Equation 2 · Part 1 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter

Symbol ṁ

\dot{m}

\dot{m}

What this part means

the mass flow.

Its job in the formula

ṁ has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

Full expressionSymbol ṁArticle meaning

Where the article explains it

with mass flow $\dot{m}$ , specific heat capacity $c_p$ , and the temperature rise $\Delta$ T across the load.

The passage around this formula

with mass flow $\dot{m}$ , specific heat capacity $c_p$ , and the temperature rise $\Delta$ T across the load. What matters for a datacenter is not $c_p$ per kilogram but the volumetric heat capacity $\rho$ $c_p$ , because the room has to physically contain the flow.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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See this notation across published equations →

Sources cited in the article section

[4] Emergence and Expansion of Liquid Cooling in Mainstream Data Centers ↗

These citations provide research context; check each source for the exact claim it supports.