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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

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/m2 ∙ 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 Ti = T and power is suddenly applied. Determine the time required for the transformer to come within 5°C of its steady-state operating temperature.

Jun 27 2020 View more View Less

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