A spherical tank for storing liquid oxygen on the space...

A spherical tank for storing liquid oxygen on the space shuttle is to be made from stainless steel of $0.80-\mathrm{m}$ outer diameter and 5 -mm wall thickness. The boiling point and latent heat of vaporization of liquid oxygen are $90 \mathrm{~K}$ and $213 \mathrm{~kJ} / \mathrm{kg}$, respectively. The tank is to be installed in a large compartment whose temperature is to be maintained at $240 \mathrm{~K}$. Design a thermal insulation system that will maintain oxygen losses due to boiling below $1 \mathrm{~kg} /$ day.

Key Concepts

Latent Heat of Vaporization

Latent heat of vaporization is the amount of energy required to convert a substance from its liquid phase to its vapor phase at constant temperature. This concept is crucial when determining how much heat absorption can lead to the boiling of the stored liquid, thereby impacting design limits for allowable heat ingress.

Thermal Conduction

Thermal conduction is the mechanism by which heat is transferred through solid materials due to a temperature gradient. In insulation system design, understanding how heat conducts through materials is essential for calculating the heat load from a warmer environment into a cold storage system, such as a cryogenic tank.

Thermal Insulation

Thermal insulation involves the selection and use of materials or systems that reduce heat flow between regions of different temperatures. The design objective is to minimize thermal energy transfer from the warmer surroundings to the chilled interior of the tank by increasing the overall thermal resistance of the system.

Heat Transfer Analysis

Heat transfer analysis uses principles from thermodynamics and conduction to estimate the rate of heat influx into a system. It involves quantifying the temperature differences, material thermal conductivities, geometrical factors, and insulation properties to ensure that the energy transfer remains below critical thresholds.

Spherical Geometry Considerations

Spherical geometry affects how heat flows through the tank’s wall due to its curvature and uniform surface area distribution. Analysis of heat conduction in a spherical shell requires careful evaluation of the radial temperature gradient and the influence of wall thickness and material properties on the overall thermal resistance.

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