The objective of this problem is to develop thermalmodels

Chapter 5, Problem 5.40

(choose chapter or problem)

The objective of this problem is to develop thermalmodels for estimating the steady-state temperature andthe transient temperature history of the electrical trans-former shown.The external transformer geometry is approximatelycubical, with a length of 32 mm to a side. The com-bined mass of the iron and copper in the transformer is0.28 kg, and its weighted-average specific heat is400 J/kg?K. The transformer dissipates 4.0 W and isoperating in ambient air at T??20C, with a convec-tion coefficient of 10 W/m2?K. List and justify theassumptions made in your analysis, and discuss limita-tions of the models.(a) Beginning with a properly defined control volume,develop a model for estimating the steady-statetemperature of the transformer, T(?). EvaluateT(?) for the prescribed operating conditions.(b) Develop a model for estimating the thermalresponse (temperature history) of the transformer ifit is initially at a temperature of Ti?T?and poweris suddenly applied. Determine the time requiredfor the transformer to come within 5C of itssteady-state operating temperature.