Asubmarine is submerged and cruising at 10 m/s (~ 20 knots). if the engines are supplying 1.67 mw of power to propel the submarine at cruising speed, estimate the average heat transfer coefficien

An estimate the average heat transfer coefficient is 2755 W/m^2K

Explanation:

The full question is:

"A submarine is submerged and cruising at 10 m/s (~ 20 knots). If the engines are supplying 1.67 MW of power to propel the submarine at cruising speed, estimate the average heat transfer coefficient between the submarine and sea if the surface area of the sub is 3140 m^2. The properties of seawater are approximately given by water at 10 C, density = 1000 kg/m^3, cp = 4189 J/kg-K, viscosity = 1225 • 10^-6 kg/m-s, k = 0.59 W/m-K and Pr = 8.81. (5200 W/m2-K)"

For this estimation we can approximate the surface area of the submarine to be the one of a sphere, thus we have

So its diameter is approximately

Thus the Reynolds number is:

Replacing values

Since we have a very high Reynolds number we know the flow is turbulent thus we can use a correlation like Dittus-Boelter

Where the Nussel number can be written as

So we have

Replacing values we get

So we get an estimate the average heat transfer coefficient as 2755 W/m^2K