Equation 1 · Part 4 · The Physical Plant: Power, Cooling, and Networks in an AI Datacenter

Temperature rise

\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T,

\Delta T

What this part means

The fluid’s temperature increase while crossing the load. A change of one kelvin is the same size as a change of one degree Celsius; the sign follows outlet minus inlet here.

Its job in the formula

Δ T is an input to the expression that computes the quantity on the left.

Full expressionTemperature riseArticle meaning

The passage around this formula

The rate at which a fluid stream removes heat is $\dot{Q} = \dot{m}\,c_p\,\Delta T = \rho\,\dot{V}\,c_p\,\Delta T$ . 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

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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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.