Strain Rate Dependence of Heat Transfer as Applied to Planar Poiseuille Flow

Principal Investigator

Denis J. Evans

Research School of Chemistry

If a fluid is forced to flow between two stationary flat plates the fluid will develop a velocity gradient between the plates. Conventional hydrodynamics predicts the velocity profile will be quartic in the separation distance. As the fluid flows viscous heating will also occur. This project aims to study viscous heating in some detail.


Billy D. Todd

Karl Travis

Peter Daivis

Research School of Chemistry


r61 - VPP, PC

What are the results to date and the future of the work?

This project was initiated to investigate the coupling of the heat flux vector to the strain rate in a simulation of planar Poiseuille flow. The original aims of the project have now been achieved, and a coupling of the heat flux to the gradient of the square of the strain rate tensor has been established. The work has been accepted for publication in Physical Review E, ('Temperature Profile for Poiseuille flow', 'Departure from Navier-Stokes hydrodynamics in confined fluids'). Another paper is to appear in Physica A ('Poiseuille Flow of Molecular Fluids') while a fourth is to appear in Journal of Chemical Physics ('A study of viscosity inhomogeneity in porous media').

The next phase of this project involves a closer examination of the coupling coefficient x, which couples the strain rate to the heat flux. In particular, we need to investigate the dependence of this coefficient on the size of the simulation cell, as well as examine the behaviour of x as a function of thermodynamic state point. These simulations are extremely time consuming to perform, and will require literally thousands of hours of supercomputer time.

What computational techniques are used?

The basic technique employed is nonequilibrium molecular dynamics. We simulate atomic and molecular liquids sandwiched between molecular walls. We also plan to calculate the coupling coefficient from the so-called sinusoidal tranverse force algorithm using the TTCF formalism. This should improve efficiency enormously for weak fields.


Daivis, P.J., Travis K.P. and Todd B.D., A technique for the calculation of mass, energy and momentum densities at planes in molecular dynamics simulations,

Journal of Chemical Physics, 104, 9651-9653 (1996).

Todd, B.D. and Evans, D.J., Mass and energy transport through slit pores: Application to planar Poiseuille flow, In Adsorption, Phase Transitions and Transport in Porous Materials (Eds A. Fuchs, N.Quirke), CECAM Workshop, Paris, September 1995, Molecular Simulation, 17, 317-332 (1996).
Travis, K.P., Daivis, P.J. and Evans, D.J., Erratum: Thermostats for molecular fluids undergoing shear flow: Application to liquid chlorine ,Journal of Chemical Physics, 105, 3893-3894 (1996).

- Appendix A