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


Principal Investigator

Denis Evans

Research School of Chemistry

Viscous heating occurs when a fluid is forced to flow between two stationary flat plates, resulting in a
temperature increase near the center of channel. Conventional hydrodynamics predicts that the temperature profile will be quartic in the plate separation distance, and the heat flux will be proportional to the temperature gradient. However, there is a small contribution to the heat flux arising in cases where the strain rate is not constant, resulting in a small perturbation in the temperature profile. This project aims to elucidate the origins of heat tranport and viscous heating.



Gary Ayton

Billy 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.

A closer examination of the coupling coefficient, motivated by the development of new thermostatting techniques for molecular dynamics computer simulations, has revealed that indeed heat can flow from one region at one temperature to another at exactly the same temperature provided that the strain rate is not constant. The mechanism for this heat transport is now understood and can be explained by a simple kinetic theory. These new results are to be published in Physical Review Letters.

The development of new thermostatting techniques is critical to this work and involves intensive testing and development. The results are of fundamental interest and address the validity of Fourier's Law in systems with non-uniform strain rates.

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

- Appendix A


coupling coefficient from the so-called sinusoidal tranverse force algorithm using the TTCF formalism. This should improve efficiency enormously for weak fields.


G. Ayton, O. G. Jepps and D. Evans, On the Validity of Fourier's Law in Systems with Non-uniform Strain Rates, to be submitted to Phys Rev. Letters.



Appendix A -