This study explores the magnetohydrodynamic(MHD)boundary layer flow of a water-based Boger nanofluid over a stretching sheet,with particular focus on the influences of nanoparticle diameter,nanolayer effects,and therm...This study explores the magnetohydrodynamic(MHD)boundary layer flow of a water-based Boger nanofluid over a stretching sheet,with particular focus on the influences of nanoparticle diameter,nanolayer effects,and thermal radiation.The primary aim is to examine how variations in nanoparticle size and nanolayer thickness affect the hydrothermal behavior of the nanofluid.The model also incorporates the contributions of viscous dissipation and Joule heating within the heat transfer equation.The governing momentum and energy equations are converted into dimensionless partial differential equations(PDEs)using appropriate similarity variables and are numerically solved using the finite element method(FEM)implemented in MATLAB.Extensive validation of this method confirms its reliability and accuracy in numerical solutions.The findings reveal that increasing the diameter of copper nanoparticles significantly enhances the velocity profile,with a more pronounced effect observed at wider inter-particle spacings.A higher solvent volume fraction leads to decreased velocity and temperature distributions,while a greater relaxation time ratio improves velocity and temperature profiles due to the increased elastic response of the fluid.Moreover,enhancements in the magnetic parameter,thermal radiation,and Eckert number lead to an elevation in temperature profiles.Furthermore,higher nanolayer thickness reduces the temperature profile,whereas particle radius yields the opposite outcome.展开更多
The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful ...The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.展开更多
Purpose:In this study,the Levenberg-Marquardt algorithm combined with a backpropagated artificial neural network(LMS-BANN)is employed to investigate the steady,incompressible flow of a Boger nanofluid between two clos...Purpose:In this study,the Levenberg-Marquardt algorithm combined with a backpropagated artificial neural network(LMS-BANN)is employed to investigate the steady,incompressible flow of a Boger nanofluid between two closely spaced symmetrical cylinders(BFCC).The research compares the effects of single and hybrid nanoparticles on velocity,pressure,and thermal distribution.Methodology:To implement LMS-BANN,the system of partial differential equations(PDEs)governing fluid dynamics is converted into a system of ordinary differential equations(ODEs)using suitable transformations.The reference dataset for LMS-BANN is generated by numerically solving these ODEs with the BVP4C method i.e Boundary Value Problem,4th-order,collocation method.Key findings:The study examines how variations in physical parameters influence the velocity and temperature profiles,utilizing regression analysis,training processes,and mean square error(MSE)graphs to evaluate and validate LMS-BANN's performance.The accuracy of the BFCC solution approximation with LMS-BANN is assessed through validation,training,and testing phases.The LMS-BANN model reported a mean square error(MSE)as small as 1.3134E−10 and practically very accurate in the prediction of the flow of fluid.Also,regression values peaked at R=1,which displays the outstanding work of the model.展开更多
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.D5000230061)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2025A1515011192).
文摘This study explores the magnetohydrodynamic(MHD)boundary layer flow of a water-based Boger nanofluid over a stretching sheet,with particular focus on the influences of nanoparticle diameter,nanolayer effects,and thermal radiation.The primary aim is to examine how variations in nanoparticle size and nanolayer thickness affect the hydrothermal behavior of the nanofluid.The model also incorporates the contributions of viscous dissipation and Joule heating within the heat transfer equation.The governing momentum and energy equations are converted into dimensionless partial differential equations(PDEs)using appropriate similarity variables and are numerically solved using the finite element method(FEM)implemented in MATLAB.Extensive validation of this method confirms its reliability and accuracy in numerical solutions.The findings reveal that increasing the diameter of copper nanoparticles significantly enhances the velocity profile,with a more pronounced effect observed at wider inter-particle spacings.A higher solvent volume fraction leads to decreased velocity and temperature distributions,while a greater relaxation time ratio improves velocity and temperature profiles due to the increased elastic response of the fluid.Moreover,enhancements in the magnetic parameter,thermal radiation,and Eckert number lead to an elevation in temperature profiles.Furthermore,higher nanolayer thickness reduces the temperature profile,whereas particle radius yields the opposite outcome.
基金Project supported by the National Natural Science Foundation of China and the Natural Science Foundationof Zhejiang Province
文摘The stream-line finite element method proposed by Luo and Tanner has been improvedand used to simulate the extrudate swell of the so called Boger fluid.The element withdiscontinuous pressure proves to be a successful choice and superior to that with continuous pressureIt is revealed that the visccsity of Newtonian solvent of the Boger fluid has a great influence on thecalculated swelling.The Weissenberg number is suggested to take the place of recoverable shear strainin Tanner′s formula to estimate the swelling of the Boger or Oldroyd-B fluids.
基金Deanship of Research and Graduate Studies at King Khalid University,KSA for funding this work through Large Research Project under grant number RGP.2/30/46.
文摘Purpose:In this study,the Levenberg-Marquardt algorithm combined with a backpropagated artificial neural network(LMS-BANN)is employed to investigate the steady,incompressible flow of a Boger nanofluid between two closely spaced symmetrical cylinders(BFCC).The research compares the effects of single and hybrid nanoparticles on velocity,pressure,and thermal distribution.Methodology:To implement LMS-BANN,the system of partial differential equations(PDEs)governing fluid dynamics is converted into a system of ordinary differential equations(ODEs)using suitable transformations.The reference dataset for LMS-BANN is generated by numerically solving these ODEs with the BVP4C method i.e Boundary Value Problem,4th-order,collocation method.Key findings:The study examines how variations in physical parameters influence the velocity and temperature profiles,utilizing regression analysis,training processes,and mean square error(MSE)graphs to evaluate and validate LMS-BANN's performance.The accuracy of the BFCC solution approximation with LMS-BANN is assessed through validation,training,and testing phases.The LMS-BANN model reported a mean square error(MSE)as small as 1.3134E−10 and practically very accurate in the prediction of the flow of fluid.Also,regression values peaked at R=1,which displays the outstanding work of the model.
