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Phase II Final Report - NASA's Institute for Advanced Concepts

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Chapter 3.0 Vehicle Design<br />

3.5 Fuel Storage and Production<br />

Figure 3-152: One-dimensional Heat Transfer <strong>for</strong> Liquid Hydrogen Tank<br />

Initially the outside surface temperature of the insulation (T s ) needs to be determined. This wall<br />

temperature is based on the heat flow into the insulation from convection and radiation and heat<br />

flow to the liquid hydrogen by conduction through the insulation.<br />

Q in = Q convection + Q radiation = h(T 8 – T s ) + εσ( T 8 4 – T s 4 )<br />

Equation 3-47<br />

Q out = Q conduction = K (T s – T LH2 ) /t i<br />

Equation 3-48<br />

Where ε is the emissivity of the insulation surface, σ is the Stefan-Boltzmann constant (5.67E-8<br />

W/m 2 °K 4 ), h is the convection coefficient <strong>for</strong> the air surrounding the tank, K is the thermal conductivity<br />

of the insulation, and t i is the insulation thickness. It is assumed that the tank is in an<br />

isolated environment in which the atmosphere surrounding the tank is still. There<strong>for</strong>e, the convection<br />

coefficient is based on natural convection of the atmosphere surrounding the tank. This<br />

coefficient can be represented by the following equation:<br />

h = N UD K g / D Equation 3-49<br />

The thermal conductivity of the carbon dioxide (which composes most of the atmosphere) (K g )<br />

is a property of the fluid at a given temperature and pressure, and D is the tank diameter. The<br />

Nusselt number (N UD ) is dependent on the geometry of the tank. Expressions <strong>for</strong> this are listed<br />

<strong>for</strong> spherical and cylindrical tank shapes [205].<br />

For a sphere:<br />

N UD = 2 + 0.589 R ad 1/4 / [1 + (0.469 /PR) 9/16 ] 4/9 Equation 3-50<br />

191

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