Infiltration

Sometimes, we must heat or cool a steady flow of air or water. We can use our sensible heat formula to calculate the power required to cool this flow.

Recall our formula for sensible heat,

Q = m c \Delta T

Now imagine we are heating a mass m of water every \Delta t minutes. We can express this as a flow rate, often called \dot{m}.

\dot{m} = \frac{m}{\Delta t}

To heat that flow rate, we have to also deliver that energy, Q, every \Delta t minutes. By the energy equation (Q = P \cdot t) we have

P = \frac{Q}{\Delta t}

So, by dividing both sides of the sensible heat equation by \Delta t we can write

Q = m c \Delta T \frac{Q}{\Delta t} = \frac{m}{\Delta t} c \Delta T P = \dot{m} c \Delta T

Air Changes

For buildings, this formula is often written as

q_{inf} = \rho c n V \Delta T

where n is the air changes per hour, or how often the air in a room or building is completely replaced. Multiplying this by V, the volume of the room, and \rho, the density of the air gives you \dot{m}.

Applications

• If you have an on-demand tankless water heater, these equations can be used to determine the power to heat that water.
• If you have a steady flow of outside air entering a conditioned space, you can determine the power to warm or cool that air.