on velocity,temperature,and concentration profiles were examined and discussed in depth by means of graphs and tables.The outcomes indicate that the velocity profile along both x and y directions augment with higher values of viscoelastic parameter.The results also confirm that an increment in the values of ratio parameter tends to grow up the velocity profile alongside y-direction.However,the velocity profile along x-direction slows down with increment in the value of third order slip parameter.Also,the results illustrate that diminution in temperature is observed for higher Sc in the region of boundary layer.Besides,both temperature and concentration can be improved via higher Biot number.The upshots also portrayed that the local skin friction coefficient augmented within mounting values of viscoelastic fluid parameter.Furthermore,for finer values of Biot number both local Nusselt number and the local Sherwood number are enlarged.In addition,the most favorable agreement is observed among the results of the present study and those of the earlier studies.展开更多
In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an invest...In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.展开更多
文摘This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquired from the partial differential equations,which are resulting from conservation of momentum,energy and species.By means of similarity transformations these ODEs were alerted into dimensionless form and solved numerically by means of bvp4c solver.The effects of different parameters on velocity,temperature,and concentration profiles were examined and discussed in depth by means of graphs and tables.The outcomes indicate that the velocity profile along both x and y directions augment with higher values of viscoelastic parameter.The results also confirm that an increment in the values of ratio parameter tends to grow up the velocity profile alongside y-direction.However,the velocity profile along x-direction slows down with increment in the value of third order slip parameter.Also,the results illustrate that diminution in temperature is observed for higher Sc in the region of boundary layer.Besides,both temperature and concentration can be improved via higher Biot number.The upshots also portrayed that the local skin friction coefficient augmented within mounting values of viscoelastic fluid parameter.Furthermore,for finer values of Biot number both local Nusselt number and the local Sherwood number are enlarged.In addition,the most favorable agreement is observed among the results of the present study and those of the earlier studies.
基金Supported by the National Natural Science Foundations of China under Grant Nos.21576023,51406008the National Key Research Program of China under Grant Nos.2016YFC0700601,2016YFC0700603,and 2016YFE0115500
文摘In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic(MHD) flow and heat transfer of an incompressible generalized Burgers' fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers' fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm,whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ_1 and retardation time λ_3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness.
