Please give me an Idea from here Mini Submarine A spherical mini submarine of di

Question

Please give me an Idea from here

Mini Submarine A spherical mini submarine of diameter 3 m is designed to be operated by two persons. The submarine is used for deep sea exploration where the water temperature may be as low as 6 degree C. It was found that under such conditions the inside air temperature is uncomfortably cold. Specify the capacity of an electric heater that will maintain an inside temperature of 21 degree C. Power source limitation requires that the heater does not use more than 500 W. Furthermore, weight consideration limits the increase in weight to a maximum of 34 Kg. The inside heat transfer coefficient is estimated to be 12 W/m2 - degree C. However there is considerable uncertainty regarding the outside heat transfer coefficient. A very rough estimate suggests that it could be as high as 100 W/m2 - degree C,

Explanation / Answer

effective heat transfer coeffecient = 1/(1/h1 + 1/h2)) = 1/( (1/12) + (1/100)) = 10.7142857142857 W/m^2 C

difference inm temp = 21-6 = 15 degrees

area = 4*pi*r^2 = 4*3.14*1.5*1.5 = 28.26 m^2
thus power = h*t*area
=>power = 10.7142857142857*28.26*15 = 4541.78571428570823 W

not within limit.
thus we have to choose a material of the submarine that is more insulated thatn the one provided so that the heat loss is not that high.
eg:
500 = 28.26*h*15
=> h = 1.1795234725171031 (effective)

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