Rock Bed Heat Storage System

A rock bed heat storage system for a room stores heat by circulating air heated by solar radiation during the day through an insulated layer of rocks. At night, when the temperature of the room decreases, a fan circulates the hot air into the room. The advantages of this are that rocks are cheap and their specific heat is high. Let and be the masses of the air and the rocks, and their specific heats, the area of the walls and ceiling, the interface between rocks and air, and the temperature outside the room. The plots are the solutions for the air temperature and the rock bed temperature .

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The resulting system of differential equations is:
,
,
where
, , .
Reference
[1] J. R. Brannan and W. E. Boyce, Differential Equations: An Introduction to Modern Methods and Applications, 2nd ed., New York: John Wiley & Sons, 2011 pp. 136–139.
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