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 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 x y 2h Pi Po B E

4. Analysis Using Comsol Multiphysics Comsol Multiphysics Modeling software will be used to determine the magnetic, hydrodynamic, and heat transfer solutions for the Hartmann Flow 1.Obtain Lorentz Force from solution to Maxwell Equations 2.Input Lorentz Force into incompressible steady state fluid flow solver 3.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. Boundary Conditions for the Hydrodynamic and Heat Transfer Analyses 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 x y 2h Ti To Flow Solution Constant Tw < Ti x y 2h Pi Po Lorentz Force F(y)

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 1.Steady State Laminar Flow 1.Magnetic Solution 2.Hydrodynamic Solution 3.Heat transfer Solution 2.Steady State Turbulent Flow 1.Magnetic Solution 2.Hydrodynamic Solution 3.Heat transfer Solution 3.Transient Flow 4.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 Elmārs Blūms, Yu. A. Mikhailov and R. Ozols, Heat and Mass Transfer in MHD Flows, World Scientific Publishing, 1987.