Fractional Viscoelastic Non-Newtonian Fluids

Project dates: 01/01/2015 - Ongoing

An important example of a fractional dynamical system arises in the study of non-Newtonian fluids where the heterogeneity of the internal temperature and the distribution of fluid density cause the transport in a viscoelastic non-Newtonian fluid to become ’anisotropic’ when an applied external force by shear flow is applied. The classical research methods of universal application and mathematical characterization used in studying Newtonian fluids are no longer applicable because non-Newtonian fluids involve complex multi-term time fractional dynamical systems with both diffusion and time fractional diffusion terms, as well as a nonlinear reaction term.

 

 


Funding / Grants

  • National Natural Science Foundation of China (Grant No. 11772046) (2018 - 2020)

Chief Investigators

Other Team Members

Chief Investigators: Professor Liancun Zheng  

Partners

Publications

  • W. Fan, F. Liu*, X. Jiang, I. Turner (2018) Some novel numerical techniques for an inverse problem of the multi-term time fractional partial differential equation. Journal of Computational and Applied Mathematics
  • Lin Liu and F. Liu (2018) Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness. Applied Mathematics Letter
  • Lin Liu, Liancun Zheng, Yu Fan, Yanping Chen and Fawang Liu (2018) Comb model for the anomalous diffusion with dual-phase-lag constitutive relation. Communications in Nonlinear Science and Numerical Simulation
  • Ming Shen, Shurui Chen, Fawang Liu (2018) Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes. Chinese Journal of Physics
  • M Shen, L Chen, M Zhang, F Liu (2018) A renovated Buongiorno’s model for unsteady Sisko nanofluid with fractional Cattaneo heat flux. International Journal of Heat and Mass Transfer
  • L. Liu, L. Zheng*, F. Liu, X. Zhang (2016) Anomalous convection diffusion and wave coupling transport of cells on comb frame with fractional Cattaneo-Christov flux. Communications in Nonlinear Science and Numerical Simulation
  • L. Liu, L. Zheng, F. Liu, L. Ma (2018) Anomalous diffusion in finite length fingers comb frame subjected with the time and space Riesz fractional Cattaneo-Christov flux and Poiseuille flow. Journal of Computational Mathematics
  • Lin Liu, Liancun Zheng, Yanping Chen, Fawang Liu (2018) Fractional anomalous convection diffusion in comb structure with Non-Fick constitutive model. Journal of Statistical Mechanics: Theory and Experiment
  • L Liu, L Zheng, Y Chen, F Liu (2018) Fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness. Journal of Heat Transfer
  • L Liu, L Zheng, Y Chen, F Liu (2018) Anomalous diffusion in comb model with fractional dual-phase-lag constitutive relation. Computers and Mathematics with Applications
  • Liu, Lin, Zheng, Liancun, Liu, Fawang (2018) Research on macroscopic and microscopic heat transfer mechanisms based on non-Fourier constitutive model. International Journal of Heat and Mass Transfer, 127 (Part B), pp.165-172.
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  • L. Liu, L. Zheng, F. Liu, X. Zhang (2017) Heat conduction with fractional Cattaneo–Christov upper-convective derivative flux model. International Journal of Thermal Sciences
  • L. Liu, L. Zheng, F. Liu (2017) Time fractional Cattaneo-Christov anomalous diffusion in comb frame with finite length of fingers. Journal of Molecular Liquids
  • L. Liu, L. Zheng, F. Liu (2017) Temporal evolution characteristics of particles distribution and fractional order moment on backbone of comb model with Cattaneo-Christov flux. Journal of Statistical Mechanics: Theory and Experiment
  • C. Sin, L. Zheng, J. Sin, F. Liu, L. Liu (2017) Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates. Applied Mathematical Modelling
  • J. Zhao，L. Zheng，X. Chen，X. Zhang，F. Liu (2017) Unsteady Marangoni convection heat transfer of fractional Maxwell fluid with Cattaneo heat flux. Applied Mathematical Modelling
  • J. Zhao, L. Zheng*, Z. Zhang, F. Liu (2016) Unsteady natural convection boundary layer heat transfer of fractional Maxwell viscoelastic fluid over a vertical plate. International Journal of Heat and Mass Transfer
  • L Feng, F Liu, I Turner, P Zhuang (2017) Numerical methods and analysis for simulating the flow of a generalized Oldroyd-B fluid between two infinite parallel rigid plates. International Journal of Heat and Mass Transfer
  • M. Pan, L. Zheng, F. Liu, C. Liu, Xuehui Chen (2017) A spatial-fractional thermal transport model for nanofluid in porous media. Applied Mathematical Modelling
  • Yan Zhang, Haojie Zhao, Fawang Liu, Yu Bai (2018) Analytical and numerical solutions of the unsteady 2D flow of MHD fractional Maxwell fluid induced by variable pressure gradient. Computers and Mathematics with Applications
  • Y. Bai, Y. Jiang, F. Liu and Y. Zhang (2017) Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation. AIP Advences
  • S. Chen, F. Liu*, I. Turner and Xiuling Hu (2018) Numerical inversion of the fractional derivative index and surface thermal flux for an anomalous heat conduction model in a multi-layer medium. Applied Mathematical Modelling
  • L. Feng, F. Liu*, I. Turner and P. Zhuang (2017) Numerical methods and analysis for simulating the flow of a generalized Oldroyd-B fluid between two infinite parallel rigid plates. International Journal of Heat and Mass Transfer
  • M. Pan, L. Zheng*, F. Liu, Z. Zhang (2016) Lie group analysis and similarity solution for fractional Blasius flow. Communications in Nonlinear Science and Numerical Simulation
  • M. Pan, L. Zheng*, F. Liu, X. Zhang (2016) Modeling heat transport in nanofluids with stagnation point flow using fractional calculus. Applied Mathematical Modelling
  • Lin Liu, Liancun Zheng, Yanping Chen, Fawang Liu (2018) Anomalous diffusion in comb model with fractional dual-phase-lag constitutive relation. Computers and Mathematics with Applications
  • L. Liu, L. Zheng*, F. Liu and Z. Zhang (2016) An improved heat conduction model with Riesz fractional Cattaneo-Christov flux. International Journal of Heat and Mass Transfer
  • C. Ming, L. Zheng*, X, Zhang, F. Liu and V. Anh (2016) Flow and heat transfer of power law fluid over a rotating disk with generalized diffusion. International Journal of Heat and Mass Transfer
  • C. Ming, F. Liu*, L. Zheng, I. Turner and V. Anh (2016) Analytical solutions of multi-term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid. Computers and Mathematics with Applications
  • J. Zhao, L. Zheng*, X, Zhang, F. Liu (2016) Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects. International Journal of Heat and Mass Transfer
  • Zhi Cao, Jinhu Zhao, Zhijiang Wang, Liancun Zheng, Fawang Liu (2016) MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid over a moving plate. Journal of Molecular Liquids