Palm oil with a density of 1200 kg/m3 and the specific heat of 2 kJ/(kg.K) is to be heated from 20oC to 80oC before further processing. The oil placed in a vessel (vessel) cylindrical upright with a diameter of 2 meters. The height of the oil vessel inside is 2 meters. For this purpose, an electric heating element with an electrical resistance type of heat is used. The electrical resistance used is a 2 mm diameter conductor wire wrapped with magnesium oxide material with a thermal conductivity of 0.4 W/(m.K) thick 2.5 mm, then coated with the outermost metal 0.5 mm thick. Occurring power density on the outermost metal layer should not be more than 25 kW/m2. Warm-up time is expected to be only about 1.5 hours. Calculate: a) Required electrical power? (in kW) b) Rating of the heater by meter length? c) Maximum temperature of the heater element?

Palm oil with a density of 1200 kg/m³ and the specific heat of 2 kJ/(kg.K) is to be heated from 20^oC to 80^oC before further processing. The oil
placed in a vessel (vessel) cylindrical upright with a diameter of 2 meters.
The height of the oil vessel inside is 2 meters. For this purpose, an electric heating element with an electrical resistance type of heat is used.
The electrical resistance used is a 2 mm diameter conductor wire wrapped
with magnesium oxide material with a thermal conductivity of 0.4 W/(m.K) thick 2.5 mm, then coated with the outermost metal 0.5 mm thick. Occurring power density on the outermost metal layer should not be more than 25 kW/m². Warm-up time is expected to be only about 1.5 hours.

Calculate:

a) Required electrical power? (in kW)

b) Rating of the heater by meter length?

c) Maximum temperature of the heater element?