Solve the below problem:
Q: A submarine is to be designed to provide a comfortable temperature for the crew of no less than 70°F. The submarine can be idealized by a cylinder 30 ft in diameter and 200 ft in length. The combined heat transfer coefficient on the interior is about 2.5 Btu/(h ft2 °F), while on the outside the heat transfer coefficient is estimated to vary from about 10 Btu/(h ft2 °F) (not moving) to 150 Btu/(h ft2 °F) (top speed). For the following wall constructions, determine the minimum size in kilowatts of the heating unit required if the sea water temperatures vary from 34 to 55°F during operation. The walls of the submarine are
(a) 1/2 in. aluminum
(b) 3/4 in. stainless steel with a 1 in. thick layer fiberglass insulation on the inside and
(c) Of sandwich construction and a 3/4in. thickness of stainless steel, a 1 in. thick layer of fiberglass insulation, and a 1/4in. thickness of aluminum on the inside. What conclusions can you draw?
GIVEN
Submarine
Inside temperature (Ti) > 70°F
Can be idealized as a cylinder
Diameter (D) = 30 ft length (L) = 200 ft
Combined heat transfer coefficients
Inside ( hci ) = 2.5 Btu/(h ft2 °F)
Outside ( hco ): not moving = 10 Btu/(h ft2 °F)
Top speed: 150 Btu/(h ft2 °F)
Sea water temperature (To) varies: 34°F < to=""><>
ASSUMPTIONS
Steady state prevails
Heat transfer can be approximated as heat transfer through a flat plate with the surface area of the cylinder
Constant thermal conductivities
Contact resistance between the difference materials isnegligible
