An Eulerian formalism is used to derive the energy equation for a system of magnetic nanoparticles in a fluid (ferrofluid) in the presence of uniform magnetic field. The energy equation proposed here contains an effective heat capacity, which has contributions from: (1) Brownian motion of nanoparticles, (2) magnetic field, (3) temperature, and (4) volume fraction of particles. The modified term quantitatively shows the negligible contribution of the first three factors but the significant effect of concentration of particles in change in heat capacity of ferrofluid. In order to have a better understanding of the problem, the equation is converted to a non dimensional form from which the role of each of physical parameters can be inferred.
Effect of Brownian Motion and External Magnetic Field on the Effective Heat Capacity of Ferrofluids
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Mousavi Kh., NS, Kumar, S, & Narayanaswamy, A. "Effect of Brownian Motion and External Magnetic Field on the Effective Heat Capacity of Ferrofluids." Proceedings of the ASME 2011 International Mechanical Engineering Congress and Exposition. Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B. Denver, Colorado, USA. November 11–17, 2011. pp. 635-644. ASME. https://doi.org/10.1115/IMECE2011-63985
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