please solve this problem in details, don't copy solutions from other tutors. i need exact answers please. thank you

4. A 1 m long aluminum wire of diameter of 1 mm is submerged in an oil bath of temperature 27 C. The wire has an electrical resistance of 0.022/m, which generates heat when current is applied to the wire. The convection coefficient between the wire and oil bath is 470 W/ mK. Assume no radiation effects. List and justify any assumptions you make. The thermal conductivity of aluminum is 237 W/mK. Hint: Recall the relationship from your introductory physics class: Power=-REL, where I is current, Reis electrical resistance, and L is length of wire.) For aluminum, heat capacity is 903 J/kg. K, density is 2702 kg/m a) If an electric current of 80 A flows through the wire, what is the steady-state temperature of the wire? b) From the time the current is first applied, how long does it take for the wire (initially at 27 C) to reach a temperature that is within 3 C of its steady state value? For full credit, you must first derive the equation that describes the relationship between the time and the temperature of the wire