A bathosphere (a manned spherical chamber for deep-sea observation, lowered by c

Question

A bathosphere (a manned spherical chamber for deep-sea observation, lowered by cable from a ship) of inside diameter 3.4 m is at an ocean depth where the water temperature is 5°C. The wall of the bathosphere is made of 5 cm thick steel (find the properties in table A-2). The convective heat transfer coefficient between the air and the inside wall is 9.2 W/m2 and that between the water and the outside wall is 860 W/m2. After the divers return to the surface they complain to the designer that the bathosphere was chilly. If the maximum power of the heater is 2.5 kW, estimate the air temperature inside the bathosphere.

Explanation / Answer

Given: ri = 1.7m, Tw = 5oC = 278 K, hi =9.2 W/m2K, ho = 860 W/m2K, Q = 2.5 kW

ro = 1.7+0.05 = 1.75m

Ksteel = 43 W/mK

Ai = 4*3.14*1.72 = 36.32 m2

Ao = 4*3.14*1.752 =38.49 m2

So,

Q = (Ti - Tw) /(R1 + R2 + R3) ...................................(1)

Where R1 = 1/Ai*hi = 3*10-3 K/W

R2 = (ro-ri)/(4*.134*r1*r2*Ksteel) = 3.1104*10-5 K/W

R3 = 1/Ao*ho = 3.02*10-5 K/W

Substituting and solving equation (1), we get

The air temperature inside the bathosphere = Ti = 285.65326 K = 12.65326 oC

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