∙On-demand water heaters. Conventional hot-water heaters...

$\bullet$ On-demand water heaters. Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. Some utility companies are encouraging the use of on- demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. No water tank is involved, so no heat is wasted. A typical household shower flow rate is 2.5 gal $/ \min (9.46 \mathrm{L} / \mathrm{min}$ ) with the tap water being heated from $50^{\circ} \mathrm{F}\left(10^{\circ} \mathrm{C}\right)$ to $120^{\circ} \mathrm{F}\left(49^{\circ} \mathrm{C}\right)$ by the on-demand heater. What rate of heat input (either electrical or from gas) is required to operate such a unit, assuming that all the heat goes into the water?

Key Concepts

Heat Energy Transfer Equation

This principle is based on the formula Q = m × cp × ?T, where Q is the energy transferred, m is the mass of the fluid, cp is the specific heat capacity, and ?T is the change in temperature. This relationship is crucial for computing the power required by an on-demand water heater to raise the temperature of the water as it flows through the system.

Unit Conversions in Thermal Systems

Accurate energy calculations require converting various units, such as volume to mass (using the fluid’s density) and time to consistent units (e.g., minutes to seconds). This ensures that the computed energy or power values are correct and easily comparable, which is particularly important when designing or analyzing heating systems.

Specific Heat Capacity

This concept describes the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin). In the context of water heating, it quantifies the energy needed to achieve a specified temperature increase in the water, which is fundamental to determining the energy input required by a heater.

Mass Flow Rate

Mass flow rate is the measure of the mass of a fluid passing through a given cross-sectional area per unit time. It is derived from the volumetric flow rate and density of the fluid. In water heating applications, converting the volumetric flow rate into a mass flow rate allows you to accurately calculate the energy needed to heat the water continuously.

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