Fluid Dynamics and Heat Transfer in a Hartmann FlowRPI Master’s Project ProposalTimothy DePuy – 9/28/2010

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

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 2hPi Po

B

E

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 Equations2. Input Lorentz Force into incompressible steady state fluid

flow solver3. Input flow solution into heat transfer solver• Solutions will be obtained for both thelaminar and turbulent flows• Solutions will be compared to analyticalsolutions from various references

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 ToFlow Solution

Constant Tw < Ti

x

y 2hPi PoLorentz Force F(y)

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

Increasing Levels of Complexity

1. Steady State Laminar Flow1. Magnetic Solution2. Hydrodynamic Solution3. Heat transfer Solution

2. Steady State Turbulent Flow1. Magnetic Solution2. Hydrodynamic Solution3. Heat transfer Solution

3. Transient Flow4. Heat Generation Due to Magnetic /Electric Fields (Joule

Heating)

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.