This example models shrink fitting of a two part assembly. A chilled tungsten rod is inserted into a slot in a heated steel frame. The rod can be fitted due to thermal expansion of the frame, and when the assembly reaches equilibrium temperature the two parts will be joined due to the ensuing pressure fit.
The model illustrates how to simulate the transient heat transfer process with two domains of different materials. The assembly is cooled due to convection through a surrounding medium kept at Tinf = 17 °C, and the time when the maximum temperature has reached 70 °C should be determined.
FEATool Multiphysics allows for modeling heat transfer through both conduction, that is heat transported by a diffusion process, and also convection, which is heat transported by a fluid due to a flow field. The heat transfer physics mode supports both these processes, and is defined by the following equation
$$ \rho C_p\frac{\partial T}{\partial t} + \nabla\cdot(-k\nabla c) + \rho C_p\mathbf{u}\cdot\nabla T = Q $$
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.
Here, the surrounding cooling medium is not modeled directly, the convective term in the heat transfer equation can therefore be dropped, and the cooling effects are incorporated into the model by using natural convection boundary conditions instead. By not directly modeling the surrounding medium significant computational savings can be made.
This model is available as an automated tutorial by selecting Model Examples and Tutorials… > Heat Transfer > Shrink Fitting of an Assembly from the File menu, and also as the MATLAB simulation m-script example ex_heattransfer5. Or alternatively, follow the video tutorial or step-by-step instructions