Ihave a 1.5m diameter cylindrical vessel that is 1.5m tall and is 8mm thick type 304 stainless steel (k ~ 16 w/m*k). inside of this vessel, i need to heat 4000l of water (assume starting temp of 25c and pressure of 1atm) to 90c using a heating element that covers half of the surface area of this cylinder. this heating element is insulated piping that uses a heat transfer oil with a u coefficient of 380 w/m^2*k. disregard any heat loss to the surroundings. how much time would it take the water to heat up to 90c using this heat transfer oil running through the pipes at 200c? how much power would the heat exchanger have to put out to maintain this timeframe?
sorry if this is slightly confusing, i am just looking to be put in the right direction.