A submarine is to be designed to provide a comfortable temperature for the crew of no less than 70 oF. The structure can be idealized as a cylinder (above), 30 ft. O.D. and 200 ft. in length (ignoring heat flow from the end caps). The wall of the submarine is a sandwich construction with a 0.75 inch thick outer layer of stainless steel, a 1.0 inch thick middle layer of fiberglass insulation, and a 0.25 inch thick inner layer of aluminum. The average sea water temperature outside the submarine is 44.5 oF and the outside film coefficient for convection 1.543E-04 BTU/sec-in2-oF. Inside the submarine, the convection film coefficient to air is 4.823E-06 BTU/sec-in2-oF.
Material Properties, thermal conductivity (in BTU/hr-ft-oF):
Stainless steel: 8.268, Fiberglass insulation: 0.028, Aluminum: 117.42
An appropriate 2D model is shown above, a symmetric slice of the
cylinder, 1 degree of 360. Use 2D solid planar, elements for the metal and insulation layers.
Be
very careful of UNITS !!
(Geometry file - ParaSolid,
available). Be sure to use 1" element thickness for the 2D model.
NOTE: Could also be solved as a 2D axisymmetric model - ParaSolid, available - representing 1" of the total cylinder length
Determine:
1) The temperature distribution through the wall of the submarine, illustrated with a temperature contour plot
2) The total heat flow (Q) through the wall of the FEA model.
2D Planar 1degree slice model |
2D axisymmetric model |
Model Plot showing 3 materials and bonded contact regions
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Environment Plot (All Boundary Conditions)
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Temperature Contour Plot
Total heat flow through the entire submarine wall:
| 2D Planar, 1 degree sector
model: Reaction Probe shows 4.5154E-05 BTU/sec entering/leaving the model |
2D Axisymmetric model: Reaction Probe shows 1.6255E-02 BTU/sec entering/leaving the model |
| Q = 360*200*12*4.5154E-05 BTU/sec = 39 BTU/sec = 140,447 BTU/hr | Q = 200*12*1.6255E-02 BTU/sec = 39 BTU/sec = 140,447 BTU/hr |
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Evaluate TEPC (each body must be checked separately) Aluminum: 3.04 % Insulation: 0.0044 % Stainless Steel: 1.19 % |
Evaluate TEPC (each body must be checked separately) Aluminum: 2.31 % Insulation: 0.003 % Stainless Steel: 1.01 % |