1. (15 points) Consider a single cylindrical battery cooled by a stream of coolant fluid with a convective heat transfer coefficient, h = 100 W/ (m 2 K). The battery has a radius R = 0.1 m and thermal conductivity, k = 1 W/ (m K). Given that the battery length, L>>R, you may disregard the axial dimension and treat this problem in 1D (only radially). What is the maximum temperature that the coolant fluid needs to have, Tcool, to ensure that the battery’s internal temperature never exceeds 400 K? 2. (10 points) Assuming a coolant temperature Tcool = 350 K, use MatLab to generate a plot of the battery internal temperature as a function of radius (r) for three possible convective heat transfer coefficients: h = 10, 100, and 1000 W/ (m 2 K). 3. (10 points) You realize that the minimum achievable coolant temperature not cold enough to maintain the battery below 400K. In less than 5 sentences, explain how you could change the design of the battery and the cooling system to lower the battery internal temperature. (e. g., you may consider changes to geometry, the coolant flow rate, the battery materials, etc.). 4. (10 points) After multiple attempts to design a better battery, you realize that you cannot afford the risk of reaching high temperatures inside the batteries. You decide to design a safety mechanism that turns off the battery (i. e., it stops generating heat) if it rea