# Shrink Fitting of an Assembly

## Model Data

Type: heat transfer

Physics Modes: heat transfer

Keywords: cooling multi domain

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 TMinf = 17 °C and a heat transfer coefficient of h = 750 W/m2 K. 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.

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. Or alternatively, follow the linked step-by-step instructions.