⏱️ Cooling Time of Metal Parts & Quenching
Calculate transient temperature drop and thermal quenching times for metallic spheres, cylinders, and slabs.
Heat Treatment & Quenching
In metallurgy and materials processing (such as forging, annealing, and steel hardening), estimating the cooling rate of hot parts is critical to controlling microstructure and mechanical properties. If a part cools too slowly, it may not reach the required hardness; if it cools too quickly, high thermal stresses can lead to cracking or warping.
Our transient conduction solvers let you model the cooling history of metal parts over time. The **Lumped Capacitance Method** is used when temperature gradients inside the part are negligible ($Bi < 0.1$), whereas the **One-Term Heisler Approximation** is applied when internal resistance is significant ($Bi \ge 0.1$).
⏱️ Run Transient Cooling Sizing
Launches the Lumped Capacitance solver configured for cooling hot steel parts in an oil quench bath (high initial temperature, steel thermal properties, and high convection coefficient).
Launch Quenching Calculator →Mathematical Formulation
1. The Biot Number Criterion ($Bi$)
$$Bi = \frac{h L_c}{k_{solid}}$$Where $L_c = V / A_s$ is the characteristic length (volume-to-surface-area ratio). If $Bi < 0.1$, the lumped capacitance method is valid.
2. Lumped Capacitance Temperature Decay
The transient temperature of the part $T(t)$ as a function of time $t$ is modeled by:
$$T(t) = T_\infty + (T_i - T_\infty) \cdot e^{-t / \tau}$$Where the thermal time constant $\tau$ is defined as:
$$\tau = \frac{\rho C_p V}{h A_s} = \frac{\rho C_p L_c}{h}$$Variables:
- $T_i$ = Initial temperature of the metal part [°C]
- $T_\infty$ = Temperature of the quenching fluid [°C]
- $\rho$ = Metal density [kg/m³]
- $C_p$ = Metal specific heat capacity [J/kg·K]
- $h$ = Convection coefficient of quench bath [W/m²·K]