Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up t...Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.展开更多
The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flo...The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.展开更多
Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved ...Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved numerically by RKF-45 method.Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters.Furthermore,the skin friction coefficient and Nusselt number are also presented in Tabs.2 and 3.It is found that the heat transfer rates are advanced in occurrence of nonlinear radiation compered to linear radiation.Also,it is noticed that velocity and temperature profile increases by increasing Prandtl parameter.展开更多
The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary dif...The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.展开更多
In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing lengt...In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing length theory and a modified mixing length were established. The results show that the modified mixing length includes the introduction of a damping function for the viscous sublayer and the second-order derivative to approximate eddy velocity. The calculated dimensionless time-smoothed velocity from the model based on Prandtl mixing length is much better than the result from the concept of eddy viscosity. The calculated eddy viscosity from the model based on modified mixing length is much better than the result from the model based on the classical Prandtl mixing length theory. And the friction factor calculated from the model based on the modified mixing length agrees well with the reported empirical relationships.展开更多
The flow field inside the combustor of a scramjet is highly complicated and the related turbulent Prandtl and Schmidt numbers have a significant impact on the effective numerical prediction of such dynamics.As in many...The flow field inside the combustor of a scramjet is highly complicated and the related turbulent Prandtl and Schmidt numbers have a significant impact on the effective numerical prediction of such dynamics.As in many cases researchers set these parameters on the basis of purely empirical laws,assessing their impact(via parametric numerical simulations)is a subject of great importance.In the present work,in particular,two test cases with different characteristics are selected for further evaluation of the role played by these non-dimensional numbers:Burrows-Kurkov case and DLR case.The numerical results indicate that these parameters influence ignition location.Moreover,the temperature distribution is more sensitive to them than to H2O mass fraction and velocity distributions.展开更多
We report a numerical study of the Prandtl-number(Pr)effects in two-dimensional turbulent Rayleigh-Bénard convection.The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the ...We report a numerical study of the Prandtl-number(Pr)effects in two-dimensional turbulent Rayleigh-Bénard convection.The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number(Ra)range from 10^(7) to 10^(10).We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr,and the flow pattern becomes plume-dominated at high Pr.The evolution in flow pattern is quantified by the Reynolds number(Re),with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and-0.87 to-0.93,respectively.It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr,but their difference becomes marginal as Ra increases.For the thermal boundary layer,the spatially averaged thicknesses for all the Pr numbers can be described byδθ~Ra^(-0.30) approximately,but the local values vary a lot for different Pr,which become more uniform with Pr increasing.展开更多
基金Supported by the Natural Science Foundation of Henan Province(092300410150)the Key Youth Teacher Foundation of Department Education of Henan Province(2011GGJS-210)the Key Youth Teacher Foundation of Huanghuai University
文摘Benard convection is studied by the asymptotic expansion methods of singular perturbation theory and the classical energy methods. For ill-prepared initial data, an exact approximating 1 solution with expansions up to any order are given and the convergence rates O（εm＋1/2）and the optimal convergence rates O（εm＋1） are obtained respectively. This improves the result of J.G. SHI.
基金Institutional Fund Projects under No.(IFP-A-2022-2-5-24)by Ministry of Education and University of Hafr Al Batin,Saudi Arabia.
文摘The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.
文摘Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved numerically by RKF-45 method.Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters.Furthermore,the skin friction coefficient and Nusselt number are also presented in Tabs.2 and 3.It is found that the heat transfer rates are advanced in occurrence of nonlinear radiation compered to linear radiation.Also,it is noticed that velocity and temperature profile increases by increasing Prandtl parameter.
文摘The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.
基金Project(20736009) supported by the National Natural Science Foundation of ChinaProject(07JJ6017) supported by the Natural Science Foundation of Hunan Province, China
文摘In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing length theory and a modified mixing length were established. The results show that the modified mixing length includes the introduction of a damping function for the viscous sublayer and the second-order derivative to approximate eddy velocity. The calculated dimensionless time-smoothed velocity from the model based on Prandtl mixing length is much better than the result from the concept of eddy viscosity. The calculated eddy viscosity from the model based on modified mixing length is much better than the result from the model based on the classical Prandtl mixing length theory. And the friction factor calculated from the model based on the modified mixing length agrees well with the reported empirical relationships.
基金supported by grants from the National Natural Science Foundation of China(No.11721202).
文摘The flow field inside the combustor of a scramjet is highly complicated and the related turbulent Prandtl and Schmidt numbers have a significant impact on the effective numerical prediction of such dynamics.As in many cases researchers set these parameters on the basis of purely empirical laws,assessing their impact(via parametric numerical simulations)is a subject of great importance.In the present work,in particular,two test cases with different characteristics are selected for further evaluation of the role played by these non-dimensional numbers:Burrows-Kurkov case and DLR case.The numerical results indicate that these parameters influence ignition location.Moreover,the temperature distribution is more sensitive to them than to H2O mass fraction and velocity distributions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11961160719,11702128,91752201,and 11772362)the Shenzhen Fundamental Research Program(Grant No.JCYJ20190807160413162)+1 种基金the Fundamental Research Funds for the Central Universities(Sun Yat-sen University under Grant No.19lgzd15)the Department of Science and Technology of Guangdong Province,China(Grant No.2019B21203001).
文摘We report a numerical study of the Prandtl-number(Pr)effects in two-dimensional turbulent Rayleigh-Bénard convection.The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number(Ra)range from 10^(7) to 10^(10).We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr,and the flow pattern becomes plume-dominated at high Pr.The evolution in flow pattern is quantified by the Reynolds number(Re),with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and-0.87 to-0.93,respectively.It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr,but their difference becomes marginal as Ra increases.For the thermal boundary layer,the spatially averaged thicknesses for all the Pr numbers can be described byδθ~Ra^(-0.30) approximately,but the local values vary a lot for different Pr,which become more uniform with Pr increasing.
