The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching she...The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.展开更多
Unsupervised clustering and clustering validity are used as essential instruments of data analytics.Despite clustering being realized under uncertainty,validity indices do not deliver any quantitative evaluation of th...Unsupervised clustering and clustering validity are used as essential instruments of data analytics.Despite clustering being realized under uncertainty,validity indices do not deliver any quantitative evaluation of the uncertainties in the suggested partitionings.Also,validity measures may be biased towards the underlying clustering method.Moreover,neglecting a confidence requirement may result in over-partitioning.In the absence of an error estimate or a confidence parameter,probable clustering errors are forwarded to the later stages of the system.Whereas,having an uncertainty margin of the projected labeling can be very fruitful for many applications such as machine learning.Herein,the validity issue was approached through estimation of the uncertainty and a novel low complexity index proposed for fuzzy clustering.It involves only uni-dimensional membership weights,regardless of the data dimension,stipulates no specific distribution,and is independent of the underlying similarity measure.Inclusive tests and comparisons returned that it can reliably estimate the optimum number of partitions under different data distributions,besides behaving more robust to over partitioning.Also,in the comparative correlation analysis between true clustering error rates and some known internal validity indices,the suggested index exhibited the highest strong correlations.This relationship has been also proven stable through additional statistical acceptance tests.Thus the provided relative uncertainty measure can be used as a probable error estimate in the clustering as well.Besides,it is the only method known that can exclusively identify data points in dubiety and is adjustable according to the required confidence level.展开更多
文摘The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.
文摘Unsupervised clustering and clustering validity are used as essential instruments of data analytics.Despite clustering being realized under uncertainty,validity indices do not deliver any quantitative evaluation of the uncertainties in the suggested partitionings.Also,validity measures may be biased towards the underlying clustering method.Moreover,neglecting a confidence requirement may result in over-partitioning.In the absence of an error estimate or a confidence parameter,probable clustering errors are forwarded to the later stages of the system.Whereas,having an uncertainty margin of the projected labeling can be very fruitful for many applications such as machine learning.Herein,the validity issue was approached through estimation of the uncertainty and a novel low complexity index proposed for fuzzy clustering.It involves only uni-dimensional membership weights,regardless of the data dimension,stipulates no specific distribution,and is independent of the underlying similarity measure.Inclusive tests and comparisons returned that it can reliably estimate the optimum number of partitions under different data distributions,besides behaving more robust to over partitioning.Also,in the comparative correlation analysis between true clustering error rates and some known internal validity indices,the suggested index exhibited the highest strong correlations.This relationship has been also proven stable through additional statistical acceptance tests.Thus the provided relative uncertainty measure can be used as a probable error estimate in the clustering as well.Besides,it is the only method known that can exclusively identify data points in dubiety and is adjustable according to the required confidence level.
