Research On Boundary Layer Problem Of Plane Stagnation-point Flow Of Non-Newtonian Fluids

Non-newtonian fluids are widely used in daily life and industry.This article mainly examine the rheological experiments of Xanthan gum solutions and Sodium carboxymethylcellulose(CMC)solutions,the thermal conductivity experiments of CMC solutions and Sodium p-toluenesulfonate solutions,the plane stagnation-point flow and heat transfer of upper-convected Oldroyd-B-power-law fluid,and the unsteady plane stagnation-point flow,heat and mass transfer of upper-convected Oldroyd-B nanofluid.The first part consists of four experiments.The first experiment is the rheological experiment of Xanthan gum solutions.The experimental results show that the flow curve conforms to the new constitutive model established,which is Oldroyd-B-power-law fluid.The second experiment is the rheological experiment of CMC solutions.The experimental results show that the flow curve conforms to the Oldroyd-B fluid constitutive model.The third experiment is the thermal conductivity experiment of CMC solutions.Through experiments,it is found that thermal conductivity with CMC solutions declines linearly as temperature rises.The fourth experiment is about the thermal conductivity experiment with Sodium p-toluenesulfonate solutions as well.The experimental data reveals that the thermal conductivity about this solution reduces with the magnify of concentration and presentes a linear function.In the second part,according to the results of rheological experiment of Xanthan gum solutions,the plane stagnation-point flow and heat transfer of upper-convected Oldroyd-B-power-law fluid along a stretching sheet is discussed.In the process of heat transfer,a new relaxation-retardation heat flux model is proposed considering the effect of retardation time.In addition,the influence of velocity gradient on heat flux is explored by analogy with the Oldroyd-B-power-law fluid constitutive model.Governing equations are changed into the ordinary differential equations through the appropriate similarity transformations,which are solved analytically by Differential Transform Method with Base Function Method(DTM-BF)and Double-parameter Transformation Expansion Method with Base Function Method(DPTEM-BF),respectively.Impacts of a series of parameters over the plane stagnation-point flow and heat transfer are discussed detailedly through the value of power-law index obtained from the rheological experiments.The third part scrutinizes the unsteady plane stagnation-point flow,heat and mass transfer of upper-convected Oldroyd-B nanofluid towards the stretching sheet.Based on the experimental results of the thermal conductivity of CMC solutions,it is considered that the thermal conductivity is a linear function of temperature.On the basis of the Cattaneo-Christov double-diffusion model,the new relaxation-retardation double-diffusion model is presented,which not only considers the influence of relaxation time,but also analyzes the impact of retardation time.The governing equations are changed into ordinary differential equations with pseudo-similarity transformations and settled by Homotopy Analysis Method(HAM).Impacts of a set of parameters with velocity,temperature and concentration curves are investigated through graphs and tables.