# Shrink Fitting of an Assembly

FEATool supports modeling heat transfer through both conduction, that is heat transported by a diffusion process, and also convection, which is heat transported through a fluid through convection by a velocity field. The heat transfer physics mode supports both these processes, and defines the following equation

$$ \rho °C_p\frac{\partial T}{\partial t} + \nabla\cdot(-k\nabla c) = Q - \rho °C_p\mathbf{u}\cdot\nabla T $$

where $\rho$ is the density, $C_p$ the heat capacity, $k$ is the thermal conductivity, $Q$ heat source term, and $\mathbf{u}$ a vector valued convective velocity field.

This example models heat conduction in the form of transient cooling
for shrink fitting of a two part assembly. A tungsten rod heated to
*84 °C* is inserted into a chilled steel frame part at *-10
°C*. The time when the maximum temperature has cooled to *70
°C* should be determined. The assembly is cooled due to
convection through a surrounding medium kept at *TM _{inf} = 17
°C* and a heat transfer coefficient of

*h = 750 W/m*. The surrounding cooling medium is not modeled directly, and the convective term is therefore omitted, but the effects are incorporated into the model by the use of natural convection boundary conditions.

^{2}KThis model is available as an automated tutorial by selecting **Model
Examples and Tutorials…** > **Heat Transfer** > **Shrink Fitting of
an Assembly** from the **File** menu. Or alternatively, follow the
linked step-by-step instructions.