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The objective of this problem is to develop thermal models for estimating the steady-state temperature and the transient temperature history of the electrical transformer shown.
The external transformer geometry is approximately cubical, with a length of 32 mm to a side. The combined mass of the iron and copper in the transformer is 0.28 kg, and its weighted-average specific heat is 400 J/kg ∙ K. The transformer dissipates 4.0 W and is operating in ambient air at T_{∞} = 20°C, with a convection coefficient of 10 W/m^{2} ∙ K. List and justify the assumptions made in your analysis, and discuss limitations of the models. (a) Beginning with a properly defined control volume, develop a model for estimating the steady-state temperature of the transformer, T(∞). Evaluate T(∞) for the prescribed operating conditions.
(b) Develop a model for estimating the thermal response (temperature history) of the transformer if it is initially at a temperature of T_{i} = T_{∞} and power is suddenly applied. Determine the time required for the transformer to come within 5°C of its steady-state operating temperature.
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