Blade Group and CDU Modeling

The thermodynamics of each blade-group (BG) with liquid-cooled plates is governed by:

Heat capacitor

\[C \,\frac{dT}{dt} \;=\; Q_{\mathrm{port}}(t)\]

where \(T\) is the BG temperature and \(Q_{\mathrm{port}}\) is the net heat flow, here equal to the server’s load:

\[Q_{\mathrm{port}} = P_{\mathrm{branch}}\]

Conduction model

\[Q_{\mathrm{flow}} \;=\; G_{c}\,(T_{\mathrm{solid}} - T_{\mathrm{fluid}})\]

with \(G_{c}\) the convective conductance (function of coolant properties and flow rate \(m_{\mathrm{flow}}\)).

Overall balance

\[\Phi\bigl(Q_{\mathrm{port}}\bigr) + Q_{\mathrm{flow}} \;=\; C \,\frac{dT_{\mathrm{server}}}{dt}\]

Here \(\Phi\) is a polynomial fit (typically quadratic term 0.015, linear 1) to expose nonlinearity for RL vs. heuristic controllers. Server-load trace example: input_04-07-24.csv.