Heat Transfer Equation

The superiority of liquid over air for cooling a high density data center is governed by the heat transfer equation: Q̇ = ṁ x C_P x ΔT

• Heat flow rate (Q̇) is a measure of how much thermal energy can be transferred per unit of time.
• Mass flow rate (ṁ) considers density, which is mass divided by a unit volume. Water is over 800 times denser than air, so moving an equivalent mass of air and water requires moving an ~800 times greater volume of air.
• Specific heat capacity (C_P) is the measure of how much energy is needed to raise the temperature of one unit mass of a material at constant pressure by 1 degree. Water has a specific heat capacity that is 4 times greater than air; in other words, water can ‘absorb’ about 4 times as much heat as air can for a given unit mass.
• ΔT is determined in part by thermal resistance (the inverse of thermal conductance), which is the measure of how difficult it is for heat to be transferred within a working fluid. At standard sea level conditions the thermal resistance of water is about 24 times lower than air. This allows for water temperatures that are closer to the CPU operating temperature.

Because water is denser, has a higher specific heat capacity, and a lower thermal resistance, heat can be removed with dramatically less volumetric flow of water versus air. Moving a fluid (gas or liquid) requires energy, so with water we can accomplish more heat transfer for the same mechanical transport energy. Additionally, inherent motor heat inefficiencies when using air cooling may be significantly reduced when liquid cooling is employed. Together, these conditions enable reduced Scope 2 data center emissions.

Explore more in our whitepaper Liquid Cooling is More Sustainable