A water storage tank for a nuclear power plant in Tennessee is 10 m high and has a 13.5 m diam

step 1 Hi. In the given problem, recovery time is the time required to heat all the water in hot water

A water storage tank for a nuclear power plant in Tennessee...

A water storage tank for a nuclear power plant in Tennessee is $10 \mathrm{~m}$ high and has a $13.5 \mathrm{~m}$ diameter. It is insulated on the top and sides with a $7.6 \mathrm{~cm}$-thick insulation of $k=0.05 \mathrm{~W} / \mathrm{m} \mathrm{K}$. The water is maintained at $22^{\circ} \mathrm{C}$ by four immersion heaters. If the power to the heaters is switched off, how long will it take the water temperature to drop to $16^{\circ} \mathrm{C}$ if the average ambient air temperature is $5^{\circ} \mathrm{C}$ ? The tank is located in a sheltered position adjacent to some large buildings. (Hint: A rough estimate of the outside heat transfer coefficient will suffice.)

Key Concepts

Thermal Energy Storage

This concept refers to the ability of a material to absorb and store heat. In systems like water tanks, the high specific heat capacity of water means significant amounts of thermal energy are stored, which influences how slowly or quickly the temperature changes when heat is lost.

Conduction Heat Transfer

Conduction is the mode of heat transfer through materials driven by a temperature gradient. In the context of insulated tanks, heat conducted through the insulation depends on the thermal conductivity of the material and its thickness, which determines how effectively heat is transferred from the water to the outer surface.

Convective Heat Transfer

Convective heat transfer involves the movement of heat between a surface and a fluid (such as air) in contact with it. The efficiency of this heat loss is characterized by the convective heat transfer coefficient and is crucial in determining the overall rate at which the stored heat is removed from the tank.

Thermal Resistance

Thermal resistance quantifies the opposition to heat flow through a material or a set of layers. In problems involving multi-layered systems like an insulated tank, individual resistances (due to conduction through insulation and convection on the surface) sum up to determine the overall resistance to heat loss.

Lumped Capacitance Analysis

This analysis simplifies the transient heat transfer problem by assuming that the temperature within the body, like the water in a tank, remains uniform over time. It allows the system to be modeled as a single thermal mass, where the rate of temperature change is governed by the balance between stored thermal energy and the heat loss through the external resistances.

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