Force and Heat Generation in a Conducting Sphere in an Alternating Magnetic Field

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dc.contributor.advisorBayazitoglu, Yildizen_US
dc.contributor.committeeMemberChapman, Alan J.en_US
dc.contributor.committeeMemberAkin, John Edward.en_US
dc.contributor.committeeMemberCox, Steven J.en_US
dc.creatorSathuvalli, Udaya Bhaskar R.en_US
dc.date.accessioned2014-08-08T22:00:28Zen_US
dc.date.available2014-08-08T22:00:28Zen_US
dc.date.issued1995en_US
dc.description.abstractThe interaction of an electrically conducting sphere with a time varying magnetic field is useful in the study of "containerless" processing methods such as electromagnetic levitation melting. The fundamental quantities of interest in this interaction are the rate of heat generation in the sphere, the Lorentz force and magnetic pressure on it. These quantities depend upon the nature of the current sources that create the magnetic field, and the material properties of the sphere. In this work, the Maxwell equations for the interaction of a sphere with an arbitrary external alternating magnetic field are first formulated. Then, the density of the induced currents in the sphere is found as a function of the external current sources and the material properties of the sphere. The current density is now used to calculate the heat generated in the sphere. Next, a method to calculate the Lorentz force on an electrically conducting sphere placed in an arbitrary sinusoidally varying magnetic field is developed and a formula for the force on the sphere is given. This formula is used to derive the special case of a sphere in an axisymmetric system of circular current loops. Numerical results for the force on a sphere on the axis of a stack of loops are presented as a function of the stack geometry. The results for the heat generation and the Lorentz force obtained in this study are compared with the results obtained by a previously used model (known as the "homogeneous model") which assumes that the external magnetic field is uniform and unidirectional. It is shown that the homogeneous model is a special case of the present model and that it underestimates heat generation significantly, and overestimates the Lorentz force. In addition, as the size of the sphere decreases, the homogeneous model gives erroneous results, approaching an order of magnitude for heat generation in a very small sphere. Subsequently, a procedure to determine the magnetic pressure distribution on the surface of a levitated liquid metal droplet is developed. The pressure distribution is calculated in terms of the geometry of the coil that creates the field. Finally, the magnetic fields of helical windings that are commonly used in the laboratory for levitation melting are calculated.en_US
dc.format.extent118 ppen_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationSathuvalli, Udaya Bhaskar R.. "Force and Heat Generation in a Conducting Sphere in an Alternating Magnetic Field." (1995) Diss., Rice University. <a href="https://hdl.handle.net/1911/76506">https://hdl.handle.net/1911/76506</a>.en_US
dc.identifier.digitalSathuvalliUen_US
dc.identifier.urihttps://hdl.handle.net/1911/76506en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMechanical engineeringen_US
dc.subjectMaterials scienceen_US
dc.titleForce and Heat Generation in a Conducting Sphere in an Alternating Magnetic Fielden_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMechanical Engineering and Materials Scienceen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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