## THERMAL SCIENCE

International Scientific Journal

### NOVEL APPROACH TO ANALYTICAL MODELLING OF STEADY-STATE HEAT TRANSFER FROM THE EXTERIOR OF TEFC INDUCTION MOTORS

**ABSTRACT**

The purpose of this paper is to propose a novel approach to analytical modelling of steady-state heat transfer from the exterior of totally enclosed fan-cooled induction motors. The proposed approach is based on the geometry simplification methods, energy balance equation, modified correlations for forced convection, the Stefan-Boltzmann law, air-flow velocity profiles, and turbulence factor models. To apply modified correlations for forced convection, the motor exterior is presented with surfaces of elementary 3-D shapes as well as the air-flow velocity profiles and turbulence factor models are introduced. The existing correlations for forced convection from a short horizontal cylinder and correlations for heat transfer from straight fins (as well as inter-fin surfaces) in axial air-flows are modified by introducing the Prandtl number to the appropriate power. The correlations for forced convection from straight fins and inter-fin surfaces are derived from the existing ones for combined heat transfer (due to forced convection and radiation) by using the forced-convection correlations for a single flat plate. Employing the proposed analytical approach, satisfactory agreement is obtained with experimental data from other studies.

**KEYWORDS**

PAPER SUBMITTED: 2015-06-26

PAPER REVISED: 2016-04-22

PAPER ACCEPTED: 2016-04-22

PUBLISHED ONLINE: 2016-05-08

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**3**, PAGES [1529 - 1542]

- Staton, D. A., Cavagnino, A., Convection heat transfer and flow calculations suitable for electric machines thermal models, IEEE Transactions on Industrial Electronics 55 (2008), 10, pp. 3509-3516.
- Romo, J. L., Adrián, M. B., Prediction of internal temperature in three-phase induction motors with electronic speed control, Electric Power Systems Research 45 (1998), 2, pp. 91-99.
- Huai, Y., Melnik, R. V. N., Thogersen, P. B., Computational analysis of temperature rise phenomena in electric induction motors, Applied Thermal Engineering 23 (2003), 7, pp. 779-795.
- Ghai, M. L., Jakob, M., Local coefficients of heat transfer for straight fins, American Society of Mechanical Engineers Paper No. 50-S-18 (1950), pp. 1-22.
- Ghai, M. L., Heat transfer in straight fins, in: General Discussion on Heat Transfer, American Society of Mechanical Engineers, USA, 1951, pp. 180-182.
- Valenzuela, M. A., Tapia, J. A., Heat transfer and thermal design of finned frames for TEFC variable speed motors, in: IEEE Proceedings of 32nd Annual Conference on IEEE Industrial Electronics - IECON 2006, Paris, France, 2006, pp. 4835-4840.
- Valenzuela, M. A., Tapia, J. A., Heat transfer and thermal design of finned frames for TEFC variable-speed motors, IEEE Transactions on Industrial Electronics 55 (2008), 10, pp. 3500-3508.
- Fuchs, E. F., Masoum, M. A. S., Power Quality in Power Systems and Electrical Machines, second ed., Elsevier Academic Press, USA, 2008, pp. 252.
- Klimenta, D. O., Hannukainen, A., An approximate estimation of velocity profiles and turbulence factor models for air-flows along the exterior of TEFC induction motors, Thermal Science, Published online: May XX, 2016, DOI: 10.2298/TSCIXXXXXXXXXXXXX.
- Xypteras, J., Hatziathanassiou, V., Thermal analysis of an electrical machine taking into account the iron losses and the deep-bar effect, IEEE Transactions on Energy Conversion 14 (1999), 4, pp. 996-1003.
- Chen, Y.-C., Chen, B.-C., Chen, C.-L., Dong, J. Q., CFD thermal analysis and optimization of motor cooling fin design, in: Proceedings of 2005 ASME Summer Heat Transfer Conference - HT2005, San Francisco, California, USA, 2005, paper ID HT2005-72567, pp. 1-5.
- Hewitt, G. F., Hall-Taylor, N. S., Annular Two-Phase Flow, Pergamon Press, Oxford, GB, 1970.
- Balachandran, P., Engineering Fluid Mechanics, PHI Learning Private Limited, New Delhi, India, 2011, pp. 232-275.
- Webster, J. G., Eren, H., Measurement, Instrumentation, and Sensors Handbook: Spatial, Mechanical, Thermal, and Radiation Measurement, second ed., CRC Press, Taylor & Francis Group, LLC, Boca Raton, USA, 2014, pp. 57.6-57.8.
- Holland, F. A., Bragg, R., Fluid Flow for Chemical Engineers, second ed., Butterworth-Heinemann, Oxford, GB, 1995, pp. 85-88.
- Kovalev, E. B., Burkovskii, A. N., Tokarenko, A. T., Heat release in channels between frame-ribbing of enclosed asynchronous motors, Elektrotekhnika 36 (1965), 11, pp. 27-29.
- Chapman, S. J., Electric Machinery Fundamentals, fifth international ed., McGraw-Hill, Inc., 2011, pp. 307-403.
- Mills, A. F., Heat Transfer, Richard D. Irwin, INC., Homewood, IL, USA, 1992, pp. 330-333.
- Cobb, E. C., Saunders, O. A., Heat transfer from a rotating disk, Proceedings of the Royal Society of London, Series A , Mathematical and Physical Sciences 236 (1956), 1206, pp. 343-351.
- Axcell, B. P., Thianpong, C., Convection to rotating disks with rough surfaces in the presence of an axial flow, Experimental Thermal and Fluid Science 25 (2001), 1-2, pp. 3-11.
- Wiberg, R., Lior, N., Heat transfer from a cylinder in axial turbulent flows, International Journal of Heat and Mass Transfer 48 (2005), 8, pp. 1505-1517.
- Kobus, C. J., Shumway, G., An experimental investigation into impinging forced convection heat transfer from stationary isothermal circular disks, International Journal of Heat and Mass Transfer 49 (2006), 1-2, pp. 411-414.
- Kobus, C. J., Wedekind, G. L., An experimental investigation into forced, natural and combined forced and natural convective heat transfer from stationary isothermal circular disks, International Journal of Heat and Mass Transfer 38 (1995), 18, pp. 3329-3339.
- ASHRAE, Chapter 4 - Heat transfer, in: 2009 ASHRAE Handbook - Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta, USA, 2009, pp. 4.1-4.34.
- Kylander, G., Thermal modelling of small cage induction motors, Ph.D. thesis, School of Electrical and Computer Engineering, Chalmers University of Technology, Göteborg, Sweden, 1995.