Speaker
Description
The fluid temperature in a heat conduction problem in a dilated pipe with a small circular cross-section is considered. The fluid flow is governed by the pressure drop. The heat exchange between the fluid and the environment is described by Newton’s cooling law and the temperature is described by the convection-diffusion equation with a stationary Poiseuille velocity. Due to pipe dilation, the fluid domain is not fixed and changes depending on the unknown temperature. By introducing a suitable change of variables, the domain becomes fixed, but the PDE becomes non-linear.
An asymptotic temperature is obtained by asymptotic analysis with respect to the small parameters (coefficient of heat expansion and ratio between pipe thickness and length). The approximation is first defined on a fixed domain (defined by the change of variables) and then on a dilated domain. By proving the error estimate for the approximation on the extended domain, the justification of the effective model is given.
