Thermal Gradients from Quenching

Many heat treating operations involve a quench—that is, an immersion in a fluid at a lower temperature in order to achieve a rapid cooling rate. It is commonly used for hardening in ferrous metals. Quench fluids include air, water, oils, and many others. From a heat transfer standpoint, quenching of a hot metal has a lot of interesting aspects: determining the heat transfer coefficient (possibly with phase change) at the surface, calculating transient temperature profiles inside the material (with implications for thermal stresses and metallurgical properties), effects of thermal transport properties (possibly time-dependent, or spatially non-uniform) on the heat transfer, and others. In this post, we’ll discuss transient temperature profiles and temperature gradients induced by quenching a one-dimensional (wide enough and long enough that the main effects are controlled by the thickness) piece of tool steel. 

 We’ll assume properties of 7.83 g/cm³ for the density, and 461 J/kgK for the specific heat capacity, and 61 W/mK for the thermal conductivity of the steel, and assume that it is quenched with water at 30 deg C from an initial temperature of 800 deg C, and a heat transfer coefficient of 8000 W/m² K. We’ll assume that the total thickness is 5 cm, and the cooling comes from both sides equally, so that from symmetry, we only need to consider the half-thickness of the material. 

This figure shows the temperature profiles across the half-thickness at various times from the

beginning of the quench. It is interesting to note that for the earliest profile (1 second), the heat transfer is behaving like it would from a semi-infinite body (early regime) and later on, there is very little temperature difference from the centerline to the front surface (late regime).





For the purposes of thinking about thermal stresses and deformation, we might be interested in knowing the maximum temperature difference within the material. This figure shows the

temperature histories of the exposed surface, where the temperature would be the lowest, and the centerline, where the temperature would be the highest. It is clear that the difference changes with time—it gets larger for a while, then it diminishes as the whole body cools.






That effect can be seen more clearly in this figure where the temperature difference is plotted

as a function of time. The maximum temperature difference for this case occurs at 5.3 seconds after the beginning of the quench, and has a magnitude of 446 deg C.