1. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 (a) Cross section of an electrical winding (courtesy of the Clarendon Laboratory, Oxford, UK). (b) Normalized steady-state temperature Φ = T/T max in a simulation of the middle cross section of a winding with internal heat generation and fixed temperature at the boundaries, obtained from the full model (1) and the homogenized model (2). In (b), l/L indicates the relative distance between adjoining wires. Figure Legend:

2. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 (a) Macroscopic domain ω, with insulated conductors in a square periodic lattice separated by a distance l ≪ L. (b) Microscopic domain or unit cell Ω with one conductor at its center of radius νc=εc/l surrounded by insulation to radius νi=εi/l. Figure Legend:

3. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 Solution of the two components of the cell problem (8)Γ1 and Γ2 according to the properties in Table 1 Figure Legend:

4. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 (a) Temperature distribution obtained from the full model Θ full and the homogenized model Θ MS in the middle cross section of wires distributed in a square lattice with δ = 1/31, with internal heat generation and Dirichlet boundary conditions. (b) Relative error Θfull−ΘMS over a range of δ. Figure Legend:

5. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 (a) Microscopic domain Y ∈ Ω related to the hexagonal lattice wires and (b) Γ1 distribution for the case hexagonal lattice with μ = 0.5 Figure Legend:

6. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 (a) Effective thermal conductivity k eq over a range of μ using different approaches and (b) steady-state temperature distribution for random distributions at μ = 0.5 Figure Legend:

7. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 Comparison of k eq estimated via the MS method, using the square lattice cell, with experimental measurements fromRef. [14] with (a) copper and (b) aluminum conductors at various filling ratios Figure Legend:

8. Date of download: 9/19/2016 Copyright © ASME. All rights reserved. From: Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method J. Heat Transfer. 2016;139(1):012101-012101-8. doi:10.1115/1.4034337 Transient normalized temperature Θ=T/Tmax as a function of the Fourier number τ=t(keq/CeqL2) in the center of the domain obtained with the MS homogenized model and the full model using a square lattice wire distribution with δ = 1/11 Figure Legend: