An Analytical Model for Non-Uniform Magnetic Field Effects on Two-Dimensional Laminar Jet Diffusion Flames

In 1846, Michael Faraday found that permanent magnets could cause candle flames to deform into equatorial disks. He believed that the change in flame shape was caused by the presence of charged particles within the flames interacting with the magnetic fields. Later researchers found that the interaction between the flame ions and the magnetic fields were much too small to cause the flame deflection. Through a force analysis, von Engel and Cozens showed that the change in the flame shape could be attributed to the diamagnetic flame gases in the paramagnetic atmosphere. Paramagnetism occurs in materials composed of atoms with permanent magnetic dipole moments. In the presence of magnetic field gradients, the atoms align with the magnetic field and are drawn into the direction of increasing magnetic field. Diamagnetism occurs when atoms have no net magnetic dipole moment. In the presence of magnetic gradient fields, diamagnetic substances are repelled towards areas of decreasing magnetism. Oxygen is an example of a paramagnetic substance. Nitrogen, carbon monoxide and dioxide, and most hydrocarbon fuels are examples of diamagnetic substances. In order to evaluate the usefulness of these magnets in altering flame behavior, a study has been undertaken to develop an analytical model to describe the change in the flame length of a laminar diffusion jet in the presence of a nonuniform magnetic field.