Fluid Dynamics and Heat Transfer in a Hartmann Flow

1. Fluid Dynamics and Heat Transfer in a Hartmann Flow RPI Master’s Project Proposal Timothy DePuy– 9/28/2010

2. Magnetohydrodynamics Applications • Hartmann flow is a specific type of flow in the field of Magnetohydrodynamics Specific Applications • Propulsion • Plasma confinement (fusion reactors) • Liquid Metal Pumping/Breaking/Mixing • Fission (sodium reactors) • Metalolergy • Microfluidic Pumping

3. Hartmann flow 2h Pi y Po x • Hartmann flow is the flow of a conductive liquid in between two parallel plates exposed to a transverse magnetic field • The plates are infinite in the x and z directions • A Lorentz force can be calculated as a result of the flow through the magnetic and electric fields B E

4. Analysis Using ComsolMultiphysics • ComsolMultiphysics Modeling software will be used to determine the magnetic, hydrodynamic, and heat transfer solutions for the Hartmann Flow • Obtain Lorentz Force from solution to Maxwell Equations • Input Lorentz Force into incompressible steady state fluid flow solver • Input flow solution into heat transfer solver • Solutions will be obtained for both the laminar and turbulent flows • Solutions will be compared to analytical solutions from various references

5. 2h y To Ti Boundary Conditions for the Hydrodynamic and Heat Transfer Analyses Flow Solution x • A pressure gradient and Lorentz force solution will be applied to the fluid, No-Slip conditions will be applied at the boundaries • A constant wall temperature and inlet temperature will be assumed. The heat transfer rate to the wall will be calculated 2h y Po Lorentz Force F(y) Pi x Constant Tw < Ti

6. Expected Results • A “flatter” flow distribution is expected, with increased velocities closer to the walls, and decreased velocities in the center of the channel • Heat transfer solution is unknown- higher velocities at the wall may increase heat transfer however lower maximum velocities will reduce mixing

7. Increasing Levels of Complexity • Steady State Laminar Flow • Magnetic Solution • Hydrodynamic Solution • Heat transfer Solution • Steady State Turbulent Flow • Magnetic Solution • Hydrodynamic Solution • Heat transfer Solution • Transient Flow • Heat Generation Due to Magnetic /Electric Fields (Joule Heating)

8. Picture References • http://en.wikipedia.org/wiki/Magnetohydrodynamic_drive • http://www.sfc-fluidics.com/technology-in-development/mpump.php • http://www.highstrangeness.tv/6170-coconut-futures-and-thermonuclear-fusion-power.html • ElmārsBlūms, Yu. A. Mikhailov and R. Ozols, Heat and Mass Transfer in MHD Flows, World Scientific Publishing, 1987.